{
 "metadata": {
  "name": "development-mean-field-master-equations"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# QuTiP development notebook for testing new TD function callback signature\n",
      "\n",
      "Copyright (C) 2011 and later, Paul D. Nation & Robert J. Johansson\n",
      "\n",
      "\n",
      "<h3 style=\"color: red\">Note: experimental and under development</h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.kernel.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip.ipynbtools import HTMLProgressBar\n",
      "from qutip.gui.progressbar import TextProgressBar"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem description\n",
      "\n",
      "Consider the mean-field laser master equation on the form (Breuer and Petruccione)\n",
      "\n",
      "$\\displaystyle \\dot\\rho = -i [H, \\rho]\n",
      "+ 2\\kappa \\mathcal{D}[a] \n",
      "+ W_{21} \\mathcal{D}[\\sigma_-] \n",
      "+ W_{12} \\mathcal{D}[\\sigma_+]\n",
      "+ g [{\\rm Tr}[\\sigma_-\\rho] a^\\dagger - {\\rm Tr}[\\sigma_+\\rho] a, \\rho]\n",
      "+ g [{\\rm Tr}[a^\\dagger\\rho] \\sigma_- - {\\rm Tr}[a\\rho] \\sigma_+, \\rho] $\n",
      "\n",
      "where the dissipator superoperator is \n",
      "\n",
      "$\\displaystyle \\mathcal{D}[a] = a\\rho a^\\dagger - \\frac{1}{2}a^\\dagger a \\rho - \\frac{1}{2}\\rho a^\\dagger a,$\n",
      "\n",
      "$W_{21}$ and $W_{12}$ are the atomic relaxation rate and pump rate, respectively, and ${\\rm Tr}[A\\rho]$ is the expectation value of the operator $A$ with respect to the density operator $\\rho$.\n",
      "\n",
      "The Hamiltonian is given by\n",
      "\n",
      "$\\displaystyle H = \\omega a^\\dagger a + \\frac{1}{2}\\omega\\sigma_z$.\n",
      "\n",
      "Except for the two last term, the above master equation is on standard Lindblad form and could, if $g = 0$, be solved with standard usage of the QuTiP solver `mesolve`.\n",
      "\n",
      "We can write the master equation above on standard Lindblad form using an effective (nonhermitian?) Hamiltonian, corresponding to a nonlinear Schrodinger equation,\n",
      "\n",
      "$\\displaystyle \\dot\\rho = -i [H_{\\rm eff}(\\rho, t), \\rho]\n",
      "+ 2\\kappa \\mathcal{D}[a] + W_{21} \\mathcal{D}[\\sigma_-] + W_{12} \\mathcal{D}[\\sigma_+]$\n",
      "\n",
      "where\n",
      "\n",
      "$\\displaystyle \n",
      "H_{\\rm eff}(\\rho, t) = \\omega a^\\dagger a + \\frac{1}{2}\\omega\\sigma_z\n",
      "+ ig\\left({\\rm Tr}[\\sigma_-\\rho] a^\\dagger - {\\rm Tr}[\\sigma_+\\rho] a\\right)\n",
      "+ ig\\left({\\rm Tr}[a^\\dagger\\rho] \\sigma_- - {\\rm Tr}[a\\rho] \\sigma_+\\right)\n",
      "$\n",
      "\n",
      "In QuTiP (development version required) we implement this effective Hamiltonian using the Python callback function format for time-dependent Hamiltonians, but to calculate $H_{\\rm eff}(t)$ we need to have access to $\\rho(t)$, and the standard QuTiP time-dependent function callback signature is\n",
      "\n",
      "    def h_t(t, args):\n",
      "        ...\n",
      "        return h_eff\n",
      "\n",
      "However, the solver `mesolve` that calls the callback function has access to $\\rho(t)$ (or $\\left|\\psi(t)\\right>$ for unitary dynamics), so it could change the callback function signature to\n",
      "\n",
      "    def h_t(t, rho, args):\n",
      "        ...\n",
      "        return h_eff\n",
      "\n",
      "To avoid breaking backwards compatibility in the API, the inclusion of rho in the function signature is optionally activated with a keyword argument (rhs_with_state=True) in Odeoptions.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### QuTiP implementation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 10\n",
      "\n",
      "w = 1.0 * 2 * pi\n",
      "g = 0.1 * 2 * pi\n",
      "kappa = 0.005\n",
      "W21 = 0.01\n",
      "W12 = 0.05\n",
      "\n",
      "tlist = linspace(0, 250, 250)\n",
      "\n",
      "# cavity operators\n",
      "a  = tensor(destroy(N), identity(2))\n",
      "ad = tensor(create(N), identity(2))\n",
      "\n",
      "# atomic operators\n",
      "sz = tensor(identity(N), sigmaz())\n",
      "sx = tensor(identity(N), sigmax())\n",
      "sm = tensor(identity(N), destroy(2))\n",
      "sp = tensor(identity(N), create(2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#psi0 = tensor(fock(N, 0), fock(2, 0)) # start with the vacuum + ground state\n",
      "psi0 = tensor(coherent(N, 0.5), fock(2, 0)) # start a small coherent sate + ground state"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theta = 0.0\n",
      "\n",
      "H = w * ad * a - 0.5 * w * (cos(2*theta) * sz + sin(2*theta) * sx)\n",
      "\n",
      "H"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation}\\text{Quantum object: dims = [[10, 2], [10, 2]], shape = [20, 20], type = oper, isHerm = True}\\\\[1em]\\begin{pmatrix}-3.142 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 3.142 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 3.142 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 9.425 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 9.425 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 47.124 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 47.124 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 53.407 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 53.407 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 59.690\\\\\\end{pmatrix}\\end{equation}"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "Quantum object: dims = [[10, 2], [10, 2]], shape = [20, 20], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ -3.14159265   0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           3.14159265   0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           3.14159265   0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           9.42477796   0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           9.42477796   0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.          15.70796327\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "   15.70796327   0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.          21.99114858   0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.          21.99114858   0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.          28.27433388   0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.          28.27433388   0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.          34.55751919\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "   34.55751919   0.           0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.          40.8407045    0.           0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.          40.8407045    0.           0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.          47.1238898    0.           0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.          47.1238898    0.\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.          53.40707511\n",
        "    0.           0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "   53.40707511   0.        ]\n",
        " [  0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.           0.           0.           0.           0.           0.\n",
        "    0.          59.69026042]]"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "e_ops = [ad * a, sm.dag() * sm, sm, sp]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c_ops = [sqrt(2*kappa) * a, sqrt(W21) * sm, sqrt(W12) * sp]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Solve without mean-field contribution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = mesolve(H, psi0, tlist, c_ops, e_ops, options=Odeoptions(store_final_state=True)) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, axes = subplots(2,1)\n",
      "\n",
      "axes[0].plot(result.times, result.expect[0], label=r'$a^\\dagger a$')\n",
      "axes[0].plot(result.times, result.expect[1], label=r'$\\sigma_+\\sigma_-$')\n",
      "axes[0].set_ylim(-0.1, 1.1)\n",
      "axes[0].legend();\n",
      "\n",
      "axes[1].plot(result.times, abs(result.expect[2]), label=r'$\\sigma_-$')\n",
      "axes[1].plot(result.times, abs(result.expect[3]), label=r'$\\sigma_+$')\n",
      "axes[1].set_ylim(-0.1, 1.1)\n",
      "axes[1].legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YmBicOXMG48aNw5QpU4xusr788ssICAjAli1b0NDQgJ/85CcoLy83SiDr7jdM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\nfCnw3QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a56302410>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Visualize the cavity final state"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wigner_fock_distribution(ptrace(result.final_state, 0));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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U81UW4EazbBfeRrMZRsmyzBreRgfX9utES3+5TiNAIwiWP0UBOvFmy9wswPLc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\nkqD+AowyNKuZUqidAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a5651a2d0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Threshold"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d = (W12 - W21) / (W12 + W21)\n",
      "\n",
      "d"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "0.6666666666666666"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gamma = 0.5 * (W12 + W21)\n",
      "\n",
      "gamma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "0.030000000000000002"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "C = d * (g/(2*pi)) ** 2 / (gamma * kappa)\n",
      "\n",
      "C"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "44.44444444444445"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Solve with mean-field contribution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\displaystyle \n",
      "H_{\\rm eff}(\\rho, t) = \\omega a^\\dagger a + \\frac{1}{2}\\omega\\sigma_z\n",
      "+ ig\\left({\\rm Tr}[\\sigma_-\\rho] a^\\dagger - {\\rm Tr}[\\sigma_+\\rho] a\\right)\n",
      "+ ig\\left({\\rm Tr}[a^\\dagger\\rho] \\sigma_- - {\\rm Tr}[a\\rho] \\sigma_+\\right)\n",
      "$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def Heff(t, rho, args):\n",
      "    \"\"\" not an optimized implementation ... \"\"\"\n",
      "    q_rho = Qobj(vec2mat(rho))\n",
      "    Heff = 1.0j * g * (expect(sm, q_rho) * ad - expect(sp, q_rho) * a) \\\n",
      "         + 1.0j * g * (expect(ad, q_rho) * sm - expect(a, q_rho) * sp)\n",
      "    \n",
      "    return args[0] + liouvillian_fast(Heff, []).data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sop_a_data = liouvillian_fast(a, []).data\n",
      "sop_ad_data = liouvillian_fast(ad, []).data\n",
      "sop_sm_data = liouvillian_fast(sm, []).data\n",
      "sop_sp_data = liouvillian_fast(sp, []).data\n",
      "\n",
      "sop_a_L_data = spre(a).data\n",
      "sop_ad_L_data = spre(ad).data\n",
      "sop_sm_L_data = spre(sm).data\n",
      "sop_sp_L_data = spre(sp).data\n",
      "\n",
      "def Heff_fast(t, rho, args):\n",
      "    \"\"\" a somewhat more optimized version ... \"\"\"\n",
      "    \n",
      "    phi_sm = expect_rho_vec1d(sop_sm_L_data, rho)\n",
      "    phi_a = expect_rho_vec1d(sop_a_L_data, rho)\n",
      "    \n",
      "    Heff = 1.0j * g * (phi_sm * sop_ad_data  - conjugate(phi_sm) * sop_a_data) \\\n",
      "         + 1.0j * g * (conjugate(phi_a) * sop_sm_data - phi_a * sop_sp_data)\n",
      "    \n",
      "    return args[0] + Heff"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = mesolve(Heff_fast, psi0, tlist, c_ops, e_ops, args=[H],\n",
      "                 options=Odeoptions(rhs_with_state=True, store_final_state=True),\n",
      "                 progress_bar=TextProgressBar())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Completed:  0.0%. Elapsed time:   0.00s. Est. remaining time: 00:00:00:00.\n",
        "Completed: 10.0%. Elapsed time:  12.88s. Est. remaining time: 00:00:01:55."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 20.0%. Elapsed time:  26.35s. Est. remaining time: 00:00:01:45."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 30.0%. Elapsed time:  39.72s. Est. remaining time: 00:00:01:32."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 40.0%. Elapsed time:  54.83s. Est. remaining time: 00:00:01:22."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 50.0%. Elapsed time:  72.08s. Est. remaining time: 00:00:01:12."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 60.0%. Elapsed time:  89.05s. Est. remaining time: 00:00:00:59."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 70.0%. Elapsed time: 106.85s. Est. remaining time: 00:00:00:45."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 80.0%. Elapsed time: 124.90s. Est. remaining time: 00:00:00:31."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 90.0%. Elapsed time: 143.07s. Est. remaining time: 00:00:00:15."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Elapsed time: 159.90s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = subplots()\n",
      "\n",
      "ax.plot(result.times, result.expect[0], label=r'$a^\\dagger a$')\n",
      "ax.plot(result.times, result.expect[1], label=r'$\\sigma_+\\sigma_-$')\n",
      "ax.set_ylim(-0.1, 3)\n",
      "ax.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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I7hsMAJg3Yh4mbJyAN6a+AXs7e+w+tRvu3d0x0lc27D8Q9QDWH1yPKf6yHP/c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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a561c4ad0>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Visualize the cavity final state"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wigner_fock_distribution(ptrace(result.final_state, 0));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RiJtft/Zrmks2B7GRaQh0UYQoNoQ1a35jo+CGaPVUrbu1yGW1xCMjI3HmzBmL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\nmwlcx54M1X0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a75d5ad90>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Solve the same problem using the list-function format"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def a_coeff(t, rho, args):\n",
      "    return - 1.0j * g * expect_rho_vec1d(sop_sp_L_data, rho)\n",
      "\n",
      "def ad_coeff(t, rho, args):\n",
      "    return + 1.0j * g * expect_rho_vec1d(sop_sm_L_data, rho)\n",
      "\n",
      "def sm_coeff(t, rho, args):\n",
      "    return + 1.0j * g * expect_rho_vec1d(sop_ad_L_data, rho)\n",
      "\n",
      "def sp_coeff(t, rho, args):\n",
      "    return - 1.0j * g * expect_rho_vec1d(sop_a_L_data, rho)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = mesolve([H, [a, a_coeff], [ad, ad_coeff], [sm, sm_coeff], [sp, sp_coeff]],\n",
      "                 psi0, tlist, c_ops, e_ops, args={}, \n",
      "                 options=Odeoptions(rhs_with_state=True, store_final_state=True),\n",
      "                 progress_bar=TextProgressBar())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Completed:  0.0%. Elapsed time:   0.00s. Est. remaining time: 00:00:00:00.\n",
        "Completed: 10.0%. Elapsed time:  16.56s. Est. remaining time: 00:00:02:29."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 20.0%. Elapsed time:  33.92s. Est. remaining time: 00:00:02:15."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 30.0%. Elapsed time:  50.92s. Est. remaining time: 00:00:01:58."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 40.0%. Elapsed time:  70.16s. Est. remaining time: 00:00:01:45."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 50.0%. Elapsed time:  92.30s. Est. remaining time: 00:00:01:32."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 60.0%. Elapsed time: 114.58s. Est. remaining time: 00:00:01:16."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 70.0%. Elapsed time: 136.75s. Est. remaining time: 00:00:00:58."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 80.0%. Elapsed time: 158.77s. Est. remaining time: 00:00:00:39."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 90.0%. Elapsed time: 180.88s. Est. remaining time: 00:00:00:20."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Elapsed time: 202.96s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = subplots()\n",
      "\n",
      "ax.plot(result.times, result.expect[0], label=r'$a^\\dagger a$')\n",
      "ax.plot(result.times, result.expect[1], label=r'$\\sigma_+\\sigma_-$')\n",
      "ax.set_ylim(-0.1, 3)\n",
      "ax.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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I7hsMAJg3Yh4mbJyAN6a+AXs7e+w+tRvu3d0x0lc27D8Q9QDWH1yPKf6yHP/c\n9088FvsYnBycsHLSSoT+KxQJ0QkI7B2I9w6+h6EeQ7EibgVqGmoQ+q9Q/HTyJ0weOhlrUtcgtzwX\nvyz+BeWXyxG1PgqThkxCRL8I3Lv1XtRqaqH+ixqfZH2CWZtmIe3PaTh/+TwmfzIZS2OW4vYZt2PJ\n1iU4UX4CK+JWIDElET/l/4QX4l5Acl4ywt8Nxzsz3kFpVSme+ekZLAhbAHcnd4x6fxQeiH4A/h7+\neCP1DfR17osRXiPw2v7XEDc4DhHeEfgy50tU1lVipO9IvLDzBQzuNRhxg+Ow89ROFFQUYITXCGSd\nycLwPsMR1DsIGaczUFxZjKEeQ5FzLgehfUMxxGMI0ovTUX65HF4uXii8WIhon2i4dHPBr2d/Rb22\nHg52Dqiur0a4dzgAIKs0Cw52DtDoNOjZvScGuQ9CZX0lTpSfgIOdAy5rLmOg+0B4OHlAfUmN8svl\ncLBzQK2mFq7dXNGze09U11ejsr4SOqGDj6sPejn1QnWDvH7SoGuAazdX9HPtBzuFHc7XnEdFbQUA\n6Pe3t7NHZV0lquqrYG9nD7dubujh2AO1mlpU1VdBo9PA2dEZLo4u0AkdahpqUKupRTf7bujh2AOO\ndo6o1dTqf9CcHJzQzb4bNDoN6rR10Og06GbfDd3su0EBBeq19WjQNcBOYQdHO0f959foNBAQcLBz\ngL3CHnaKxjqfQMt/qFr6o9bSY/JHsm2YDXhfX1+o1Wr9a7VaDT8/P4Nt3K66JXPatGl46KGHUF5e\nDk8TM0MnJibqn8fFxSEuLs7k+x4pPYKE6AT9a4VCgVuG3oIfT/6IB6IfMNg2syQTUT5R5j4GYnxk\nwN8ffT9OnAD8/P4X8N7GAT/abzTeq/0A4TILUKU4DXunapzJCUCYr1y2K8UBkffehF2nduHO4Dsh\nhMDP+T9j1eTGbpoTBk3A3V/djfLL5fDs4Yltx7Zh1rBZ+vVBvYPg6+aL5LxkzAiagU+PfIpF4Yv0\n6xeEL8CzPz+LksoSnKs5hx0nduBf0/8FAPB29cZTNz2FJ3Y8gY/nfIxVe1YhaUESAMDZ0Rmrp67G\nsqRleHbcs1i5eyVS/5wKZ0dn/brp/56OaJ9olNWU4ZfFv6C7Q3fcH30/8ivyMWTNEDjaO+LVKa9i\nSeQSAMCP9/yI+C/j4b/WHyP7j8S+Jfvg7uSOuSFz8d9j/8VTO55CgGcAvr77a31PpiWRS/BW2lvY\nemwr3rjehyCxAAARdUlEQVT1DdzqfysUCgVWTV6F9RnrcbryNJ4c+yTmhsyFncIOGp0GqlwV0orS\n8Nz453DL0FvgaO+Iem09VLkqlFaV4q6QuzBpyCTY29mjpqEGaUVpyK/IxzM3PYNQr1DYKexQXV+N\nPYV7oBVaBHgGINAzEAqFAmerzyLnXA50QgeltxK9nXtDJ3Q4VXEKhRcL4drNFQGeAXB3cketphan\nKk6h/HI5BrgPgI+rD+zt7KHRaVBVX4WLtRfh7OiMPs59oBVaFF8qxqW6S3B2dIZvT190t++Oi3UX\ncbb6LHRCh949esOjh4f8PtVX4VLdJWh0Grh1c4NrN1dohRZV9VWoaahBD4cecOnmAgc7B9Q01KC6\nvhp2Cjs4Ozqju0N3NGgbcFlzGQ3aBjg5OMHJQY6PUaetQ52mDg52Duju0B32ClneK9dlujt0h4Od\nA3RChwZtAzQ6DRzsHOBoL2eh0eq0+rC/mgItH7CvpYP7tfSY1h4s0Fr27tqLfbv36V+/htdu/GDC\njIaGBjF06FCRn58v6urqhFKpFDk5OQbbnDlzRuh0OiGEEGlpaWLQoEEmj9XMW+lptBrR48Ue4lLt\nJYPlGzM3irlfzjXa/vHkx8VLu18ye8x9hftE1PooodMJ4e8vxD/+IcT4j8aLH0/8aLStuqJY4Kne\norxcfqZvcr4RASumi6eflusvXBDC1VWIlSkvi0dUjwghhDhcclgMXTPU6Fh3f3W3WJu6VgghRNi/\nwsTewr0G6zcf3Sxi348VpVWlwuNlD1F0schg/d9+/JsY88EYMer9UeL9g+8brKttqBVD1wwVvV7u\nJZ744QmDdTqdTry8+2Ux9dOp4t9H/m1UrsySTPHKnldEaVWp0brzNedF9tlso+VEZB0tzU6T+za3\ngUqlEkFBQcLf31+sWrVKCCHEu+++K959910hhBDr1q0ToaGhQqlUijFjxoj9+/e3qpC/n/tdDHlz\niNHy/Av5ot9r/fQ/JldM3DhRJOcmmz1mdX216PFiD7F7X63w9hbCy1sreq7qKc5VnzPaNjdXCPsn\nBojc87lCCCGe3P6kuP+zF8TQoUI0NAixbZsQt9wixH71fhH+TrgQQoindzwtntr+lNGxdhXsEkFv\nBYmdBTuF96veQqPVGKzXaDUieF2w8H3dV6z4ZYXR/lqdVjz03UNi4saJQqvTGpf1fK4ouFBg9rMT\nUedm0YBvKy0t5FfZX4lZm2YZLdfpdKLvP/sK9UW1wTL3l9xN1kSvFf5OuJj3+AGRmCjE5LknRK//\n8zO53ddfC+Hz2FzxadanQgghQt8OFXsL94px44T4/HMh5s0TYuVKIeo19aLnSz3FsbJjwu8NP3G0\n9KjJMoe/Ey7cVrk1+SP0Q94PYuWulUY/XNceh4i6ptYEfIcbquBo6VGEe4UbLVcoFBjpOxLpxenw\n6ymvA+RX5MOtu5u+t4050f1i8PVXGXjhnRjUpmXi8AGlye2ysoCQnqORWpSKmP4xuFB7AaP9RuPv\nf5d3qwYHA+vXA472jnhp8ksY99E4+PX0wwivESbL/OqUV1F+uRxTA6aafL9b/W/Frf63mi17V22L\nJKLW6XgBf/Yo5o2YZ3LdqP6jcKD4AO4MvhOAvMAa2S/S5LbXGuAQA12/DAQFASVHtqPyaBw0GsDh\nmjOQlQXcHj8TK7NvQp2mDncOvxN2CjtMnQr8/e/AAw/I+VUBYGnMUhRUFCDMK6zJ920uvImILKXD\njUVz9OzRJgNzpO9IpJ9O178+VHKo2R40VzhfiIGd3wEIIbCj8Dv41czE0aPG22VkALNuCsJTY5/C\nB5kfYG7IXADyTtVnn5WjRl6hUCjwzyn/xCLlIuMDERFZWYeqwddr61F4sdDkyI8AMLL/SBw8fRA6\noYOdwg6ZZzLxYMyDLTp21UklRI9yrE1bCxdHF9wcNgz79gGRV/0DoKQEuHxZztL0+ODH0bN7T6MB\nzIiIOosOVYMvqCiAX08/fd/ca/V16Ys+zn1wtPQohBA4WHKwxU00x7K74b7+a7D8h+W4Peh2jB0L\n7NtnuE1GhhwhUqGQI1EmxCQYjC9PRNSZWCXg30x9Ez/n/2y0/ET5iSZr71fEB8dj86+bob6khlan\n1V9wbc6vvwJ/ir0Dy0Yuwz3KezB2LLD3mvHLrgQ8EZEtaPcmGiEEVqeuhmcPTxx64JBBD5G88jz4\ne5ifz25B+ALM+HwmSi5cxMLwhS3qYVJXB5w8CQwfrsBbyrdkObwBjQb4/Xdg+HC5XUYGcP/9Zg5E\nRNSJtHsNPrc8F1qdFkIIfHf8O4N1Tc28dLUwrzDUXHDDxwc3ofK751v0nsePy3b17lcNF69QALNn\nA//5j3yt08FoEg8ios6s3QN+x4kdmOI/BU/f9DTePvC2wboTF5pvolEoFHDN/BueCHsTX2zsjcrK\n5t/z11/l7EzXmjOnMeB37JATYvv6tvSTEBF1bO0e8NtPbseUoVMQNzgO6cXpBqPGtaQGX1EBlO9c\ngFV3L0ZUlPGFUlOys+WMS9eaMEHW7ouLgTVrgMceA3hPERHZinYNeJ3QIaUgBZOHTIaPmw+cHZ1R\nUFEAQI5md+riKQzpNcTsMfbvB0aOBBwdZUDv3Nn8+/76q+mA79YNSEgAxo4FDh4E/vjHG/hQREQd\nVLteZD1XfQ6Odo7wdvUGAET3j0bG6Qxozw9BlX0R+jj3QQ/HHmaPsXs3MP5/kzBNmACsWNH8+2Zn\nm26iAYCXXgKmTAGqqgAnp+v5NEREHVu7Brz6khoD3BtniIrxicHBkoP48LW7AP9jCBhlvnkGAPbs\nAZ7/37XVMWOAw4eBmhrA2dn09jU1QFERDKbXu9akSU2vIyLqrNq1iabwYiEGug/Uv47uH40DxRnY\nvx9IObkX4R5jzO4vhAz0Kz1dXFwApVI22zTl99+BwEDZpENE1JW0a8CrL6oxoGdjDT7aJxoHig/C\nb4CAR8ROlGfebH5/NeDqCnh4NC6bMAHYtavpfZpqfycisnXtG/CX1AY1eG9Xb7hqB2DQLd/joksG\njnw/1uz+2dlASIjhsuYutDbVg4aIyNa1a8AXXCg0qMEDQL+C5Ujr+yCG9xmO3F97QqNpYmcAOTnG\nF0tvuknegVpba3qfo0ebvsBKRGTL2jXgj50xrMELARR+twD2jhrEDbkZPj5AXl7T+5vqDePmJmv1\n6enG2zc0yH7yY83/w4CIyCa1cxt8oUEvmrIyQNfQHR/N/hAPRD+AsDCYHKP9ClNNNIBspvnZeOwy\n7N8ve8/07dsGhSci6mTaNeArdefQ362//vXx40BQEHD7sBkY3mc4wsOBI0dM7yuEbKIxFfB33AF8\n8YXc5mrJycBtt7XhByAi6kTaNeDta73hYNfY9f5KwF9hrgZ/pQeNp6fxujFj5IiRmZmGy3/4AZhq\neipUIiKb164Bry0faFDLvp6Az8yUfd5NUSiABQuAzz9vXJaXJ4cIHj269eUmIuqM2jXgHWsGoqSk\n8fWxY4YBHxAAnDkDkyNEHjgAjBrV9LEXLQI+/RQoKJCvly8HnnmGNzgRUdfVrgHvZR+I48cbXx8/\nDgwb1vjawUHW0jMyjPdNTzcf8EFBclLsmTOBhx6SNfi//KXtyk5E1Nm0a8AP6dkY8FotcOKE8Rgx\nY8YYDwEshAz9kSPNH/+xx4A//xnw8wP++185WiQRUVfVroONjejfGPBqNdCnjxxP5mpjxgAbNxou\ny8uT/d29vc0fX6GQIU9ERO1cg48NCEJurnz+22+G7e9XjBkDpKYadnlsrv2diIiMNRvwycnJGD58\nOAIDA/HKK6+Y3ObRRx9FYGAglEolMq/tq3iV6BBPfQ3+55+Bm02MLebrK4f+vfJDAAApKewNQ0R0\nvcwGvFarxbJly5CcnIycnBxs2rQJv/32m8E2KpUKeXl5yM3NxXvvvYelS5c2eTx/f+DUKdlLxtxN\nSGPGNI4QWV0NbNkCzJt3fR+MiKirMxvw6enpCAgIwODBg+Ho6Ih58+Zh69atBtts27YNixcvBgDE\nxsaioqICpaWlJo/n5ATMni0n7Dh9unFc92vdcw+werW8ELtlixxLhpNhExFdH7MBX1xcjAEDGseO\n8fPzQ3FxcbPbFBUVNXnMZ56RE1xPmQLY25veZvp0eVH15Zdl0N93X0s+ChERXc1swCsUihYdRFwz\nCIy5/ZRKYP584K67zL2vDPdPPgHuvFP2bScioutjtpukr68v1Gq1/rVarYafn5/ZbYqKiuDbRHtK\nYmIiADmFXu/ecQDimnzvuDh5pysRUVeSkpKClJSUNjmWQlxb/b6KRqPBsGHD8NNPP6F///4YNWoU\nNm3ahODgYP02KpUK69atg0qlQmpqKpYvX47U1FTjN1IojGr6RERkXmuy02wN3sHBAevWrcPUqVOh\n1Wpx3333ITg4GOvXrwcAJCQkYPr06VCpVAgICICLiws2bNhwQwUhIqK2ZbYG36ZvxBq8XkpKCuLi\n4qxdjA6B56IRz0UjnotGrcnOdr2TlaS2al+zBTwXjXguGvFctA0GPBGRjWLAExHZqHZrg4+IiEBW\nVlZ7vBURkc1QKpU4fPjwDe3bbgFPRETti000REQ2igFPRGSjLB7wLRlP3pYNHjwY4eHhiIyMxKj/\nzVpSXl6OKVOmICgoCLfeeisqKiqsXErLWLJkCby9vREWFqZfZu6zv/TSSwgMDMTw4cOxfft2axTZ\nYkydi8TERPj5+SEyMhKRkZFISkrSr7Plc6FWqzFx4kSEhoZixIgRWLt2LYCu+d1o6ly02XdDWJBG\noxH+/v4iPz9f1NfXC6VSKXJyciz5lh3O4MGDxfnz5w2WPfnkk+KVV14RQgjx8ssvi6efftoaRbO4\nXbt2iUOHDokRI0bolzX12bOzs4VSqRT19fUiPz9f+Pv7C61Wa5VyW4Kpc5GYmChef/11o21t/VyU\nlJSIzMxMIYQQlZWVIigoSOTk5HTJ70ZT56KtvhsWrcG3ZDz5rkBccx376jH0Fy9ejP/85z/WKJbF\njR8/Hh4eHgbLmvrsW7duxfz58+Ho6IjBgwcjICAA6enp7V5mSzF1LgDj7wZg++eiX79+iIiIAAC4\nuroiODgYxcXFXfK70dS5ANrmu2HRgG/JePK2TqFQ4JZbbkFMTAzef/99AEBpaSm8/zeDuLe3d5MT\npNiipj776dOnDUYq7SrflbfeegtKpRL33XefvkmiK52LgoICZGZmIjY2tst/N66ci9H/m5+0Lb4b\nFg34lo4nb8v27t2LzMxMJCUl4e2338bu3bsN1isUii57npr77LZ+XpYuXYr8/HwcPnwYPj4++Otf\n/9rktrZ4LqqqqhAfH481a9bAzc3NYF1X+25UVVVh7ty5WLNmDVxdXdvsu2HRgG/JePK2zsfHBwDQ\nt29f3HHHHUhPT4e3tzfOnDkDACgpKYGXl5c1i9iumvrs1zOvgK3w8vLSB9mf//xn/T+1u8K5aGho\nQHx8PBYtWoQ5c+YA6LrfjSvnYuHChfpz0VbfDYsGfExMDHJzc1FQUID6+np88cUXmDVrliXfskOp\nqalBZWUlAKC6uhrbt29HWFgYZs2ahY8//hgA8PHHH+v/p3YFTX32WbNmYfPmzaivr0d+fj5yc3P1\nvY5sVUlJif75t99+q+9hY+vnQgiB++67DyEhIVi+fLl+eVf8bjR1Ltrsu2GJK8NXU6lUIigoSPj7\n+4tVq1ZZ+u06lJMnTwqlUimUSqUIDQ3Vf/7z58+LyZMni8DAQDFlyhRx4cIFK5fUMubNmyd8fHyE\no6Oj8PPzEx999JHZz75y5Urh7+8vhg0bJpKTk61Y8rZ37bn48MMPxaJFi0RYWJgIDw8Xs2fPFmfO\nnNFvb8vnYvfu3UKhUAilUikiIiJERESESEpK6pLfDVPnQqVStdl3g0MVEBHZKN7JSkRkoxjwREQ2\nigFPRGSjGPBERDaKAU9EZKMY8ERENooBT0RkoxjwREQ26v8DX3UC9lrfL3wAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a55b56410>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Solve with mean-field contribution, but without dissipation (using sesolve)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tlist = linspace(0, 50, 150)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H_data = H.data\n",
      "a_data = a.data\n",
      "ad_data = ad.data\n",
      "sm_data = sm.data\n",
      "sp_data = sp.data\n",
      "\n",
      "def Heff_func(t, psi, args):\n",
      "    \n",
      "    phi_sm = expect_psi(sm_data, psi[:, newaxis])\n",
      "    phi_a  = expect_psi(a_data, psi[:, newaxis])\n",
      "    phi_sp = expect_psi(sp_data, psi[:, newaxis])\n",
      "    phi_ad = expect_psi(ad_data, psi[:, newaxis])\n",
      "    \n",
      "    Heff = 1.0j * g * (phi_sm * ad_data - phi_sp * a_data) \\\n",
      "         + 1.0j * g * (phi_ad * sm_data - phi_a * sp_data)\n",
      "    \n",
      "    return H_data + Heff"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = sesolve(Heff_func, psi0, tlist, e_ops,\n",
      "                 options=Odeoptions(rhs_with_state=True, store_final_state=True),\n",
      "                 progress_bar=TextProgressBar())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Completed:  0.0%. Elapsed time:   0.00s. Est. remaining time: 00:00:00:00.\n",
        "Completed: 10.0%. Elapsed time:   1.82s. Est. remaining time: 00:00:00:16."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 20.0%. Elapsed time:   3.62s. Est. remaining time: 00:00:00:14."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 30.0%. Elapsed time:   5.42s. Est. remaining time: 00:00:00:12."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 40.0%. Elapsed time:   7.22s. Est. remaining time: 00:00:00:10."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 50.0%. Elapsed time:   9.03s. Est. remaining time: 00:00:00:09."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 60.0%. Elapsed time:  10.84s. Est. remaining time: 00:00:00:07."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 70.0%. Elapsed time:  12.67s. Est. remaining time: 00:00:00:05."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 80.0%. Elapsed time:  14.48s. Est. remaining time: 00:00:00:03."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 90.0%. Elapsed time:  16.32s. Est. remaining time: 00:00:00:01."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Elapsed time:  18.13s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = subplots()\n",
      "\n",
      "ax.plot(result.times, real(result.expect[0]), label=r'$a^\\dagger a$')\n",
      "ax.plot(result.times, real(result.expect[1]), label=r'$\\sigma_+\\sigma_-$')\n",
      "ax.set_ylim(-0.1, 1)\n",
      "ax.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DZfny5UY7S3Nzc8nPz4/y843Hb/V/6tAhMfjeGI98/4jFDoiuPPnjk/RmxpsG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\ncqJcasgxdAkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a56180890>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Solve the same problem with list function format"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def a_coeff(t, psi, args):\n",
      "    return - 1.0j * g * expect_psi(sp_data, psi[:, newaxis])\n",
      "\n",
      "def ad_coeff(t, psi, args):\n",
      "    return + 1.0j * g * expect_psi(sm_data, psi[:, newaxis])\n",
      "\n",
      "def sm_coeff(t, psi, args):\n",
      "    return + 1.0j * g * expect_psi(ad_data, psi[:, newaxis])\n",
      "\n",
      "def sp_coeff(t, psi, args):\n",
      "    return - 1.0j * g * expect_psi(a_data, psi[:, newaxis])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = sesolve([H, [a, a_coeff], [a.dag(), ad_coeff], [sm, sm_coeff], [sp, sp_coeff]],\n",
      "                 psi0, tlist, e_ops, \n",
      "                 options=Odeoptions(rhs_with_state=True, store_final_state=True),\n",
      "                 progress_bar=TextProgressBar())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Completed:  0.0%. Elapsed time:   0.00s. Est. remaining time: 00:00:00:00.\n",
        "Completed: 10.0%. Elapsed time:   1.89s. Est. remaining time: 00:00:00:16."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 20.0%. Elapsed time:   3.76s. Est. remaining time: 00:00:00:15."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 30.0%. Elapsed time:   5.63s. Est. remaining time: 00:00:00:13."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 40.0%. Elapsed time:   7.52s. Est. remaining time: 00:00:00:11."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 50.0%. Elapsed time:   9.39s. Est. remaining time: 00:00:00:09."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 60.0%. Elapsed time:  11.25s. Est. remaining time: 00:00:00:07."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 70.0%. Elapsed time:  13.10s. Est. remaining time: 00:00:00:05."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 80.0%. Elapsed time:  14.96s. Est. remaining time: 00:00:00:03."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Completed: 90.0%. Elapsed time:  16.85s. Est. remaining time: 00:00:00:01."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Elapsed time:  18.73s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = subplots()\n",
      "\n",
      "ax.plot(result.times, real(result.expect[0]), label=r'$a^\\dagger a$')\n",
      "ax.plot(result.times, real(result.expect[1]), label=r'$\\sigma_+\\sigma_-$')\n",
      "ax.set_ylim(-0.1, 1)\n",
      "ax.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DZfny5UY7S3Nzc8nPz4/y843Hb/V/6tAhMfjeGI98/4jFDoiuPPnjk/RmxpsG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\ncqJcasgxdAkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a55968bd0>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Solve with mean-field contribution and dissipation using mcsolve"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tlist = linspace(0, 250, 250)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = mcsolve(Heff_func, psi0, tlist, c_ops, e_ops, ntraj=64,\n",
      "                 options=Odeoptions(rhs_with_state=True, store_final_state=True, gui=False, num_cpus=4),\n",
      "                 progress_bar=TextProgressBar())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Completed:  1.6%. Elapsed time: 141.29s. Est. remaining time: 00:02:28:21.\n",
        "Completed: 10.9%. Elapsed time: 505.69s. Est. remaining time: 00:01:08:37.\n",
        "Completed: 20.3%. Elapsed time: 884.28s. Est. remaining time: 00:00:57:49.\n",
        "Completed: 31.2%. Elapsed time: 1122.07s. Est. remaining time: 00:00:41:08.\n",
        "Completed: 40.6%. Elapsed time: 1404.55s. Est. remaining time: 00:00:34:12.\n",
        "Completed: 50.0%. Elapsed time: 1624.73s. Est. remaining time: 00:00:27:04.\n",
        "Completed: 60.9%. Elapsed time: 1885.82s. Est. remaining time: 00:00:20:08.\n",
        "Completed: 70.3%. Elapsed time: 2173.70s. Est. remaining time: 00:00:15:17.\n",
        "Completed: 81.2%. Elapsed time: 2467.79s. Est. remaining time: 00:00:09:29.\n",
        "Completed: 90.6%. Elapsed time: 2683.16s. Est. remaining time: 00:00:04:37.\n",
        "Completed: 100.0%. Elapsed time: 2915.00s. Est. remaining time: 00:00:00:00.\n",
        "Elapsed time: 2915.10s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = subplots()\n",
      "\n",
      "ax.plot(result.times, real(result.expect[0]), label=r'$a^\\dagger a$')\n",
      "ax.plot(result.times, real(result.expect[1]), label=r'$\\sigma_+\\sigma_-$')\n",
      "ax.set_ylim(-0.1, 3)\n",
      "ax.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eLzVqVHZtGGNvOh6qoIogAubNA375RXPB/WXOSzx8/lAzO2eMaRUO8Gp04oTo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\nluIAzxhjWur/ASgOHqKFdEr1AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a560bac10>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Using the list function format and mcsolve"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = mcsolve([H, [a, a_coeff], [ad, ad_coeff], [sm, sm_coeff], [sp, sp_coeff]],\n",
      "                 psi0, tlist, c_ops, e_ops, args={}, ntraj=512,\n",
      "                 options=Odeoptions(rhs_with_state=True, store_final_state=True, gui=False, num_cpus=4),\n",
      "                 progress_bar=TextProgressBar())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Completed:  0.2%. Elapsed time:  37.77s. Est. remaining time: 00:05:21:39.\n",
        "Completed: 10.2%. Elapsed time: 518.60s. Est. remaining time: 00:01:16:27.\n",
        "Completed: 20.1%. Elapsed time: 1019.87s. Est. remaining time: 00:01:07:29.\n",
        "Completed: 30.1%. Elapsed time: 1520.25s. Est. remaining time: 00:00:58:54.\n",
        "Completed: 40.0%. Elapsed time: 2034.98s. Est. remaining time: 00:00:50:47.\n",
        "Completed: 50.0%. Elapsed time: 2513.66s. Est. remaining time: 00:00:41:53.\n",
        "Completed: 60.2%. Elapsed time: 3036.83s. Est. remaining time: 00:00:33:31.\n",
        "Completed: 70.1%. Elapsed time: 3589.60s. Est. remaining time: 00:00:25:29.\n",
        "Completed: 80.1%. Elapsed time: 4684.49s. Est. remaining time: 00:00:19:25.\n",
        "Completed: 90.0%. Elapsed time: 5647.46s. Est. remaining time: 00:00:10:24.\n",
        "Completed: 100.0%. Elapsed time: 6778.12s. Est. remaining time: 00:00:00:00.\n",
        "Elapsed time: 6778.18s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = subplots()\n",
      "\n",
      "ax.plot(result.times, real(result.expect[0]), label=r'$a^\\dagger a$')\n",
      "ax.plot(result.times, real(result.expect[1]), label=r'$\\sigma_+\\sigma_-$')\n",
      "ax.set_ylim(-0.1, 3)\n",
      "ax.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f1a560d3190>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Software versions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip.ipynbtools import version_table\n",
      "\n",
      "version_table()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>matplotlib</td><td>1.4.x</td></tr><tr><td>Python</td><td>3.3.1 (default, Apr 17 2013, 22:30:32) \n",
        "[GCC 4.7.3]</td></tr><tr><td>SciPy</td><td>0.13.0.dev-d74fd00</td></tr><tr><td>Cython</td><td>0.19.1</td></tr><tr><td>QuTiP</td><td>2.3.0.dev-b354119</td></tr><tr><td>Numpy</td><td>1.8.0.dev-75cdf3d</td></tr><tr><td>IPython</td><td>1.0.dev</td></tr><tr><td>OS</td><td>posix [linux]</td></tr><tr><td colspan='2'>Thu Jul 04 15:30:06 2013 JST</td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "<IPython.core.display.HTML at 0x7f1a55f8e090>"
       ]
      }
     ],
     "prompt_number": 35
    }
   ],
   "metadata": {}
  }
 ]
}