Lecture on Open quantum systems.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# A short Introduction to Open Quantum Systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### From master equations to exact numerical methods\n",
    "\n",
    "Jupyter Notebook version: http://goo.gl/LpUaR1  \n",
    "\n",
    "Neill Lambert, RIKEN, nwlambert@gmail.com\n",
    "\n",
    "#### Partially based on:\n",
    "- Ahsan Nazir's Lecture Notes on Open quantum systems https://workspace.imperial.ac.uk/people/Public/anazir1/open_systems_notes.pdf\n",
    "\n",
    "- \"The theory of open quantum systems\" by H.-P. Breuer and F. Petruccione.\n",
    "\n",
    "- Robert Johansson's series of Lectures on QuTiP \n",
    "/~https://github.com/jrjohansson/qutip-lectures\n",
    "\n",
    "- Uses QuTiP\n",
    "http://qutip.org/\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "# Outline:\n",
    "\n",
    "## Part 1\n",
    "\n",
    "- Motivation:  from quantum optics and physical chemistry to quantum technologies\n",
    "\n",
    "\n",
    "- The Lindblad Master equation; a quick derivation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "## Part 2\n",
    "\n",
    "\n",
    "- QuTiP examples and applications\n",
    "\n",
    "    - Direct integration\n",
    "    \n",
    "    - Monte-Carlo simulation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "    \n",
    "## Part 3\n",
    "\n",
    "\n",
    "- Beyond the Master Equation: Exact numerical methods for bosonic baths\n",
    "\n",
    "    - The Hierarchy Equations of Motion\n",
    "    \n",
    "    - The Reaction Coordinate\n",
    "    \n",
    "    \n",
    "- Conclusions "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Motivation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Every quantum system inevitably interacts with its environment.  \n",
    "\n",
    "In general, it is impossible for us to model the whole dynamics of the system and environment.\n",
    "\n",
    "So the goal of the theory of open quantum systems is to construct minimal solvable models and methods which account for the influence of the environment on the system.\n",
    "\n",
    "\n",
    "<img src=\"sys-env.png\" height=\"400\" width=\"400\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "# The motivation for the study of open quantum systems arises from:\n",
    "\n",
    "1. **Describing real experiments** involving quantum degrees of freedom in contact with an environment, and real measurements, e.g.,\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## Quantum optics\n",
    "<img src=\"QED.png\" height=\"400\" width=\"400\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Quantum technologies\n",
    "\n",
    "<img src=\"qtech1.png\" height=\"400\" width=\"400\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Physical chemistry and Chemical physics\n",
    "<img src=\"fmo.png\" height=\"600\" width=\"600\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Motivation\n",
    "\n",
    "### 2) **Developing a theory of ``quantum dissipation''** and more recently, quantum thermodynamics.\n",
    "\n",
    "- E.g., the Caldeira-Leggett model allows us to derive classical dissipation/friction from a quantum foundation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "### 3) In **quantum technologies and devices** this is typically an unwanted interaction.  \n",
    "\n",
    "- If its unavoidable, or even strong, to what degree can we work around it or mitigate it? \n",
    "\n",
    "(e.g., using feedback, environment engineering, decoherence free spaces, topological protection)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Part 1: The Lindblad Master equation; a quick derivation\n",
    "\n",
    "\n",
    "Steps:\n",
    "\n",
    "1) A few definitions: density matrix, system and environment (bath) Hamiltonians\n",
    "\n",
    "2) Born - Markov approximations\n",
    "\n",
    "3) The bath correlation function\n",
    "\n",
    "4) An explicit example:  the spin-boson model\n",
    "\n",
    "5) The secular approximation!\n",
    "\n",
    "6) And finally, the Lindblad Master Equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Definitions: The density operator\n",
    "\n",
    "When a quantum system is effectively \"closed\" we describe its dynamics and evolution in terms of a pure state $|\\psi(t)\\rangle$ whose evolution is determined by a Hamiltonian and the Schrodinger equation\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} |\\psi(t)\\rangle = -i H(t) |\\psi(t)\\rangle$$\n",
    "\n",
    "More generally, for open systems it is convenient to use the density operator, which for a pure state, is given by\n",
    "\n",
    "$$\\rho = |\\psi(t)\\rangle \\langle \\psi(t)|$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "When describing one part of a larger composite system, as is the case for open systems \n",
    "<span style=\"color:red\">when we trace out the environment degress of freedom</span>,  the loss of knowledge about the influence of the other systems introduces \n",
    "<span style=\"color:red\">statistical uncertainty</span>. \n",
    "\n",
    "This then gives rise to mixed states, in terms of a statistical ensemble of possible pure states, such that;\n",
    "\n",
    "$$\\rho = \\sum_n p_n |\\psi_n(t)\\rangle \\langle \\psi_n(t)|$$\n",
    "\n",
    "\n",
    "The evolution of the density operator obeys the Liouville-von Neumann equation of motion,\n",
    "\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\rho(t) = -i [H(t), \\rho(t)]$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "\n",
    "The density operator itself has some important properties;\n",
    "\n",
    "-- For pure states $\\rho^2=\\rho$\n",
    "\n",
    "-- It is Hermitian $\\rho^{\\dagger} = \\rho$.\n",
    "\n",
    "-- It has trace one $\\mathrm{Tr}\\rho = 1$.\n",
    "\n",
    "-- Expectation values of system operators can be evaluated as $\\langle A \\rangle =\\mathrm{Tr}(A\\rho)$.\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The system and environment Hamiltonians\n",
    "\n",
    "Ultimately the influence of a large environment on a systems evolution is to induce statistical uncertainty into its dynamical evolution.  \n",
    "\n",
    "This gives rise to dissipation (emission and absorbtion of energy) and dephasing (localization into particular states).\n",
    "\n",
    "The philosophy we will describe here is to start with an \n",
    "<span style=\"color:red\"> explicit Hamiltonian description of the system (**S**) and the full Environment (**E**) </span>, with the Hilbert space\n",
    "\n",
    "$$\\mathcal{H} = \\mathcal{H}_S \\otimes \\mathcal{H}_E$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "and then \n",
    "<span style=\"color:red\"> derive effective models, or equations of motion,</span> for the redused density operator of the system alone, after tracing out the environment degrees of freedom, i.e.,\n",
    "\n",
    "$$\\rho_S(t) = \\mathrm{Tr}_E[\\rho(t)]$$ \n",
    "\n",
    "since $\\rho_S(t)$ descrives all pertinent and accessible information about the system itself.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "The full dynamics of the system and environment would in principle be described by the Hamiltonian\n",
    "\n",
    "$$H = H_S + H_E + H_I$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "In general, one can describe the evolution of the whole system and environment, \n",
    "<span style=\"color:red\"> in the interaction picture </span>, as \n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}(t) = -i [\\tilde{H}_I(t), \\tilde{\\rho}(t)]$$\n",
    "\n",
    "where the interaction pictures moves the free evolution of both the system and environment into the operators themselves,\n",
    "such that\n",
    "\n",
    "$$\\tilde{H}_I(t) = e^{i(H_S + H_E)t} H_I e^{-i(H_S + H_E)t}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Formally we can solve the equation of motion with\n",
    "\n",
    "$$\\tilde{\\rho}(t) = \\rho(0) - i \\int_0^t ds [\\tilde{H}_I(s),\\tilde{\\rho}(s)]$$\n",
    "\n",
    "Substituting this into the RHS of the original equation of motion, and formally \n",
    "<span style=\"color:red\"> tracing out the environment degrees of freedom </span>, gives,\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) = -i \\mathrm{Tr}_E[\\tilde{H}_I(t), \\tilde{\\rho}(0)]  -  \\int_0^t ds \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(s),\\tilde{\\rho}(s)]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Born Approximation\n",
    "\n",
    "This is still an intractable equation of motion.  To make progress we must make a series of \n",
    "<span style=\"color:red\">assumptions</span>:\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "-- \n",
    "<span style=\"color:red\"> **Factorizable initial conditions** </span>: We assume that at $t=0$ the system and environment are seperable, such that \n",
    "\n",
    "$$\\rho(0) = \\rho_S(0) \\otimes \\rho_E(0)$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "-- <span style=\"color:red\"> **The Born approximation**</span>: In addition, we assume that the density matrix <span style=\"color:red\">factorises</span> at all times, and that the <span style=\"color:red\"> environment state is time-independent</span>,\n",
    "\n",
    "$$\\rho(t) = \\rho_S(t) \\rho_E(0)$$\n",
    "\n",
    "This assumes that the environment is mostly unaffacted by the interaction with the system. (Any excitations emitted by the system quickly decay in the environment)\n",
    "\n",
    "-- Note: We also remove the first term on the RHS (for many examples it is zero, or it can be cancelled with a c-number term in the system Hamiltonian).\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Under these assumptions,\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) =  - \\int_0^t ds \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(s),\\tilde{\\rho_S}(s)\\rho_E]$$\n",
    "\n",
    "This equation of motion assumes weak coupling, as the system and environment remain seperable; \n",
    "\n",
    "... but it still includes some <span style=\"color:red\"> time non-local behavior</span> as the state of the system depends on its history (via the integral over $s$), and thus its past interaction with the bath.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The Markov Approximation\n",
    "\n",
    "We can now make what is known as the <span style=\"color:red\"> **Markov** </span> assumption, to eliminate this history. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "We assume \n",
    "\n",
    "$$\\tilde{\\rho}_S(s) \\rightarrow \\tilde{\\rho}_S(t)$$\n",
    "\n",
    "in the integral.  \n",
    "\n",
    "This assumptions implies there is a seperation of time scales between environment (**$\\tau_E$**) and system relaxation time (**$\\tau_R$**) and any intrinsic system time scales (**$\\tau_S$**), \n",
    "\n",
    "$$\\tau_E \\ll \\tau_R, \\tau_S$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "I.e., if the environment were to be perturbed by the system, it relaxes back to equilibrium faster than the typical time scale of the evolution (**relaxation** and coherent evolution) of the system. \n",
    "\n",
    "This seems like a consistent assumption to make alongside the **Born approximation**, since that also implies the environment remains in equilibrium.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now we have, after substituting $\\tilde{\\rho}_S(s) \\rightarrow \\tilde{\\rho}_S(t)$\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) =  - \\int_0^t ds \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(s),\\tilde{\\rho}_S(t)\\rho_E]$$\n",
    "\n",
    "\n",
    "\n",
    "This is sometimes called the Redfield equation; it local in time, but <span style=\"color:red\">not quite completely Markovian</span> (we still have $t$ in the integral limits).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "We can simplifiy this further by removing the reference to $t$ in the limits of the integral, by choosing $s=t-\\tau$, and letting the upper limit go to infinity;  \n",
    "\n",
    "In other words, we assume that the integrand  dissappears fast compared to the system time scales.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "Thus we arrive at the <span style=\"color:red\">fully Markovian master equation</span>;\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) =  -  \\int_0^{\\infty} d\\tau \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(t-\\tau),\\tilde{\\rho}_S(t)\\rho_E]$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Describing the bath with a correlation function\n",
    "\n",
    "The system depends on the environment properties via the two-time bath correlation functions. For example, lets explicitly define the system-environment interaction term as,\n",
    "\n",
    "$$H_I = A \\otimes B$$\n",
    "\n",
    "where $A$ is a Hermitian system operator, and $B$ a Hermitian bath operator.  (An explicit example will soon make this a little clearer).\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "In the interaction picture \n",
    "\n",
    "$$\\tilde{H} = A(t) \\otimes B(t)$$\n",
    "\n",
    "Our Markovian master equation contains terms like:\n",
    "\n",
    "$$ \\mathrm{Tr_E}[B(t)B(t-\\tau)\\rho_E]$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "If we assume the initial state of the environment is a steady state, i.e., it does not evolve under $H_E$, these terms are <span style=\"color:red\">\"stationary\"</span>,  $C(\\tau) = \\mathrm{Tr_E}[B(\\tau)B\\rho_E]$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Inserting these various terms into our Markovian master equation, and moving back to the Schrodinger picture, one obtains\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] - \\int_0^{\\infty} d\\tau \\left( [A,[A(-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)A(-\\tau),A]C(-\\tau)\\right)$$\n",
    "\n",
    "This equation in itself is useful, and can be developed and applied to certain problems (see part 3). \n",
    "\n",
    "However, it is still not in the famous <span style=\"color:red\">**Lindblad**</span> form, and does not guarantee positivity of the density matrix as it is evolved.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note: In general there may be a sum of interactions in the interaction Hamiltonian, in which case the integral contains a sum of terms for each interaction part, and the correlation functions are generalized $\\tilde{H} = \\sum_{\\alpha}A_{\\alpha}(t) \\otimes B_{\\alpha}(t)$\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] - \\sum_{\\alpha,\\beta}\\int_0^{\\infty} d\\tau \\left( [A_{\\alpha},[A_{\\beta}(-\\tau)\\rho_S(t)]C_{\\alpha\\beta}(\\tau) + [\\rho_S(t)A_{\\beta}(-\\tau),A_{\\alpha}]C_{\\beta\\alpha}(-\\tau)\\right)$$\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "Interestingly, there is still not yet any assumption about the timescales $\\tau_S$, due to $H_S$, and the relaxation $\\tau_R$, induced by the bath. \n",
    "\n",
    "If we perform an additional approximation, and <span style=\"color:red\">neglect terms due to system evolution which are very fast compared to the relaxation time scale $\\tau_R$</span>, we can obtain a **Secular master equation** which is in **Lindblad form**. \n",
    "\n",
    "In other words, we will assume, $\\tau_S\\ll \\tau_R$, so that now, the Born-Markov-Secular master equation will be valid when\n",
    "\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "It is a little cumbersome to the general derivation of this step, so let us move onto an explicit example. However, one note;  the above **non-secular** form of the master equation is **may be** applicable even if the relaxation time scale and the system time scale are comparable, and thus it is useful in and of itself. (See Chapter 3.6 in Breuer and Pettrucione).\n",
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The spin-boson model\n",
    "\n",
    "The archetypical example of an open quantum system is where the \"system\" is a two-level system, a spin, described by:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<span style=\"color:red\">Pauli spin matrices</span>\n",
    "\n",
    "\\begin{align}\n",
    "\\sigma_{x} = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix},\\quad\n",
    "\\sigma_{y} = \\begin{pmatrix} 0 & -i \\\\ i & 0 \\end{pmatrix}, \\quad\n",
    "\\sigma_{z} = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix},\n",
    "\\end{align}\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "While the bath is a continuum of <span style=\"color:red\"> boson modes </span>, or harmonic oscillators, described by creation and annihilation operators $b_k$, obeying the commutation relations $[b_k,b_k']=\\delta_{k,k'}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "This model is important because it can be used to describe the behavior of <span style=\"color:red\">atoms, molecules or a qubits</span>  interacting with the electromagnetic field, vibrational phonons, etc.  E.g, the loss rate $\\gamma$ in a typical cavity QED example could be described by this model\n",
    "\n",
    "<img src=\"QED.png\" width=\"400\" height=\"400\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The total Hamiltonian is then,\n",
    "\n",
    "$$H= H_S + H_E + H_I$$\n",
    "\n",
    "where\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$ H_S = \\frac{\\epsilon}{2} \\sigma_z$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "$$ H_E = \\sum_k \\omega_k b_k^{\\dagger}b_k$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$ H_I = \\sigma_x \\sum_k g_k (b_k^{\\dagger}+b_k)= (\\sigma_+ +\\sigma_-)\\sum_k g_k (b_k^{\\dagger}+b_k)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In the <span style=\"color:red\">interaction picture</span> the interaction Hamiltonian is \n",
    "\n",
    "$$\\tilde{H}_I(t) = e^{i(H_S + H_E)t} H_I e^{-i(H_S + H_E)t}$$\n",
    "\n",
    "   \n",
    "\n",
    "$$ \\tilde{H}_I =  (\\sigma_+e^{i\\epsilon t} +\\sigma_-e^{-i\\epsilon t})\\sum_k g_k (b_k^{\\dagger}e^{i\\omega_k t}+b_ke^{-i\\omega_k t})$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Inserting this into our master equation, we find,\n",
    "\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) =  - \\int_0^{\\infty} d\\tau \\left( [\\sigma_x(t),[\\sigma_x(t-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)\\sigma_x(t-\\tau),\\sigma_x(t)]C(-\\tau)\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "\n",
    "Recall that the bath correlation functions are defined as\n",
    "\n",
    "$$C(\\tau) = \\mathrm{Tr_E}[B(\\tau)B\\rho_E]$$\n",
    "\n",
    "Where\n",
    "\n",
    "$$B(t) = \\sum_k g_k\\{ b_k^{\\dagger}e^{i\\omega_k t}+ b_ke^{-i\\omega_k t}\\}$$\n",
    "\n",
    "$$C(t)=\\mathrm{Tr_E}[ (\\sum_k g_k  \\{b_k^{\\dagger}e^{i\\omega_k t}+ b_ke^{-i\\omega_k t}\\}) (\\sum_{k'} g_{k'}\\{ b_{k'}^{\\dagger}+ b_{k'}\\}) \\rho_E]$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Assuming that the initial state of the environment is a thermal state\n",
    "\n",
    "$$\\rho_E = e^{-H_E / k_B T} / Z$$  \n",
    "\n",
    "$$Z=\\mathrm{Tr}(e^{-H_E / k_B T})$$\n",
    "\n",
    "lets us evaluate this quite easily;\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "The only non-zero terms come from \n",
    "\n",
    "$$\\mathrm{Tr_E}[b_k b_{k'}^{\\dagger}\\rho_E]=\\delta_{kk'}[1+n(\\omega_k)]$$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\mathrm{Tr_E}[ b_{k'}^{\\dagger} b_k\\rho_E]=\\delta_{kk'}n(\\omega_k)$$\n",
    "\n",
    "where $n(\\omega) =(e^{\\omega/k_B T} - 1)^{-1}$.\n",
    "\n",
    "Is the Bose-Einstein occupation number."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Then\n",
    "\n",
    "$$C(t)= \\sum_k \\left(g_k^2 e^{i\\omega_k t}n(\\omega_k)+ g_k^2 e^{-i\\omega_k t}[1+n(\\omega_k)]\\right)$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can then move to a continuum representation by turning the sum into an integral, and defining the **spectral density**\n",
    "\n",
    "<span style=\"color:red\">\n",
    "$$J(\\omega) = \\sum_k g_k^2\\delta(\\omega-\\omega_k)$$\n",
    "</span>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega \\{J(\\omega) e^{i\\omega t}n(\\omega)+ J(\\omega) e^{-i\\omega t}[1+n(\\omega)]\\}$$\n",
    "\n",
    "**Note: sometimes it is useful to rewrite this in terms of real and imaginary parts. See part 3!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The secular approximaton\n",
    "\n",
    "Let us return to the master equation, in the interaction picture;\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) =  - \\int_0^{\\infty} d\\tau \\left( [\\sigma_x(t),[\\sigma_x(t-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)\\sigma_x(t-\\tau),\\sigma_x(t)]C(-\\tau)\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We are going to do two things:\n",
    "\n",
    "    \n",
    "    \n",
    "- Neglect terms come from products of system operators that rotate quickly... this is the <span style=\"color:red\">secular approximation!</span>\n",
    "\n",
    "Its equivalent in this case to a <span style=\"color:red\">rotating wave approximation</span>;  and for it be valid, the relaxation rate has to be smaller than the system frequency.  \n",
    "\n",
    "    \n",
    "- Evaluate the integral over $\\tau$ and $\\omega$\n",
    "\n",
    "This is a lot of algebra, so lets just do one term.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## First, the secular approximation:\n",
    "\n",
    "Recall that, in the interaction picture:\n",
    "\n",
    "$$\\sigma_x(t) =(\\sigma_+e^{i\\epsilon t} +\\sigma_-e^{-i\\epsilon t})$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "So the first term in the master equation contains products like\n",
    "\n",
    "$$ \\sigma_x(t)\\sigma_x(t-\\tau)= (\\sigma_+^2e^{2i\\epsilon t}e^{-i\\epsilon \\tau} +\\sigma_-^2e^{-2i\\epsilon t}e^{i\\epsilon \\tau}+\\sigma_+\\sigma_-e^{i\\epsilon \\tau} + \\sigma_-\\sigma_+e^{-i\\epsilon \\tau})$$\n",
    "\n",
    "We neglect terms oscillating with frequency <span style=\"color:red\">$2i\\epsilon$. </span> (Actually in this particular product of operators those terms are zero anyway, because the operators squared are zero, but the equivalent terms in products like  $\\sigma_x(t-\\tau)\\rho_s(t) \\sigma_x(t)$ must be neglected in this way..)\n",
    "\n",
    "Now we see why this is the same as a rotating wave approximation, and that it is valid if \n",
    "\n",
    "$$\\tau_S \\ll \\tau_R$$ \n",
    "\n",
    "i.e., when the relaxation rate is smaller than the system frequencies.  Now we have the seperation of time scales\n",
    "\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Second, some integrals\n",
    "\n",
    "For the remaining terms, that do not rotate at this frequency, we have to evaluate integrals like,\n",
    "\n",
    "$$  \\sigma_+\\sigma_- \\rho_S(t)  \\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau}C(\\tau)$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Using our earlier definition of the correlation function\n",
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega \\{J(\\omega) e^{i\\omega t}n(\\omega)+ J(\\omega) e^{-i\\omega t}[1+n(\\omega)]\\}$$\n",
    "\n",
    "We have to evaluate\n",
    "\n",
    "$$\\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau}C(\\tau) =  \\int_0^{\\infty}d\\omega \\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau} \\{J(\\omega) e^{i\\omega \\tau}n(\\omega)+ J(\\omega) e^{-i\\omega \\tau}[1+n(\\omega)]\\}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can do the $\\tau$ integral first, using the formula,\n",
    "\n",
    "$$\\int_0^{\\infty} d\\tau e^{\\pm i\\epsilon \\tau} = \\pi \\delta(\\epsilon) \\pm i \\frac{\\mathcal{P}}{\\epsilon}$$\n",
    "\n",
    "$\\mathcal{P}$ is the Cauchy principal value. The imaginary term leads to environment-induced energy shifts (sometimes called Lamb shifts.  Here we neglect this term, for simplicity.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We see that the delta function lets us then evaluate the frequency integral, and thus,\n",
    "\n",
    "$$\\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau}C(\\tau)= \\pi J(\\epsilon) (n(\\epsilon)+1)$$\n",
    "\n",
    "\n",
    "Thus for this term, the right hand side of the master equation becomes \n",
    "\n",
    "$$  \\sigma_+\\sigma_- \\rho_S(t)  \\left[\\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau}c(\\tau)\\right] =  \\pi J(\\epsilon) (n(\\epsilon)+1) \\sigma_+\\sigma_- \\rho_S(t) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "# The **Lindblad master equation**\n",
    "\n",
    "\n",
    "We are almost there! If we repeat this for each term in the master equation, and collect terms, and move back to the schrodinger picture, we find a master equation in what is known as the Lindblad master equation \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "<span style=\"color:blue\">\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[\\frac{\\epsilon}{2}\\sigma_z,\\rho(t)] $$</span>\n",
    "<span style=\"color:green\">$$+ \\gamma(\\epsilon) \\left(n(\\epsilon)+1\\right)\\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] $$</span>\n",
    "<span style=\"color:red\">$$+ \\gamma(\\epsilon) n(\\epsilon)\\left[2\\sigma_+ \\rho_S(t)\\sigma_- - \\{\\sigma_-\\sigma_+,\\rho_S\\}\\right]$$\n",
    "</span>\n",
    "\n",
    "\n",
    "\n",
    "Note we have redefined $ \\gamma(\\epsilon)\\equiv \\pi J(\\epsilon)$.  \n",
    "\n",
    "The first part is the \n",
    "<span style=\"color:blue\">coherent system evolution</span>, the second part describes <span style=\"color:green\">spontaneous and stimulated emission</span>, and the third part describes <span style=\"color:red\">absorption</span>.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Why is this so great?\n",
    "\n",
    "- This Lindblad form guarantees positivity:  we will always have a physical density matrix.\n",
    "\n",
    "- It is easy to evaluate, and can be derived for many types of systems.  \n",
    "\n",
    "(see part 2 for more examples).\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "# To recap, it is valid when:\n",
    "\n",
    "- The <span style=\"color:red\">**Born approximation**</span> applies:  the coupling is weak such that we can assume $\\rho(t) = \\rho_S(t)\\otimes\\rho_E$\n",
    "\n",
    "- The <span style=\"color:red\">**Markov approximation**</span> applies:  the bath returns to equilibrium on a time scale $\\tau_E$ which is faster than the relaxation of the system induced by that bath $\\tau_R$. \n",
    "\n",
    "- The <span style=\"color:red\">**secular approximation**</span> applies:  the system time scales are small (i.e., higher frequency) than the relaxation time scales.  In other words, $\\epsilon > \\pi J(\\epsilon) (n(\\epsilon)+1)$.\n",
    "\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "** Two questions (maybe obvious?) **:\n",
    "\n",
    "- Does the secular approximation break at high temperatures?\n",
    "\n",
    "- How valid is the non-secular master equation when the relaxation time becomes of order of the system time scales?   (see part 3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Solution to the Lindblad master equation\n",
    "\n",
    "The spin-boson example is analytically solvable in a few lines.  \n",
    "\n",
    "This is easily done by writing out equations of motion for the matrix elements of the master equation\n",
    "\n",
    "\n",
    "<span style=\"color:blue\">\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[\\frac{\\epsilon}{2}\\sigma_z,\\rho(t)] $$</span>\n",
    "<span style=\"color:green\">$$+ \\gamma(\\epsilon) \\left(n(\\epsilon)+1\\right)\\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] $$</span>\n",
    "<span style=\"color:red\">$$+ \\gamma(\\epsilon) n(\\epsilon)\\left[2\\sigma_+ \\rho_S(t)\\sigma_- - \\{\\sigma_-\\sigma_+,\\rho_S\\}\\right]$$\n",
    "</span>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "which give\n",
    "\n",
    "\n",
    "$$\\dot{\\rho}_{ee}(t) = -2 \\gamma (n+1) \\rho_{ee}(t) + 2\\gamma n \\rho_{gg}(t)$$\n",
    "$$\\dot{\\rho}_{gg}(t) = -2 \\gamma (n) \\rho_{gg}(t) + 2\\gamma (n+1) \\rho_{ee}(t)$$\n",
    "$$\\dot{\\rho}_{eg}(t) = -2 [\\gamma (2n+1) + i\\epsilon] \\rho_{eg}(t)$$\n",
    "$$\\dot{\\rho}_{ge}(t) = -2 [\\gamma (2n+1) - i\\epsilon] \\rho_{ge}(t)$$\n",
    "\n",
    "We an see that the populations are coupled with rates corresponding to the emission and absorption.  The off-diagonal matrix elements decay proportional to the coupling the environment.   This is decoherence!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "The solutions to these equations are very simple for zero temperature ($n=0$), where we see:\n",
    "\n",
    "$$\\rho_{ee}(t) = e^{-2 \\gamma t} \\rho_{ee}(0) $$\n",
    "$$\\rho_{gg}(t) = 1-2 e^{-2 \\gamma t} \\rho_{ee}(0)$$\n",
    "$$\\rho_{eg}(t) = e^{- \\gamma t}e^{ - i\\epsilon t} \\rho_{eg}(0)$$\n",
    "$$\\rho_{ge}(t) = e^{- \\gamma t}e^{  i\\epsilon t} \\rho_{ge}(0)$$\n",
    "\n",
    "The off diagonal terms decay at half the speed of the relaxation terms, leading to the infamous <span style=\"color:red\">$T_1 = 2T_2$</span> relationship.\n",
    "\n",
    "In the general case, it can be tedious to construct and solve such equations of motion.  \n",
    "\n",
    "So... lets use QuTiP to play with some examples.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "## Part 2\n",
    "\n",
    "\n",
    "- QuTiP examples and applications\n",
    "\n",
    "    - Direct integration\n",
    "    \n",
    "    - Monte-Carlo simulation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# QuTiP:  A brief introduction\n",
    "\n",
    "The Quantum Toolbox in Python was developed primarily by Robert Johansson and Paul Nation.\n",
    "\n",
    "http://qutip.org/devs.html\n",
    "\n",
    "It has a variety of built-in solvers for solving the dynamics via: \n",
    "- the Schrodinger equation, \n",
    "- master equations, \n",
    "- Floquet formalism, \n",
    "- Monte-Carlo quantum trajectories, \n",
    "- stochastic Schrodinger/master equations, \n",
    "- the Hierarchy method, the reaction coordinate method, etc.\n",
    "- supports time-dependance in Hamiltonians, Lindblads, etc.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "It based around a quantum object class which can be used to represent state vectors, operators, and superoperators.\n",
    "\n",
    "It is composed of a numerical matrix, and various properties that define its dimensionality, etc.\n",
    "<img src=\"qobj.png\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from qutip import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Recalling our example of a single two-level system described by the Pauli spin matrices\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "\\sigma_{x} = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix},\\quad\n",
    "\\sigma_{y} = \\begin{pmatrix} 0 & -i \\\\ i & 0 \\end{pmatrix}, \\quad\n",
    "\\sigma_{z} = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix},\n",
    "\\end{align}\n",
    "\n",
    "In QuTiP we can define this manually, or with predefined operators:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.  0.]\n",
       " [ 0. -1.]]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sz = Qobj([[1,0], [0,-1]]) # the sigma-z Pauli operator\n",
    "sz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.  0.]\n",
       " [ 0. -1.]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sz = sigmaz() # the sigma-z Pauli operator\n",
    "sz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sz.tr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2L, 2L), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -1.0j\\\\1.0j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2L, 2L), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 0.+0.j  0.-1.j]\n",
       " [ 0.+1.j  0.+0.j]]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy = sigmay()\n",
    "\n",
    "sy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2L, 2L), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0j\\\\-1.0j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2L, 2L), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 0.+0.j  0.+1.j]\n",
       " [ 0.-1.j  0.+0.j]]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.conj()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Our simple Hamiltonian from before was diagonal in the 'z' basis.\n",
    "\n",
    "We can define and solve the Lindblad Master equation we solved analytically earlier in few lines:\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[\\frac{\\epsilon}{2}\\sigma_z,\\rho(t)] \\\\\n",
    "+ \\gamma(\\epsilon) \\left(n(\\epsilon)+1\\right)\\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] \\\\\n",
    "+ \\gamma(\\epsilon) n(\\epsilon)\\left[2\\sigma_+ \\rho_S(t)\\sigma_- - \\{\\sigma_-\\sigma_+,\\rho_S\\}\\right]$$\n",
    "\n",
    "QuTiP has several options on how to solve this type of formula.  \n",
    "\n",
    "The default is \"mesolve\" which takes Qobj definitions of the Hamiltonian, and the Lindblad, and converts them into what a set of coupled equations in matrix form, as we did earlier. It then directly solves this set of coupled ODEs.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "First define the Hamiltonian $H_S = \\frac{\\epsilon}{2}\\sigma_z$ \n",
    "\n",
    "and initial condition $psi(t=0) = |1\\rangle$,  $\\rho(0) = |1\\rangle\\langle 1|$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       "Qobj data =\n",
       "[[ 1.]\n",
       " [ 0.]]"
      ]
     },
     "execution_count": 323,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "eps = 1.0\n",
    "\n",
    "# Hamiltonian\n",
    "H = 0.5 * eps * sigmaz()\n",
    "\n",
    "\n",
    "# initial state.  \n",
    "N = 2 # number of states in the Hilbert space\n",
    "n = 0 # the state that will be occupied (python counts from zero)\n",
    "\n",
    "psi0 = basis(N, n)     \n",
    "psi0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "We can define our Lindblad master equation by just defining the rates and the operator which goes into master equation.\n",
    "\n",
    "Here we have two operators; one which causes emission, \n",
    "\n",
    "$ \\gamma(\\epsilon) \\left(n(\\epsilon)+1\\right)\\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] $\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "sm = destroy(2).dag()\n",
    "gamma = 0.1\n",
    "n_th = 0.0\n",
    "\n",
    "#FYI: QuTiPs definition of a Lindblad differs from our derivation by a factor of '2'\n",
    "#c_ops\n",
    "c_ops = [np.sqrt(2 * gamma*(n_th + 1)) * sm]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The other absorption:\n",
    "\n",
    "$$ \\gamma(\\epsilon) n(\\epsilon)\\left[2\\sigma_+ \\rho_S(t)\\sigma_- - \\{\\sigma_-\\sigma_+,\\rho_S\\}\\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "sp = sm.dag()\n",
    "\n",
    "c_ops.append(np.sqrt(2 * gamma * n_th) * sp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Next define the time steps we want to solve the equations for, and run the \"mesolve\" function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# list of times for which the solver should store the state vector\n",
    "tlist = np.linspace(0, 50, 1000)\n",
    "result = mesolve(H, psi0, tlist, c_ops, [])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Calculate some expectation values, and compare to analytical result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiQAAADsCAYAAABE172AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17a58c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Since our initial state was the excited state, we can get the probability of being in the excited state\n",
    "#at time t with:\n",
    "Pe = expect(result.states, psi0*psi0.dag())\n",
    "\n",
    "#we can compare this to our analytical result\n",
    "PeAna = [np.exp(-2 * gamma * t) for t in tlist]\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1,1, figsize=(6,2))\n",
    "axes.plot(tlist, Pe)\n",
    "axes.plot(tlist, PeAna, color='r',ls='--')\n",
    "axes.set_xlabel(r'$t$', fontsize=20)\n",
    "axes.set_ylabel(r\"$\\rho_{ee}$\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "If we assume non-zero temperature, the steady state (the long-time solution) of the master equation predicts a thermal state.\n",
    "\n",
    "Analytically, setting the LHS of our equaitons to zero, and soliving, gives the disribution:\n",
    "\n",
    "$$\\rho_{ee} = \\frac{n}{(1+2n)}$$\n",
    "$$\\rho_{gg} = \\frac{1+n}{(1+2n)}$$\n",
    "\n",
    "Which is equivalent to the thermal distribution:\n",
    "\n",
    "$$ \\rho = e^{H_S/k_B T}/Z $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Lets check this two ways in QuTiP.  First with steadystate() function, then with the thermal_dm() function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.25  0.  ]\n",
      " [ 0.    0.75]]\n"
     ]
    }
   ],
   "source": [
    "gamma = 0.1\n",
    "n_th = 0.5\n",
    "\n",
    "c_ops = [np.sqrt(2 * gamma * n_th) * sp, np.sqrt(2 * gamma*(n_th + 1)) * sm]\n",
    "\n",
    "rhoss = steadystate(H,c_ops)\n",
    "print(rhoss)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.25\n",
      "0.75\n"
     ]
    }
   ],
   "source": [
    "#Compare to analytical prediction\n",
    "print(n_th / (1+ 2 * n_th))\n",
    "print((1+n_th) / (1+ 2 * n_th))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.75  0.  ]\n",
      " [ 0.    0.25]]\n"
     ]
    }
   ],
   "source": [
    "#Built in function to calculate thermal state with occupation n_th\n",
    "print(thermal_dm(2, n_th))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let us try a slightly more interesting example, the **Jaynes-Cumming Model** of cavity QED, which describes a single two level system coherently interacting with a single-mode cavity\n",
    "\n",
    "<img src=\"QED.png\" width=400 height=400/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The interaction between the TLS and the cavity is coherent, while the losses are incoherent.\n",
    "\n",
    "Normally, one must fully rederive the master equation, as the Hamiltonian of the system is now different.\n",
    "\n",
    "However, if $g$ is small compared to the cavity and \"atom\" frequencies, we can assume that derivation for uncoupled systems is still valid (i.e., the eigenstates and eigenenergies dont change much).\n",
    "\n",
    "\n",
    "\n",
    "$$H_S = \\frac{\\epsilon}{2} \\sigma_z + \\omega_c a^{\\dagger}a + g(\\sigma_+ a+\\sigma_- a^{\\dagger})$$\n",
    "\n",
    "$$ g \\ll \\epsilon, \\omega_c$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "If we assume both atom and cavity are weakly coupled to independant environments (external EM modes, leaky mirror, etc), we can model this system with the following Lindblad Master Equation \n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] \\\\\n",
    "+ \\gamma \\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] \\\\\n",
    "+ \\kappa \\left[2a \\rho_S(t)a^{\\dagger} - \\{a^{\\dagger}a,\\rho_S\\}\\right] $$\n",
    "\n",
    "As with the atom, the cavity can decay into its environment even at zero temperature.\n",
    "\n",
    "(Note we assumed zero temperature, for simplicity, and that the rates are \"flat\", so not really dependant on energy.  Also the coupling is small, so that the eigenstates of the system are not far from the uncoupled basis.)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In QuTiP, we use the tensor function to create operators for composite systems, thus the operators and Hamiltonian of the above example are defined as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# cavity mode operator.  We truncate the Fock states at \"4\"\n",
    "N=4\n",
    "a = tensor(destroy(N), qeye(2))\n",
    "\n",
    "# qubit/atom operators\n",
    "sz = tensor(qeye(N), sigmaz())   # sigma-z operator\n",
    "sm = tensor(qeye(N), destroy(2).dag()) # sigma-minus operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[4, 2], [4, 2]], shape = (8, 8), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.5         0.          0.          0.05        0.          0.          0.\n",
      "   0.        ]\n",
      " [ 0.         -0.5         0.          0.          0.          0.          0.\n",
      "   0.        ]\n",
      " [ 0.          0.          1.5         0.          0.          0.07071068\n",
      "   0.          0.        ]\n",
      " [ 0.05        0.          0.          0.5         0.          0.          0.\n",
      "   0.        ]\n",
      " [ 0.          0.          0.          0.          2.5         0.          0.\n",
      "   0.08660254]\n",
      " [ 0.          0.          0.07071068  0.          0.          1.5         0.\n",
      "   0.        ]\n",
      " [ 0.          0.          0.          0.          0.          0.          3.5\n",
      "   0.        ]\n",
      " [ 0.          0.          0.          0.          0.08660254  0.          0.\n",
      "   2.5       ]]\n"
     ]
    }
   ],
   "source": [
    "#We define system paramaters and the Hamiltonian in the same way as before\n",
    "\n",
    "wc = 1.0 # cavity frequency\n",
    "eps = 1.0 # qubit/atom frenqency\n",
    "g = 0.05  # coupling strength\n",
    "\n",
    "# the Jaynes-Cumming Hamiltonian\n",
    "H = wc * a.dag() * a + 0.5 * eps * sz + g * (a * sm.dag() + a.dag() * sm)\n",
    "\n",
    "print(H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Again, we can create operators that describe the Lindblad master equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "$$\\gamma \\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] \\\\$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "gamma = 0.005\n",
    "c_ops = []\n",
    "c_ops.append(np.sqrt(2 * gamma) * sm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "And for the photon loss:\n",
    "\n",
    "$$\\kappa \\left[2a \\rho_S(t)a^{\\dagger} - \\{a^{\\dagger}a,\\rho_S\\}\\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "kappa = 0.005\n",
    "c_ops.append(np.sqrt(2 * kappa) * a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# intial state, lets start with an excited atom and no photons\n",
    "psi0 = tensor(basis(N,0), basis(2,0))   \n",
    "\n",
    "tlist = np.linspace(0,100,501)\n",
    "output = mesolve(H, psi0, tlist, c_ops, [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1dbaf3f6b38>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAADgCAYAAADsbXoVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dbaf057240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_c = expect(output.states, a.dag()*a)\n",
    "n_a = expect(output.states, sm.dag()*sm)\n",
    "\n",
    "fig, axes = plt.subplots(1, 1, figsize=(6,3))\n",
    "\n",
    "axes.plot(tlist, n_c, label=\"Cavity\")\n",
    "axes.plot(tlist, n_a, label=\"Atom excited state\")\n",
    "axes.legend(loc=0)\n",
    "axes.set_xlabel('Time')\n",
    "axes.set_ylabel('Occupation probability')\n",
    "axes.set_title('Vacuum Rabi oscillations')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can plot the Wigner function of the cavity with built in functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAxYAAAGFCAYAAABg02VjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLIQQQgghhBDJ9v/slBNhRr2mCAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20510898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We can plot the Wigner function of the cavity with built in functions\n",
    "\n",
    "import matplotlib as mpl\n",
    "\n",
    "t_idx = np.where([tlist == t for t in [0.0, 25.0, 60, 90]])[1]\n",
    "rho_list = np.array(output.states)[t_idx]\n",
    "\n",
    "fig_grid = (2, len(rho_list)*2)\n",
    "fig = plt.figure(figsize=(2*len(rho_list),4))\n",
    "xvec = np.linspace(-3,3,200)\n",
    "\n",
    "for idx, rho in enumerate(rho_list):\n",
    "    rho_cavity = ptrace(rho, 0)\n",
    "    W = wigner(rho_cavity, xvec, xvec)\n",
    "    ax = plt.subplot2grid(fig_grid, (0, 2*idx), colspan=2)\n",
    "    ax.contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-.25,.25), cmap=plt.get_cmap('RdBu'))\n",
    "    ax.set_title(r\"$t = %.1f$\" % tlist[t_idx][idx], fontsize=16)\n",
    "\n",
    "# plot the cavity occupation probability in the ground state\n",
    "ax = plt.subplot2grid(fig_grid, (1, 1), colspan=(fig_grid[1]-2))\n",
    "ax.plot(tlist, n_c, label=\"Cavity\")\n",
    "ax.plot(tlist, n_a, label=\"Atom excited state\")\n",
    "ax.legend()\n",
    "ax.set_xlabel('Time')\n",
    "ax.set_ylabel('Occupation probability');\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"wigner1.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"wigner1.png\" width=600 height=600/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeQAAAHkCAYAAADvrlz5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7808358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_wigner(ptrace(rho_list[1],0), figsize=(6,6),projection='3d', alpha_max=3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Monte-Carlo solutions\n",
    "\n",
    "One downside to solving the master equation in this way is that the size of the matrix of equations we have to construct and solve scales as $N^2$, where $N$ is the number of states in the Hilbert space. Another approach is to \"unravel\" the master equation as a sum of trajectories, and then solve a stochastic equation for the state vector  state $\\left|\\psi(t)\\right>$, instead of the density matrix.  Physically this corresponds to continously monitoring the environment, and conditioning the information about the system we gain.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "For a quantum system that interacts with its environment. The dynamics of the wave function is given by the Schrodinger equation,\n",
    "\n",
    "<center>\n",
    "$\\displaystyle\\frac{d}{dt}\\left|\\psi(t)\\right> = - i H_{\\rm eff} \\left|\\psi(t)\\right>$\n",
    "</center>\n",
    "\n",
    "where the Hamiltonian is an effective Hamiltonian that, in addition to the system Hamiltonian $H_S$, also contains a non-Hermitian contribution due to the interaction with the environment:\n",
    "\n",
    "<center>\n",
    "$\\displaystyle H_{\\rm eff}(t) = H - \\frac{i}{2}\\sum_n c_n^\\dagger c_n$\n",
    "</center>\n",
    "\n",
    "where $c_n$ are the collapse operators that we usually put in the Lindblad Master equation (and by definition we have included the rates in the operators).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Since the effective Hamiltonian is non-Hermitian, the norm of the wavefunction is decreasing with time, which to first order in a small time step $\\delta t$ is given by $\\langle\\psi(t+\\delta t)|\\psi(t+\\delta t)\\rangle \\approx 1 - \\delta p\\;\\;\\;$, where \n",
    "\n",
    "<center>\n",
    "$\\displaystyle \\delta p = \\delta t \\sum_n \\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>$\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "The decreasing norm is used to determine when so-called quantum jumps are to be imposed on the dynamics.  This corresponds to observing a photon being emitted into the environment, in which case we apply a \"quantum jump\", so that the new wavefunction at $t+\\delta t$ is given by\n",
    "<center>\n",
    "$\\left|\\psi(t+\\delta t)\\right> = c_n \\left|\\psi(t)\\right>/\\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>^{1/2}$ \n",
    "</center>\n",
    "\n",
    "In practise we compare $\\delta p$ to a random number in the range [0, 1]. If the norm has decreased below the randomly chosen number, we apply the quantum jump for a randomly chosen collapse operator $c_n$, weighted so the probability that the collapse being described by the nth collapse operator is given by\n",
    "    \n",
    "<center>\n",
    "$\\displaystyle P_n = \\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>/{\\delta p}$ \n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.1%. Run time:  16.02s. Est. time left: 00:00:02:23\n",
      "20.0%. Run time:  16.70s. Est. time left: 00:00:01:06\n",
      "30.1%. Run time:  17.63s. Est. time left: 00:00:00:40\n",
      "40.0%. Run time:  18.33s. Est. time left: 00:00:00:27\n",
      "50.0%. Run time:  19.03s. Est. time left: 00:00:00:19\n",
      "60.1%. Run time:  19.80s. Est. time left: 00:00:00:13\n",
      "70.0%. Run time:  20.43s. Est. time left: 00:00:00:08\n",
      "80.1%. Run time:  21.09s. Est. time left: 00:00:00:05\n",
      "90.0%. Run time:  21.75s. Est. time left: 00:00:00:02\n",
      "100.0%. Run time:  22.39s. Est. time left: 00:00:00:00\n",
      "Total run time:  22.50s\n"
     ]
    }
   ],
   "source": [
    "ntraj = [1, 5, 15, 904] # list of number of trajectories to avg. over\n",
    "\n",
    "mc = mcsolve(H, psi0, tlist, c_ops, [a.dag()*a], ntraj)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"monte.png\" width=400 height=400/>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAicAAALCCAYAAAAF2XPsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwo3qKwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbc8b898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.font_manager\n",
    "leg_prop = matplotlib.font_manager.FontProperties(size=10)\n",
    "\n",
    "fig, axes = plt.subplots(4, 1, sharex=True, figsize=(6,8))\n",
    "\n",
    "fig.subplots_adjust(hspace=0.1) # reduce space between plots\n",
    "\n",
    "for idx, n in enumerate(ntraj):\n",
    "\n",
    "    axes[idx].step(tlist, mc.expect[idx][0], 'b', lw=2)\n",
    "    axes[idx].plot(tlist, expect(output.states,a.dag()*a), 'r--', lw=1.5)\n",
    "    \n",
    "    \n",
    "    axes[idx].set_yticks(np.linspace(0, 2, 5))\n",
    "    axes[idx].set_ylim([0, 1.5])\n",
    "    axes[idx].set_ylabel(r'$\\left<N\\right>$', fontsize=14)\n",
    "    \n",
    "    if idx == 0:\n",
    "        axes[idx].set_title(\"Ensemble Averaging of Monte Carlo Trajectories\")\n",
    "        axes[idx].legend(('Single trajectory', 'master equation', 'steady state'), prop=leg_prop)\n",
    "    else:\n",
    "        axes[idx].legend(('%d trajectories' % n, 'master equation', 'steady state'), prop=leg_prop)\n",
    "        \n",
    "\n",
    "axes[3].xaxis.set_major_locator(plt.MaxNLocator(4))\n",
    "axes[3].set_xlabel('Time (sec)',fontsize=14);\n",
    "fig.savefig(\"monte.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Monte Carlo Master Equation: a quick summary\n",
    "\n",
    "- For small systems, its actually slower than a direct solution, but for large systems it can save memory\n",
    "\n",
    "\n",
    "<img src=\"qutipbench.png\" width=400 /> <img src=\"qutipbenchcaption.png\" width=400/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Monte Carlo Master Equation: a quick summary\n",
    "\n",
    "- For small systems, its actually slower than a direct solution, but for large systems it can save memory\n",
    "- Easy to run in parrallel, using multiple cores, etc.\n",
    "- It can give an intuitive picture of measurement.  \n",
    "- Stochastic master equations for arbitrary unravellings are supported in QuTiP.  \n",
    "- These can be used to model continous homodyne and heterodyne measurement, feedback, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Ultra-strong coupling\n",
    "\n",
    "If $g$ becomes comparable to the bare system frequencies, the Hamiltonian and the master equation defined above becomes incorrect (e.g., it does not give the ground state as the steady state at zero temperature).\n",
    "\n",
    "More precesilty, we should use the full Rabi Hamiltonian, instead of the Jaynes Cummings model, and rederive the master equation, defining the system-environment coupling operator in terms of the true system eigensates, and so on. In doing so, we arrive at, e.g.,\n",
    "\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] \\\\\n",
    "+ \\sum_{\\Gamma=\\gamma,\\kappa}\\left(\\sum_{j,k>j}\\Gamma_{j,k}n(\\Delta_{j,k},T) \\mathcal{D}\\left[|k\\rangle\\langle j|\\right] \\rho(t) \\right.\\\\\n",
    "\\left. + \\sum_{j,k>j}\\Gamma_{j,k}\\left[1+n(\\Delta_{j,k},T)\\right] \\mathcal{D}\\left[|j\\rangle\\langle k|\\right] \\rho(t)\\right)$$\n",
    "\n",
    "Where \n",
    "\n",
    "$\\gamma_{j,k}= \\pi J(\\Delta_{j,k}) |\\langle j|\\sigma_x | k \\rangle |^2$, \n",
    "\n",
    "$\\kappa_{j,k}= \\pi J(\\Delta_{j,k}) |\\langle j|(a+a^{\\dagger}) | k \\rangle |^2$,\n",
    "\n",
    "$\\mathcal{D}\\left[|j\\rangle\\langle k|\\right]\\rho(t)=2|j\\rangle\\langle k| \\rho |k\\rangle\\langle j| - |k\\rangle\\langle k|\\rho - \\rho |k\\rangle\\langle k|$, \n",
    "\n",
    "$\\Delta_{j,k} = E_j - E_k$.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#USC master equation, zero temperature\n",
    "#Steady state as a function of coupling strength\n",
    "\n",
    "N=4\n",
    "a = tensor(destroy(N), qeye(2))\n",
    "\n",
    "# qubit/atom operators\n",
    "sz = tensor(qeye(N), sigmaz())   # sigma-z operator\n",
    "sx= tensor(qeye(N), sigmax())   # sigma-z operator\n",
    "sm = tensor(qeye(N), destroy(2).dag()) # sigma-minus operator\n",
    "x=a+a.dag()\n",
    "wc = 1.0 # cavity frequency\n",
    "eps = 1.0 # qubit/atom frenqency\n",
    "\n",
    "\n",
    "# the Jaynes-Cumming Hamiltonian\n",
    "H0 = wc * a.dag() * a + 0.5 * eps * sz \n",
    "\n",
    "H1=sx*x\n",
    "\n",
    "\n",
    "g_vec = np.linspace(0.1,0.5, 50)  # coupling strength vector\n",
    "\n",
    "psi_list = []\n",
    "state_list = []\n",
    "energy_list = []\n",
    "\n",
    "rho_list = []\n",
    "rho_list_alt = []\n",
    "rho_list_old = []\n",
    "\n",
    "\n",
    "\n",
    "Nmax=N*2\n",
    "\n",
    "kappa=0.01\n",
    "gamma=0.01\n",
    "\n",
    "\n",
    "for g in g_vec:\n",
    "\n",
    "    H = H0 + g * H1\n",
    "    #print(g)\n",
    "    # find the groundstate and its energy\n",
    "    gnd_energy, gnd_state = H.groundstate()\n",
    "    all_energy, all_state = H.eigenstates()\n",
    "    \n",
    "    #store the states and energies\n",
    "    state_list.append(all_state)\n",
    "    energy_list.append(all_energy)\n",
    "    \n",
    "    # store the ground state\n",
    "    psi_list.append(gnd_state)\n",
    "    collapse_list = []\n",
    "    for j in range(Nmax):\n",
    "        \n",
    "        for k in range(j,Nmax):\n",
    "            rate = np.absolute(x.matrix_element(all_state[j].dag(),all_state[k]))**2 * kappa\n",
    "            if rate > 0.0:\n",
    "                collapse_list.append((np.sqrt(rate)*all_state[j]*all_state[k].dag()))\n",
    "            \n",
    "            rate = np.absolute(sx.matrix_element(all_state[j].dag(),all_state[k]))**2 * gamma\n",
    "            if rate > 0.0:\n",
    "                collapse_list.append((np.sqrt(rate)*all_state[j]*all_state[k].dag()))\n",
    "            \n",
    "            \n",
    "            \n",
    "    L = liouvillian(H, collapse_list)\n",
    "    \n",
    "    rho_ss = steadystate(H, collapse_list)\n",
    "    rho_list.append(rho_ss)\n",
    "  \n",
    "    #compare to incorrect ME SS\n",
    "    rho_list_old.append(steadystate(H, [np.sqrt(kappa) * a, np.sqrt(gamma) * sm]))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "na = sm.dag() * sm  # atom\n",
    "nc = a.dag() * a    # cavity\n",
    "na_expt = expect(na, rho_list) # qubit  occupation probability\n",
    "nc_expt = expect(nc, rho_list) # cavity occupation probability   \n",
    "nc_gnd = expect(nc,psi_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAEYCAYAAABRMYxdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dbb1a8c630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "#Difference in master equations as a function of coupling strengthreproducing figure 1 in blais paper\n",
    "\n",
    "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,4))\n",
    "\n",
    "axes.plot(g_vec, nc_expt, 'r', linewidth=2, label=\"cavity\")\n",
    "axes.plot(g_vec, na_expt, 'b', linewidth=2, label=\"atom\")\n",
    "axes.set_ylabel(\"Cavity occupation\", fontsize=16)\n",
    "axes.set_xlabel(\"coupling strength\", fontsize=16)\n",
    "axes.legend(loc=0)\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAEYCAYAAABRMYxdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dbb1b48ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,4))\n",
    "\n",
    "axes.plot(g_vec, expect(nc, rho_list), 'r', linewidth=2, label=\"cavity\")\n",
    "axes.plot(g_vec, expect(na, rho_list), 'b', linewidth=2, label=\"atom\")\n",
    "axes.plot(g_vec, expect(nc, rho_list_old), 'g--', linewidth=2, label=\"cavity old\")\n",
    "axes.plot(g_vec, expect(na, rho_list_old), 'm--', linewidth=2, label=\"atom old\")\n",
    "axes.plot(g_vec, expect(nc, psi_list), 'y--', linewidth=2, label=\"cavity gnd\")\n",
    "\n",
    "axes.set_ylabel(\"Occupation\", fontsize=16)\n",
    "axes.set_xlabel(\"coupling strenght\", fontsize=16)\n",
    "axes.legend(loc=0)\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAEaCAYAAAAc+S1WAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dbb177f240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,4))\n",
    "\n",
    "axes.plot(g_vec, expect(nc, rho_list_old)-expect(nc, rho_list), 'r', linewidth=2, label=\"cavity\")\n",
    "#axes.plot(g_vec/(2*pi), expect(na, rho_list), 'b', linewidth=2, label=\"atom\")\n",
    "#axes.plot(g_vec/(2*pi), expect(nc, rho_list_old), 'g--', linewidth=2, label=\"cavity old\")\n",
    "#axes.plot(g_vec/(2*pi), expect(na, rho_list_old), 'm--', linewidth=2, label=\"atom old\")\n",
    "axes.set_ylabel(\"difference in cavity Occupation\", fontsize=16)\n",
    "axes.set_xlabel(\"coupling strengtt\", fontsize=16)\n",
    "axes.legend(loc=0)\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    }
   ],
   "source": [
    "#dynamics, and non-secular master equation (not verified, take with a grain of salt!)\n",
    "\n",
    "N=8\n",
    "a = tensor(destroy(N), qeye(2))\n",
    "\n",
    "# qubit/atom operators\n",
    "sz = tensor(qeye(N), sigmaz())   # sigma-z operator\n",
    "sx= tensor(qeye(N), sigmax())   # sigma-z operator\n",
    "sm = tensor(qeye(N), destroy(2).dag()) # sigma-minus operator\n",
    "x=a+a.dag()\n",
    "wc = 1.0 # cavity frequency\n",
    "eps = 1.0 # qubit/atom frenqency\n",
    "\n",
    "\n",
    "H0 = wc * a.dag() * a + 0.5 * eps * sz \n",
    "\n",
    "H1=sx*x\n",
    "\n",
    "\n",
    "psi_list = []\n",
    "state_list = []\n",
    "energy_list = []\n",
    "\n",
    "rho_list = []\n",
    "rho_list_alt = []\n",
    "rho_list_old = []\n",
    "\n",
    "\n",
    "\n",
    "Nmax=N*2\n",
    "\n",
    "kappa=0.5\n",
    "#cavity loss\n",
    "#kappa=0.1\n",
    "#qubit (atomic) loss)\n",
    "gamma=0.5\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "H = H0 + 0.01 * H1\n",
    "#print(g)\n",
    "# find the groundstate and its energy\n",
    "gnd_energy, gnd_state = H.groundstate()\n",
    "all_energy, all_state = H.eigenstates()\n",
    "\n",
    "#store the states and energies\n",
    "state_list.append(all_state)\n",
    "energy_list.append(all_energy)\n",
    "\n",
    "# store the ground state\n",
    "psi_list.append(gnd_state)\n",
    "collapse_list = []\n",
    "for j in range(Nmax):\n",
    "\n",
    "    for k in range(j,Nmax):\n",
    "        rate = np.absolute(x.matrix_element(all_state[j].dag(),all_state[k]))**2 * kappa\n",
    "        if rate > 0.0:\n",
    "            collapse_list.append((np.sqrt(rate)*all_state[j]*all_state[k].dag()))\n",
    "\n",
    "        rate = np.absolute(sx.matrix_element(all_state[j].dag(),all_state[k]))**2 * gamma\n",
    "        if rate > 0.0:\n",
    "            collapse_list.append((np.sqrt(rate)*all_state[j]*all_state[k].dag()))\n",
    "\n",
    "\n",
    "tlist = np.linspace(0, 30, 500)\n",
    "\n",
    "#psi0 = H.groundstate()[1]\n",
    "\n",
    "psi0 = tensor(basis(N,0), basis(2,0))\n",
    "output = mesolve(H, psi0, tlist, collapse_list, [a.dag() * a, sm.dag() * sm])\n",
    "outputalt = mesolve(H, psi0, tlist, [np.sqrt(kappa) * a,np.sqrt(gamma) * sm], [a.dag() * a, sm.dag() * sm])\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "dimensions = dims(H)\n",
    "Nmax = dimensions[1][0]        #hilbert space \n",
    "#Nmax = 2       #hilbert space \n",
    "print(Nmax)\n",
    "L=0\n",
    "PsipreEta=0\n",
    "PsipreX=0\n",
    "\n",
    "all_energy, all_state = H.eigenstates()\n",
    "Q=sx\n",
    "Apre = spre(Q)\n",
    "Apost = spost(Q)\n",
    "for j in range(Nmax):\n",
    "    for k in range(Nmax):\n",
    "        A = Q.matrix_element(all_state[j].dag(), all_state[k])\n",
    "        #A = sh.matrix_element(all_state[j].dag(), all_state[k])\n",
    "        delE = (all_energy[j] - all_energy[k])\n",
    "        if np.absolute(A) > 0.0:\n",
    "            if abs(delE) > 0.0:\n",
    "                #X = (0.5 * np.pi * gamma*(all_energy[j] - all_energy[k])\n",
    "                if delE> 0.0:\n",
    "                    X = (0.25 * gamma * A)\n",
    "                    eta = (0.25 * gamma * A)\n",
    "                \n",
    "                if delE < 0.0:\n",
    "                    X = (0.25 * gamma * A)\n",
    "                    eta = -(0.25 * gamma * A)\n",
    "                \n",
    "                \n",
    "                #eta = (0.5 * np.pi * gamma *\n",
    "                PsipreX = PsipreX + X * all_state[j]*all_state[k].dag()\n",
    "                PsipreEta = PsipreEta + (eta * all_state[j]\n",
    "                                         * all_state[k].dag())\n",
    "\n",
    "A = Q\n",
    "L = ((-spre(A * PsipreX)) + (sprepost(A, PsipreX))\n",
    "     +(sprepost(PsipreX, A)) + (-spost(PsipreX * A))\n",
    "     +(spre(A * PsipreEta)) + (sprepost(A, PsipreEta))\n",
    "     +(-sprepost(PsipreEta, A)) + (-spost(PsipreEta * A)))           \n",
    "Q=x\n",
    "Apre = spre(Q)\n",
    "Apost = spost(Q)\n",
    "\n",
    "PsipreEta=0\n",
    "PsipreX=0\n",
    "\n",
    "for j in range(Nmax):\n",
    "    for k in range(Nmax):\n",
    "        A = Q.matrix_element(all_state[j].dag(), all_state[k])\n",
    "        #A = sh.matrix_element(all_state[j].dag(), all_state[k])\n",
    "        delE = (all_energy[j] - all_energy[k])\n",
    "        if np.absolute(A) > 0.0:\n",
    "            if abs(delE) > 0.0:\n",
    "                #X = (0.5 * np.pi * gamma*(all_energy[j] - all_energy[k])\n",
    "                if delE> 0.0:\n",
    "                    X = (0.25 * kappa * A)\n",
    "                    eta = (0.25 * kappa * A)\n",
    "                if delE < 0.0:\n",
    "                    eta = -(0.25 * kappa * A)\n",
    "                    X = (0.25 * kappa * A)\n",
    "                \n",
    "                #X = (0.25 * kappa * A)\n",
    "                #eta = (0.5 * np.pi * gamma *\n",
    "                \n",
    "                PsipreX = PsipreX + X * all_state[j]*all_state[k].dag()\n",
    "                PsipreEta = PsipreEta + (eta * all_state[j]\n",
    "                                         * all_state[k].dag())\n",
    "\n",
    "A = Q\n",
    "L += ((-spre(A * PsipreX)) + (sprepost(A, PsipreX))\n",
    "     +(sprepost(PsipreX, A)) + (-spost(PsipreX * A))\n",
    "     +(spre(A * PsipreEta)) + (sprepost(A, PsipreEta))\n",
    "     +(-sprepost(PsipreEta, A)) + (-spost(PsipreEta * A)))           \n",
    "\n",
    "outputnonsec = mesolve(H, psi0, tlist, [L], [a.dag() * a, sm.dag() * sm])\n",
    "#outputnonsec = mesolve(H, psi0, tlist, [L], [])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1dbb396a588>"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAD8CAYAAAABtxyxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAqBCMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dbb38827f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,4))\n",
    "axes.plot(tlist, output.expect[0], 'r', linewidth=2, label=\"USC ME\")\n",
    "axes.plot(tlist, outputalt.expect[0], 'g', linewidth=2, label=\"weak coupling ME\")\n",
    "axes.plot(tlist, outputnonsec.expect[0], 'y--', linewidth=2, label=\"weak coupling ME non sec\")\n",
    "axes.legend(loc=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Other reasons to use QuTiP\n",
    "\n",
    "- Open source science\n",
    "- Promotes reproducibility\n",
    "- Has even more functionality, including \n",
    "    - Quantum optimal control library (CRAB, GOAT, and other animals)\n",
    "    - QIP library\n",
    "    - functions to calculate spectra, counting statistics, etc\n",
    "    - Supports arbitrary time-dependance, in Hamiltonian and Lindblad collapse operators\n",
    "    - Active development community."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "    \n",
    "## Part 3\n",
    "\n",
    "\n",
    "- Beyond the Master Equation: Exact numerical methods for bosonic baths\n",
    "\n",
    "    - The Hierarchy Equations of Motion, Tanimura and Ueda, (1989)\n",
    "    \n",
    "    - The Reaction Coordinate, Illes-Smith, Lambert and Nazir, PRA, (2014)\n",
    "    \n",
    "    \n",
    "- Conclusions "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Non-Markovian systems\n",
    "\n",
    "In some situations the assumption that $\\tau_E \\ll \\tau_S, \\tau_R$ breaks down. E.g.,\n",
    "\n",
    "- Hyperfine Interaction between electron spins and nuclear spins in quantum dots \n",
    "- Superconducting qubits strongly coupled to open transmission lines\n",
    "- Molecular systems strongly interacting with their environment, e.g., energy transfer in photosynthetic complexes strongly couples to protein \"vibrations\".\n",
    "\n",
    "\n",
    "A recent review:\n",
    "\"Dynamics of non-Markovian open quantum systems\"\n",
    "Inés de Vega and Daniel Alonso\n",
    "Rev. Mod. Phys. 89, 015001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Bosonic environments\n",
    "\n",
    "The choice of a bosonic environment, or in general, a Gaussian environment, simplifies the problem to some degree.\n",
    "\n",
    "Using the fact that the cumulants of a <span style=\"color:red\">Gaussian</span> system truncate at second order, one can show (see Breur and Petruccione, 3.6.4, or Jian Ma et al, PRA 2012) that there is a formal solution (assuming that at $t=0$, $\\rho(0) = \\rho_S(0)\\otimes \\rho_E(0)$ ),\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$ \\tilde{\\rho}_S(t) = \\mathcal{T} \\exp\\left( - \\int_0^t dt_2 \\int_0^{t_2} A^{\\times}(t_2)[C^R(t_2-t_1) A(t_1)^{\\times} + i C^I(t_2-t_1)A(t_1)^{\\circ}]\\right)\\rho_S(0) $$\n",
    "\n",
    "Where, as before $A(t)$ is the system operator which couples to the environment, \n",
    "\n",
    "$C(t)$ is the correlation function of the environment, split into real and imaginary parts, \n",
    "\n",
    "$A^{\\times}B \\equiv [A,B]$ and $A^{\\circ}B = \\{A,B\\}$.  \n",
    "\n",
    "$\\mathcal{T}$ is the time-ordering operator, which means that all terms have to reordered so that time arguments increase from right to left.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Directly solving or using this equation is intractable;  however, by assuming that we can write the correlation functions as a sum of exponentials, and taking repeated time-derivatives, one can derive the <span style=\"color:red\">hierarchy equations of motion.</span>\n",
    "\n",
    "Again assuming that the initial bath state is a thermal state, and recalling that \n",
    "\n",
    "$$J(\\omega) = \\sum_k g_k^2\\delta(\\omega-\\omega_k)$$\n",
    "\n",
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega \\{J(\\omega) e^{i\\omega t}n(\\omega)+ J(\\omega) e^{-i\\omega t}[1+n(\\omega)]\\}$$\n",
    "\n",
    "we can rewrite  this as\n",
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega J(\\omega)\\left[ \\mathrm{coth}\\left(\\frac{\\beta\\omega}{2}\\right)\\cos \\left(\\omega t\\right) - i \\sin \\left(\\omega t)\\right)\\}\\right]$$\n",
    "\n",
    "$\\beta = 1/ k_B T$, the temperature of the initial environment state.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "For some choices of spectral density, this does have the analytical form of a sum of exponentials, e.g. a Lorentzian.  Traditionally, the Drude-Lorentz form is chosen,\n",
    "\n",
    "$$J(\\omega) = \\frac{\\omega}{\\pi} \\frac{2\\lambda \\gamma}{(\\gamma^2 + \\omega^2)} $$\n",
    " \n",
    "Inserting this into $C(\\tau)$ one finds,\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$C(\\tau) = \\sum_{k=0}^{\\infty} c_k e^{-v_k|\\tau|}$$\n",
    "\n",
    "\n",
    "Where $v_k = 2 \\pi k/\\beta$ for $k\\geq1$, and $v_0 = \\gamma$, and $c_0 = \\lambda \\gamma [-i + \\mathrm{cot}\\left(\\beta \\gamma /2\\right)]$ and $c_k = (4 \\lambda \\gamma/\\beta) v_k/(v_k^2 - \\gamma^2)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def cot(x):\n",
    "    return 1./np.tan(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "E.g., for $\\gamma = 1.0$, $\\lambda = 1.25$, $\\beta = 0.95$:\n",
    "\n",
    "\n",
    "<img src=\"drude.png\" width=800 /> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\nwlam\\Anaconda3\\lib\\site-packages\\numpy\\core\\numeric.py:531: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAm0AAADcCAYAAAAiApZHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzCwD/wNsha3mAnTkSQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dbb326eb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#A quick plot of the spectral density and environment correlation functions\n",
    "\n",
    "gamma = 1.0\n",
    "\n",
    "lam = 2.5/2.\n",
    "\n",
    "T = 1/0.95\n",
    "\n",
    "wlist = np.linspace(0, 10, 1000)\n",
    "tlist = np.linspace(0, 5, 1000)\n",
    "J = [w * 2 * lam * gamma / (np.pi*(gamma**2 + w**2)) for w in wlist]\n",
    "\n",
    "def c(t):\n",
    "    c_temp =[]\n",
    "    c_temp.append(lam * gamma * (-1.0j + cot(gamma / (2 * T))) * np.exp(-gamma * t))\n",
    "    for k in range(1,5):\n",
    "        vk = 2 * np.pi * k * T\n",
    "        c_temp.append( (4 * lam * gamma * T * vk / (vk**2 - gamma**2))  * np.exp(- vk * t) ) \n",
    "    return c_temp\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, sharex=False, figsize=(10,3))\n",
    "\n",
    "fig.subplots_adjust(hspace=0.1) # reduce space between plots\n",
    "\n",
    "\n",
    "\n",
    "axes[0].plot(wlist, J, color='r',ls='--')\n",
    "axes[0].set_xlabel(r'$\\omega$', fontsize=20)\n",
    "axes[0].set_ylabel(r\"$J(\\omega)$\", fontsize=16);\n",
    "\n",
    "\n",
    "axes[1].plot(tlist, [np.real(sum(c(t))) for t in tlist], color='r',ls='--',label=\"c(t) real\")\n",
    "axes[1].plot(tlist, [np.imag(sum(c(t))) for t in tlist], color='g',ls='--',label=\"c(t) imaginary\")\n",
    "axes[1].plot(tlist, [c(t)[0] for t in tlist], color='b',ls='--',label=\"k=0 real\")\n",
    "axes[1].plot(tlist, [c(t)[1] for t in tlist], color='y',ls='--',label=\"k=1 real\")\n",
    "axes[1].set_xlabel(r'$t$', fontsize=20)\n",
    "axes[1].set_ylabel(r\"$C(t)$\", fontsize=16);\n",
    "\n",
    "axes[1].legend(loc=0)\n",
    "\n",
    "fig.savefig(\"drude.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Given these assumptions (<span style=\"color:red\">seperable initial condition, bosonic environment initially in a thermal state</span>), one can derive the hierachy, which looks like the following\n",
    "\n",
    "$$\\dot{\\rho}^n(t) = -(iH_S^{\\times} + \\sum_{k=0}^M\\, n_k \\,v_k)\\,\\rho^{n}(t)$$\n",
    "$$ - i \\sum_{k=0}^M\\, A^{\\times}\\, \\rho^{n^+_k}(t)$$\n",
    "$$ -i  \\sum_{k=0}^M n_k(c_k\\, A\\,\\rho^{n^-_k}(t) - c_k^*\\,\\rho^{n^-_k}(t)\\, A)$$\n",
    "\n",
    "This is a set of coupled equations for a hierarchy of \"density matrices\" labelled by an index $n$.  \n",
    "\n",
    "In this case $n = \\{n_1,n_2,..n_m,...,n_M\\}$: itcontains M indices, $0$ to $M$, a cut-off in the number of exponentials.  \n",
    "\n",
    "Each element runs from $0$ to $N_c$, an additional cut-off term.\n",
    "\n",
    "$n^+_k$ means one increases the $k$th component of $n_k$ by $1$, while  $n^-_k$ means decrease by $1$. $n= \\{0,0,0,..0\\}$ denotes the physical density matrix. All the rest are \"auxiliary\" non-normalized density matrices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Comparing BMS master equation and the HEOM\n",
    "\n",
    "Lets try and see the breakdown of the BMS (Born-Markov-Secular) master equation as we increase the bath correlation time\n",
    "\n",
    "First try lets try some parameters where BMS should work, $\\gamma=10 \\epsilon$, $\\lambda = 0.05 \\epsilon$, $\\beta = \\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#Calculates  generic non-secular master equation\n",
    "#This is experimental, and should be used with a grain of salt\n",
    "\n",
    "\n",
    "import time\n",
    "import warnings\n",
    "import numpy as np\n",
    "import scipy.sparse as sp\n",
    "from numpy import matrix\n",
    "from numpy import linalg\n",
    "from qutip import spre, spost, sprepost, thermal_dm, mesolve, Odeoptions\n",
    "from qutip import tensor, identity, destroy, sigmax, sigmaz, basis, qeye, dims\n",
    "from qutip.ui.progressbar import BaseProgressBar, TextProgressBar\n",
    "def Lnonsec(Hsys, Q, tlist, initial_state, Temperature,\n",
    "            return_vals, eigen_sparse=False, options=None,progress_bar=None):\n",
    "    \n",
    "\n",
    "    if progress_bar is None:\n",
    "        progress_bar = BaseProgressBar()\n",
    "    elif progress_bar is True:\n",
    "        progress_bar = TextProgressBar()\n",
    "        \n",
    "    if options is None:\n",
    "        options = Options()\n",
    "    output = None\n",
    "    \n",
    "    dot_energy, dot_state = Hsys.eigenstates(sparse=eigen_sparse)\n",
    "    deltaE = dot_energy[1] - dot_energy[0]\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    dimensions = dims(Q)\n",
    "    Nmax = dimensions[1][0]        #hilbert space \n",
    "    #Nmax = 2       #hilbert space \n",
    "    \n",
    "    H = Hsys\n",
    "    L=0\n",
    "    PsipreEta=0\n",
    "    PsipreX=0\n",
    "\n",
    "    all_energy, all_state = H.eigenstates(sparse=eigen_sparse)\n",
    "    Apre = spre(Q)\n",
    "    Apost = spost(Q)\n",
    "    for j in range(Nmax):\n",
    "        for k in range(Nmax):\n",
    "            A = Q.matrix_element(all_state[j].dag(), all_state[k])\n",
    "            #A = sh.matrix_element(all_state[j].dag(), all_state[k])\n",
    "            delE = (all_energy[j] - all_energy[k])\n",
    "            if np.absolute(A) > 0.0:\n",
    "                if abs(delE) > 0.0:\n",
    "                    #X = (0.5 * np.pi * gamma*(all_energy[j] - all_energy[k])\n",
    "                    X = (0.5  * np.pi * J0(all_energy[j] - all_energy[k])\n",
    "                         * (np.cosh((all_energy[j] - all_energy[k]) /\n",
    "                            (2 * Temperature))\n",
    "                         / (np.sinh((all_energy[j] - all_energy[k]) /\n",
    "                            (2 * Temperature)))) * A)\n",
    "                    #eta = (0.5 * np.pi * gamma *\n",
    "                    eta = (0.5 *  np.pi *\n",
    "                           J0(all_energy[j] - all_energy[k]) * A)\n",
    "                    PsipreX = PsipreX + X * all_state[j]*all_state[k].dag()\n",
    "                    PsipreEta = PsipreEta + (eta * all_state[j]\n",
    "                                             * all_state[k].dag())\n",
    "                else:\n",
    "                    #X =0.5  * np.pi* J0(0.) * A * 2 * Temperature\n",
    "                    X =0.5  * np.pi* J02(0.)* A  * 2 * Temperature\n",
    "                    #X =0.5 * np.pi * gamma * A * 2 * Temperature\n",
    "                    PsipreX=PsipreX+X*all_state[j]*all_state[k].dag()\n",
    "\n",
    "    A = Q\n",
    "    L = ((-spre(A * PsipreX)) + (sprepost(A, PsipreX))\n",
    "         +(sprepost(PsipreX, A)) + (-spost(PsipreX * A))\n",
    "         +(spre(A * PsipreEta)) + (sprepost(A, PsipreEta))\n",
    "         +(-sprepost(PsipreEta, A)) + (-spost(PsipreEta * A)))           \n",
    "\n",
    "    #Setup the operators and the Hamiltonian and the master equation \n",
    "    #and solve for time steps in tlist\n",
    "    psi0 = ( initial_state)\n",
    "    output = mesolve(H, psi0, tlist, [L], return_vals, options=options,progress_bar=progress_bar)\n",
    "    \n",
    "    return output\n",
    "              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "eps = 1.0    # Tunnelling term\n",
    "Hsys =  0.5 * eps * sigmaz()\n",
    "#Coupling operator to the bath:\n",
    "sm = destroy(2).dag()\n",
    "Q = sigmax()\n",
    "\n",
    "\n",
    "gamma = 10.                # Cutoff frequency of DL spectral density\n",
    "lam = 0.05           # Coupling strength of DL spectral density\n",
    "\n",
    "temperature = 1.     # Temperature of environment\n",
    "\n",
    "tlist = np.linspace(0, 20, 800) #time steps\n",
    "\n",
    "psi0=(basis(2,0)+basis(2,1))/np.sqrt(2.)  #initial state of system.\n",
    "rho0=psi0*psi0.dag()\n",
    "\n",
    "Ncut = 10\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk=4\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/(np.pi * ((energy**2) + (gamma**2)))\n",
    "def nbs(energy,Temperature):\n",
    "    beta=1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "#spectral density/w at w=0\n",
    "def J02(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma /(np.pi * ((gamma**2)))\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The relaxation time is roughly \n",
    "$\\tau_R \\approx 1/\\pi J(\\epsilon)n(\\epsilon)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "173.546464674\n"
     ]
    }
   ],
   "source": [
    "print(1/(np.pi * J0(1.0) * nbs(1.0,temperature)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest environment correlation times are\n",
    "$\\tau_E \\approx 1/\\gamma,  1/2 \\pi k_B T $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\n",
      "0.15915494309189535\n"
     ]
    }
   ],
   "source": [
    "print(1/gamma)\n",
    "print(1/(2 * np.pi * temperature))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system time scale is $\\tau_S \\approx 1/\\epsilon$, so $\\tau_E \\ll \\tau_S \\ll \\tau_R$ for the Born-Markov-Secular approximation seems valid. Let's check.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Configure the solver\n",
    "from qutip.nonmarkov.heom import HSolverDL\n",
    "hsolver = HSolverDL(Hsys, Q, lam, temperature, Ncut, Nk, gamma, stats=True,)\n",
    "resultHEOM = hsolver.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#lets compare to the BMS solution,\n",
    " \n",
    "resultMEsec = mesolve(Hsys, rho0, tlist, [np.sqrt(2*np.pi*J0(1.0)*(nbs(1.0,temperature)+1))*sm,np.sqrt(2*np.pi*J0(1.0)*nbs(1.0,temperature))*sm.dag()], [])\n",
    "resultMEnonsec = Lnonsec(Hsys, Q, tlist, rho0, temperature, [])\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "<img src=\"heom1.png\" width=800 /> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\nwlam\\Anaconda3\\lib\\site-packages\\numpy\\core\\numeric.py:531: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6gAAAG+CAYAAACeUSmHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dbb38c8f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P1p=rho0\n",
    "psi01 = (basis(2,0)-basis(2,1))/np.sqrt(2.)\n",
    "P12p=psi0*psi01.dag()\n",
    "\n",
    "P1HEOM=expect(resultHEOM.states,P1p)\n",
    "P12HEOM=expect(resultHEOM.states,P12p)\n",
    "\n",
    "\n",
    "P1ME=expect(resultMEsec.states,P1p)\n",
    "P12ME=expect(resultMEsec.states,P12p)\n",
    "import matplotlib.gridspec as gridspec\n",
    "\n",
    "P1MENS=expect(resultMEnonsec.states,P1p)\n",
    "P12MENS=expect(resultMEnonsec.states,P12p)\n",
    "\n",
    "fig = plt.figure(figsize=(15,6))\n",
    "gs1 = gridspec.GridSpec(1, 2)\n",
    "gs1.update(wspace=.5, hspace=1.3) # set the spacing between axes. \n",
    "########################################################################\n",
    "axes1 = plt.subplot(gs1[0])\n",
    "\n",
    "\n",
    "\n",
    "axes1.plot(tlist, P1HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes1.plot(tlist , P1ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes1.plot(tlist , P1MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes1.set_ylabel(r'$\\rho_{11}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "axes1.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "\n",
    "ticks = [0,0.5,1.0]\n",
    "axes1.set_yticks(ticks)\n",
    "axes1.set_yticklabels([\"0\",\"0.5\",\"1.0\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes1.set_xticks(ticks)\n",
    "axes1.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "axes1.legend(loc=4, fontsize=12)\n",
    "\n",
    "axes1.set_title('$\\lambda=0.05 \\epsilon $, $\\gamma = 10 \\epsilon $, $k_{B}T=\\epsilon $ ',fontsize=24,y=1.05,x=1.0)\n",
    "\n",
    "axes2 = plt.subplot(gs1[1])\n",
    "\n",
    "axes2.plot(tlist, P12HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes2.plot(tlist , P12ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes2.plot(tlist , P12MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes2.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "axes2.set_ylabel(r'$\\rho_{12}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "\n",
    "ticks = [0,-.1,-.2]\n",
    "axes2.set_yticks(ticks)\n",
    "axes2.set_yticklabels([\"0\",\"-0.1\",\"-0.2\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes2.set_xticks(ticks)\n",
    "axes2.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "#axes1.set_xlim(-1.2, 1.2);\n",
    "axes2.set_ylim(-0.25,0.);\n",
    "\n",
    "axes2.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "fig.savefig(\"heom1.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Next try lets try some parameters where BMS should break, $\\gamma=0.1 \\epsilon$, $\\lambda = 0.2 \\epsilon$, $\\beta = \\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "eps = 1.0    # Tunnelling term\n",
    "Hsys =  0.5 * eps * sigmaz()\n",
    "#Coupling operator to the bath:\n",
    "sm = destroy(2).dag()\n",
    "Q = sigmax()\n",
    "\n",
    "\n",
    "gamma = .1                # Cutoff frequency of DL spectral density\n",
    "lam = 0.2           # Coupling strength of DL spectral density\n",
    "\n",
    "temperature = 1.     # Temperature of environment\n",
    "\n",
    "tlist = np.linspace(0, 20, 800) #time steps\n",
    "\n",
    "psi0=(basis(2,0)+basis(2,1))/np.sqrt(2.)  #initial state of system.\n",
    "rho0=psi0*psi0.dag()\n",
    "\n",
    "Ncut = 25\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk=3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/(np.pi * ((energy**2) + (gamma**2)))\n",
    "def nbs(energy,Temperature):\n",
    "    beta=1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "#spectral density/w at w=0\n",
    "def J02(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma /(np.pi * ((gamma**2)))\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The relaxation time is roughly \n",
    "$\\tau_R \\approx 1/\\pi J(\\epsilon)n(\\epsilon)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "43.3866161686\n"
     ]
    }
   ],
   "source": [
    "print(1./(np.pi*J0(1.0)*nbs(1.0,temperature)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest environment correlation times are\n",
    "$\\tau_E \\approx 1/\\gamma,  1/2 \\pi k_B T $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n",
      "0.15915494309189535\n"
     ]
    }
   ],
   "source": [
    "print(1/gamma)\n",
    "print(1/(2 * np.pi * temperature))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system time scale is $\\tau_S \\approx 1/\\epsilon$, so $\\tau_S \\ll \\tau_R$ seems ok, but now $\\tau_E > \\tau_S$, so Markov approximation should break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Configure the solver\n",
    "from qutip.nonmarkov.heom import HSolverDL\n",
    "hsolver = HSolverDL(Hsys, Q, lam, temperature, Ncut, Nk, gamma, stats=True)\n",
    "resultHEOM = hsolver.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#lets compare to the BMS solution,\n",
    " \n",
    "resultMEsec = mesolve(Hsys, rho0, tlist, [np.sqrt(2*np.pi*J0(1.0)*(nbs(1.0,temperature)+1.))*sm,np.sqrt(2*np.pi*J0(1.0)*nbs(1.0,temperature))*sm.dag()], [])\n",
    "resultMEnonsec = Lnonsec(Hsys, Q, tlist, rho0, temperature, [])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "<img src=\"heom2.png\" width=800 />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\nwlam\\Anaconda3\\lib\\site-packages\\numpy\\core\\numeric.py:531: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6gAAAG+CAYAAACeUSmHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x152a4d1d780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "P1p=rho0\n",
    "psi01 = (basis(2,0)-basis(2,1))/np.sqrt(2.)\n",
    "P12p=psi0*psi01.dag()\n",
    "\n",
    "P1HEOM=expect(resultHEOM.states,P1p)\n",
    "P12HEOM=expect(resultHEOM.states,P12p)\n",
    "\n",
    "\n",
    "P1ME=expect(resultMEsec.states,P1p)\n",
    "P12ME=expect(resultMEsec.states,P12p)\n",
    "\n",
    "\n",
    "P1MENS=expect(resultMEnonsec.states,P1p)\n",
    "P12MENS=expect(resultMEnonsec.states,P12p)\n",
    "\n",
    "import matplotlib.gridspec as gridspec\n",
    "fig = plt.figure(figsize=(15,6))\n",
    "\n",
    "gs1 = gridspec.GridSpec(1, 2)\n",
    "gs1.update(wspace=.5, hspace=1.3) # set the spacing between axes. \n",
    "########################################################################\n",
    "axes1 = plt.subplot(gs1[0])\n",
    "\n",
    "axes1.plot(tlist, P1HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes1.plot(tlist , P1ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes1.plot(tlist , P1MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_ylabel(r'$\\rho_{11}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "axes1.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "\n",
    "ticks = [0,0.5,1.0]\n",
    "axes1.set_yticks(ticks)\n",
    "axes1.set_yticklabels([\"0\",\"0.5\",\"1.0\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes1.set_xticks(ticks)\n",
    "axes1.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "axes1.legend(loc=4, fontsize=12)\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_title('$\\lambda=0.2 \\epsilon$, $\\gamma = 0.1 \\epsilon$, $k_{B}T=\\epsilon $ ',fontsize=24,y=1.05,x=1.0)\n",
    "\n",
    "\n",
    "\n",
    "axes2 = plt.subplot(gs1[1])\n",
    "\n",
    "\n",
    "axes2.plot(tlist, P12HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes2.plot(tlist , P12ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes2.plot(tlist , P12MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes2.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "axes2.set_ylabel(r'$\\rho_{12}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "\n",
    "ticks = [0,-.1,-.2]\n",
    "axes2.set_yticks(ticks)\n",
    "axes2.set_yticklabels([\"0\",\"-0.1\",\"-0.2\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes2.set_xticks(ticks)\n",
    "axes2.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "#axes1.set_xlim(-1.2, 1.2);\n",
    "axes2.set_ylim(-0.25,0.);\n",
    "\n",
    "axes2.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "\n",
    "fig.savefig(\"heom2alt.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Next try lets try some parameters where secular approximation should break, but Born-Markov is ok $\\gamma=10 \\epsilon$, $\\lambda = 0.5 \\epsilon$, $\\beta = 0.25\\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "eps = 1.0    # Tunnelling term\n",
    "Hsys =  0.5 * eps * sigmaz()\n",
    "#Coupling operator to the bath:\n",
    "sm = destroy(2).dag()\n",
    "Q = sigmax()\n",
    "\n",
    "\n",
    "gamma = 10.                # Cutoff frequency of DL spectral density\n",
    "lam = .5           # Coupling strength of DL spectral density\n",
    "\n",
    "temperature = 4.     # Temperature of environment\n",
    "\n",
    "tlist = np.linspace(0, 20, 800) #time steps\n",
    "\n",
    "psi0=(basis(2,0)+basis(2,1))/np.sqrt(2.)  #initial state of system.\n",
    "#psi0=basis(2,0)  #initial state of system.\n",
    "rho0=psi0*psi0.dag()\n",
    "\n",
    "Ncut = 20\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk=3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/(np.pi * ((energy**2) + (gamma**2)))\n",
    "def nbs(energy,Temperature):\n",
    "    beta=1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "#spectral density/w at w=0\n",
    "def J02(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma /(np.pi * ((gamma**2)))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The relaxation time is roughly \n",
    "$\\tau_R \\approx 1/\\pi J(\\epsilon)n(\\epsilon)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.23411209098\n"
     ]
    }
   ],
   "source": [
    "print(1./(np.pi*J0(1.0)*(nbs(1.0,temperature)+1.)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest environment correlation times are\n",
    "$\\tau_E \\approx 1/\\gamma,  1/2 \\pi k_B T $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\n",
      "0.039788735772973836\n"
     ]
    }
   ],
   "source": [
    "print(1/gamma)\n",
    "print(1/(2 * np.pi * temperature))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system time scale is $\\tau_S \\approx 1/\\epsilon$, so now $\\tau_R \\approx \\tau_S$, so Secular appoximation should break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Configure the solver\n",
    "from qutip.nonmarkov.heom import HSolverDL\n",
    "hsolver = HSolverDL(Hsys, Q, lam, temperature, Ncut, Nk, gamma, stats=True)\n",
    "resultHEOM = hsolver.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#lets compare to the BMS solution,\n",
    " \n",
    "resultMEsec = mesolve(Hsys, rho0, tlist, [np.sqrt(2*np.pi*J0(1.0)*(nbs(1.0,temperature)+1.))*sm,np.sqrt(2*np.pi*J0(1.0)*nbs(1.0,temperature))*sm.dag()], [])\n",
    "resultMEnonsec = Lnonsec(Hsys, Q, tlist, rho0, temperature, [])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "<img src=\"heom4.png\" width=800 />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 541,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABR4AAAJxCAYAAAAkWq5GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJB4BAAAAAAAARN3/B/XDICsjBfmLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24c80780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "P1p=rho0\n",
    "psi01 = (basis(2,0)-basis(2,1))/np.sqrt(2.)\n",
    "\n",
    "P12p=psi0*psi01.dag()\n",
    "\n",
    "P1HEOM=expect(resultHEOM.states,P1p)\n",
    "P12HEOM=expect(resultHEOM.states,P12p)\n",
    "\n",
    "\n",
    "P1ME=expect(resultMEsec.states,P1p)\n",
    "P12ME=expect(resultMEsec.states,P12p)\n",
    "\n",
    "\n",
    "P1MENS=expect(resultMEnonsec.states,P1p)\n",
    "P12MENS=expect(resultMEnonsec.states,P12p)\n",
    "\n",
    "import matplotlib.gridspec as gridspec\n",
    "fig = plt.figure(figsize=(15,6))\n",
    "\n",
    "gs1 = gridspec.GridSpec(1, 2)\n",
    "gs1.update(wspace=.5, hspace=1.3) # set the spacing between axes. \n",
    "########################################################################\n",
    "axes1 = plt.subplot(gs1[0])\n",
    "\n",
    "axes1.plot(tlist, P1HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes1.plot(tlist , P1ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes1.plot(tlist , P1MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation nonsecular \")\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_ylabel(r'$\\rho_{11}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "axes1.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "\n",
    "ticks = [0,0.5,1.0]\n",
    "axes1.set_yticks(ticks)\n",
    "axes1.set_yticklabels([\"0\",\"0.5\",\"1.0\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes1.set_xticks(ticks)\n",
    "axes1.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "axes1.legend(loc=4, fontsize=12)\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_title('$\\lambda=0.5 \\epsilon$, $\\gamma = 10 \\epsilon$, $k_{B}T=4\\epsilon $ ',fontsize=24,y=1.05,x=1.0)\n",
    "\n",
    "\n",
    "\n",
    "axes2 = plt.subplot(gs1[1])\n",
    "\n",
    "\n",
    "axes2.plot(tlist, P12HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes2.plot(tlist , P12ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation Secular\")\n",
    "axes2.plot(tlist , P12MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes2.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "axes2.set_ylabel(r'$\\rho_{12}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "\n",
    "ticks = [0,-.1,-.2]\n",
    "axes2.set_yticks(ticks)\n",
    "axes2.set_yticklabels([\"0\",\"-0.1\",\"-0.2\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes2.set_xticks(ticks)\n",
    "axes2.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "#axes1.set_xlim(-1.2, 1.2);\n",
    "axes2.set_ylim(-0.25,0.);\n",
    "\n",
    "axes2.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "\n",
    "fig.savefig(\"heom4.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The HEOM and FMO\n",
    "\n",
    "The HEOM method became slightly more well known after being applied to the FMO (Fenna-Matthews-Olsen) complex (Ishizaki and Fleming, PNAS, 2009).\n",
    "\n",
    "<img src=\"fmo.png\" width=600/>\n",
    "\n",
    "Figure adapted from N. Lambert et al., Nat. Phys. (2013)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The HEOM and FMO\n",
    "\n",
    "In a minimal model, we can write the Hamiltonian of the $7$ sites as,\n",
    "\n",
    "$$ H = \\sum_{j=1}^7 \\epsilon_j |j\\rangle\\langle j| + \\sum_{j,j'} J_{j,j'} \\left(|j\\rangle \\langle j'| + c.c \\right)$$\n",
    "\n",
    "This can be reconstructed via a combination of ab initio model and spectroscopy to be, e.g., \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[7], [7]], shape = (7, 7), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}200.0 & -87.700 & 5.500 & -5.900 & 6.700 & -13.700 & -9.900\\\\-87.700 & 320.0 & 30.800 & 8.200 & 0.700 & 11.800 & 4.300\\\\5.500 & 30.800 & 0.0 & -53.500 & -2.200 & -9.600 & 6.0\\\\-5.900 & 8.200 & -53.500 & 110.0 & -70.700 & -17.0 & -63.300\\\\6.700 & 0.700 & -2.200 & -70.700 & 270.0 & 81.100 & -1.300\\\\-13.700 & 11.800 & -9.600 & -17.0 & 81.100 & 420.0 & 39.700\\\\-9.900 & 4.300 & 6.0 & -63.300 & -1.300 & 39.700 & 230.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[7], [7]], shape = (7, 7), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 200.   -87.7    5.5   -5.9    6.7  -13.7   -9.9]\n",
       " [ -87.7  320.    30.8    8.2    0.7   11.8    4.3]\n",
       " [   5.5   30.8    0.   -53.5   -2.2   -9.6    6. ]\n",
       " [  -5.9    8.2  -53.5  110.   -70.7  -17.   -63.3]\n",
       " [   6.7    0.7   -2.2  -70.7  270.    81.1   -1.3]\n",
       " [ -13.7   11.8   -9.6  -17.    81.1  420.    39.7]\n",
       " [  -9.9    4.3    6.   -63.3   -1.3   39.7  230. ]]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Multiple by h*c*100 to get joules from inverse centimeters\n",
    "idFMO = Qobj([[200, -87.7, 5.5, -5.9, 6.7, -13.7, -9.9],\n",
    "                    [-87.7, 320, 30.8, 8.2, 0.7, 11.8, 4.3],\n",
    "                    [5.5, 30.8, 0, -53.5, -2.2, -9.6, 6.0],\n",
    "                    [-5.9, 8.2, -53.5, 110, -70.7, -17.0, -63.3],\n",
    "                    [6.7, 0.7, -2.2, -70.7, 270, 81.1, -1.3],\n",
    "                    [-13.7,11.8, -9.6, -17.0 ,81.1, 420, 39.7],\n",
    "                    [-9.9, 4.3, 6.0, -63.3, -1.3, 39.7, 230]])\n",
    "idFMO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Using the HEOM, and assuming the Drude-Lorentz spectral density describes the $7$ independant baths, one finds, e.g., (T = 300 K, $1/\\gamma = 166$ fs, $1/\\lambda=6.6$ ps)\n",
    "\n",
    "from A. Fruchtman, N. Lambert, E. Gauger, Scientific Reports 2016:\n",
    "\n",
    "<img src=\"fmo2.png\" />\n",
    "\n",
    "Dashed lines: HEOM, solid lines: quasi-non-Markov master equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Generalizing the spectral density\n",
    "\n",
    "The Drude-Lorentz spectral density is convenient because we can <span style=\"color:red\">analytically expand it as exponentials </span>.\n",
    "\n",
    "In other cases, we can <span style=\"color:red\">numerically calculate</span> the correlation functions, and then <span style=\"color:red\">numerically fit</span> them to a sum of exponentials.\n",
    "\n",
    "As a simple example, we can bench-mark against the analytically solvable \"pure dephasing model\", i.e., we set the coupling operator equal to the system Hamiltonian \n",
    "\n",
    "(see A. fruchtman, N. Lambert, E. Gauger, Scientific Reports 2016 for more interesting examples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"ohmic.png\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"superohmic.png\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Conclusions\n",
    "\n",
    "The study of open quantum systems lets us model how a system interacts with it environment in various limits:\n",
    "\n",
    "- Weak coupling, no bath memory (Markov), and weak damping gives us the Lindblad Born-Markov-Secular master equation\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$\n",
    "- We can still solve the non-secular case if need be\n",
    "$$\\tau_E \\ll \\tau_S, \\tau_R$$\n",
    "- Exact methods (HEOM, reaction coordinate, etc) give insight into strongly correlated system-bath problems\n",
    "\n",
    "$$\\tau_E \\approx \\tau_S \\approx \\tau_R$$\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}