Lecture-15-Nonclassically-driven-atoms.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Lecture 15: Nonclassically driven atoms (cascaded quantum systems)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Author: J. R. Johansson (robert@riken.jp), http://dml.riken.jp/~rob/\n",
      "\n",
      "The latest version of this [IPython notebook](http://ipython.org/ipython-doc/dev/interactive/htmlnotebook.html) lecture is available at [http://github.com/jrjohansson/qutip-lectures](http://github.com/jrjohansson/qutip-lectures).\n",
      "\n",
      "The other notebooks in this lecture series are indexed at [http://jrjohansson.github.com](http://jrjohansson.github.com)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Introduction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In Chapter 12 (Cascaded quantum systems) in Quantum Noise by Gardiner and Zoller (Springer, 3rd edition), a few examples of nonclassically driven atoms are given. In this notebook we solve for the dynamics of those systems using QuTiP."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Two-level atom driven by squeezed light"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The master equation for a two-level atom driven by a squeezed light can be written as (Ch. 12.2.2 in Quantum Noise)\n",
      "\n",
      "$$\n",
      "\\dot\\rho = -i[H, \\rho] + \\kappa\\mathcal{D}[a]\\rho + \\gamma\\mathcal{D}[\\sigma_-]\\rho\n",
      "-\\sqrt{\\eta\\kappa\\gamma}\\{[\\sigma_+, a\\rho] + [\\rho a^\\dagger, \\sigma_-]\\}\n",
      "$$\n",
      "\n",
      "where\n",
      "\n",
      "$$\n",
      "H = i\\frac{1}{2}(E {a^\\dagger}^2 - E^* a^2)\n",
      "$$\n",
      "\n",
      "and\n",
      "\n",
      "$$\n",
      "\\mathcal{D}[a]\\rho = a \\rho a^\\dagger - \\frac{1}{2}\\rho a^\\dagger a - \\frac{1}{2}a^\\dagger a\\rho\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$\n",
      "\\dot\\rho = -i[H, \\rho] + \\kappa\\mathcal{D}[a]\\rho + \\gamma\\mathcal{D}[\\sigma_-]\\rho\n",
      "-\\sqrt{\\eta\\kappa\\gamma}\\{\\sigma_+a\\rho - a\\rho\\sigma_+ + \\rho a^\\dagger\\sigma_- - \\sigma_-\\rho a^\\dagger\\}\n",
      "$$\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 10\n",
      "gamma = 1\n",
      "eta = 0.9"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def solve(N, gamma, kappa, eta):\n",
      "    \n",
      "    E = kappa * 0.25\n",
      "    \n",
      "    # create operators\n",
      "    a = tensor(destroy(N), identity(2))\n",
      "    sm = tensor(identity(N), destroy(2))\n",
      "\n",
      "    # Hamiltonian\n",
      "    H = 0.5j * (E * a.dag() ** 2 - conjugate(E) * a ** 2)\n",
      "\n",
      "    # master equation superoperators\n",
      "    L0 = liouvillian(H, [sqrt(kappa) * a, sqrt(gamma) * sm])\n",
      "    L1 = - sqrt(kappa * gamma * eta) * (\n",
      "        spre(sm.dag() * a) - spre(a) * spost(sm.dag()) + \n",
      "        spost(a.dag() * sm) - spre(sm) * spost(a.dag()))\n",
      "    \n",
      "    L = L0 + L1\n",
      "    \n",
      "    # steady state\n",
      "    rhoss = steadystate(L)\n",
      "    \n",
      "    # correlation function and spectrum\n",
      "    taulist = linspace(0, 500, 2500)\n",
      "    c = correlation_2op_1t(L, rhoss, taulist, [], sm.dag(), sm)\n",
      "    w, S = spectrum_correlation_fft(taulist, c)\n",
      "    \n",
      "    ww = hstack([fliplr(-array([w])).squeeze(), w])\n",
      "    SS = hstack([fliplr(array([S])).squeeze(), S])\n",
      "\n",
      "    return rhoss, ww, SS"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rhoss2, w2, S2 = solve(N, gamma, 2, eta)\n",
      "rhoss4, w4, S4 = solve(N, gamma, 4, eta)\n",
      "rhoss8, w8, S8 = solve(N, gamma, 8, eta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wigner_fock_distribution(rhoss2.ptrace(0));\n",
      "wigner_fock_distribution(rhoss4.ptrace(0));\n",
      "wigner_fock_distribution(rhoss8.ptrace(0));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/local/lib/python3.4/dist-packages/qutip/visualization.py:869: UserWarning: Deprecated: Use plot_wigner_fock_distribution\n",
        "  warnings.warn(\"Deprecated: Use plot_wigner_fock_distribution\")\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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wYezevRspKSkoKSnBtWvXMGXKFGzbts1hvaSkJOV+QkICEhISvF0qUa2Tnp6O9PR0Veuq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\nA4488BRfp4pbAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fafc6cc7dd8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zSouNMEuW4LYPcnu2ABdEAVq9CK1OA2OpBEOABsU6jaVVH6hFcKDO6XsL1gMl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\nA4488BRfp4pbAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fafc6cc7a90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zSouNMEuW4LYPcnu2ABdEAVq9CK1OA2OpBEOABsU6jaVVH6hFcKDO6XsL1gMl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\nA4488BRfp4pbAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fafc6cc7ac8>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots()\n",
      "ax.plot(w2, S2 / S2.max(), label=r'$\\kappa = 2$')\n",
      "ax.plot(w4, S4 / S4.max(), label=r'$\\kappa = 4$')\n",
      "ax.plot(w8, S8 / S8.max(), label=r'$\\kappa = 8$')\n",
      "ax.plot(w8, 0.25/((0.5 * gamma)**2 + w8**2), 'k:', label=r'Lorentian')\n",
      "ax.legend()\n",
      "ax.set_ylabel(r'Flouresence spectrum', fontsize=16)\n",
      "ax.set_xlabel(r'$\\omega$', fontsize=18)\n",
      "ax.set_xlim(-2, 2);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dm6VLl7JixQqio6MB+OWXX5g1a5ZZlZRIDCE+Pp74+HgA1qxRDuKpiTQ9fec0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\nU4FTAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fafc6c789e8>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fig. 12.4 in Quantum Noise."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Two-level atom driven by antibunched light: coherent excitation of the source atom"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The master equation given in Sec. 12.3.1 in Quantum Noise, for two coupled atoms where the first atom (source atom) is irradiated with coherent light, and the second atom is irradiated by the antibunched light emitted from the source atom, is:\n",
      "\n",
      "$$\n",
      "\\dot\\rho = -i[H, \\rho] + \\gamma_1\\mathcal{D}[\\sigma^-_{1}]\\rho + \\gamma_2\\mathcal{D}[\\sigma^-_{2}]\\rho\n",
      "-\\sqrt{(1-\\epsilon_1)(1-\\epsilon_2)\\gamma_1\\gamma_2}\n",
      "([\\sigma_2^+, \\sigma_1^-\\rho] + [\\rho\\sigma_1^+, \\sigma_2^-])\n",
      "$$\n",
      "\n",
      "where\n",
      "\n",
      "$$\n",
      "H = -i\\sqrt{\\epsilon_1\\gamma_1}(E\\sigma_1^+ - E^*\\sigma_1^-)\n",
      "$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "e1 = 0.5\n",
      "e2 = 0.5\n",
      "\n",
      "gamma1 = 2\n",
      "gamma2 = 2\n",
      "\n",
      "E = 2 / sqrt(e1 * gamma1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sm1 = tensor(destroy(2), identity(2))\n",
      "sp1 = sm1.dag()\n",
      "sm2 = tensor(identity(2), destroy(2))\n",
      "sp2 = sm2.dag()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H = -1j * sqrt(e1 * gamma1) * (E * sp1 - conjugate(E) * sm1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L0 = liouvillian(H, [sqrt(gamma1) * sm1, sqrt(gamma2) * sm2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L1 = - sqrt((1 - e1) * (1 - e2) * gamma1 * gamma2) * \\\n",
      "        (spre(sp2 * sm1) - spre(sm1) * spost(sp2) + \n",
      "         spost(sp1 * sm2) - spre(sm2) * spost(sp1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L = L0 + L1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# steady state\n",
      "rhoss = steadystate(L)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# correlation function and spectrum\n",
      "taulist = linspace(0, 4, 250)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G2_11 = correlation_4op_1t(L, rhoss, taulist, [], sp1, sp1, sm1, sm1)\n",
      "g2_11 = G2_11 / (expect(sp1*sm1, rhoss) * expect(sp1*sm1, rhoss))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G2_22 = correlation_4op_1t(L, rhoss, taulist, [], sp2, sp2, sm2, sm2)\n",
      "g2_22 = G2_22 / (expect(sp2*sm2, rhoss) * expect(sp2*sm2, rhoss))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G2_12 = correlation_4op_1t(L, rhoss, taulist, [], sp2, sp1, sm1, sm2)\n",
      "g2_12 = G2_12 / (expect(sp1*sm1, rhoss) * expect(sp2*sm2, rhoss))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G2_21 = correlation_4op_1t(L, rhoss, taulist, [], sp1, sp2, sm2, sm1)\n",
      "g2_21 = G2_21 / (expect(sp2*sm2, rhoss) * expect(sp1*sm1, rhoss))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots()\n",
      "\n",
      "ax.plot(taulist, g2_11, label=r'$g^{(2)}_{11}(\\tau)$')\n",
      "ax.plot(taulist, g2_22, label=r'$g^{(2)}_{22}(\\tau)$')\n",
      "ax.plot(taulist, g2_12, label=r'$g^{(2)}_{12}(\\tau)$')\n",
      "ax.plot(taulist, g2_21, label=r'$g^{(2)}_{21}(\\tau)$')\n",
      "\n",
      "ax.legend(loc=4)\n",
      "ax.set_xlabel(r'$\\tau$');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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S2B0ZycCWtr7Pnft5/p6zM+qECeTeMZIDPc2cLDlDdmk250vOU1JVUrMYRu+g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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fafc6ab83c8>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fig. 12.6 in Quantum Noise."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Two-level atom driven by antibunched light: incoherent excitation of the source atom"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When the source atom is irradiated with incoherent light, the master equation becomes (Sec. 12.3.2 in Quantum Noise)\n",
      "\n",
      "$$\n",
      "\\dot\\rho = \n",
      "\\gamma_1\\mathcal{D}[\\sigma^-_{1}]\\rho + \n",
      "\\gamma_2\\mathcal{D}[\\sigma^-_{2}]\\rho +\n",
      "\\kappa(\\bar{N} + 1)\\mathcal{D}[a]\\rho + \n",
      "\\kappa\\bar{N}\\mathcal{D}[a^\\dagger]\\rho \n",
      "-\\sqrt{2\\kappa\\eta_1\\gamma_1} ([\\sigma_1^+, a\\rho] + [\\rho a^\\dagger, \\sigma_1^-])\n",
      "-\\sqrt{\\eta_2\\gamma1\\gamma_2} ([\\sigma_2^+, \\sigma_1^-\\rho] + [\\rho\\sigma_1^+, \\sigma_2^-])\n",
      "$$\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 10\n",
      "\n",
      "e1 = 0.5\n",
      "e2 = 0.5\n",
      "ek = 0.5\n",
      "\n",
      "n_th = 1\n",
      "kappa = 0.1\n",
      "gamma1 = 1\n",
      "gamma2 = 1\n",
      "\n",
      "E = 0.025\n",
      "\n",
      "taulist = linspace(0, 5, 250)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a   = tensor(destroy(N), identity(2), identity(2))\n",
      "sm1 = tensor(identity(N), destroy(2), identity(2))\n",
      "sp1 = sm1.dag()\n",
      "sm2 = tensor(identity(N), identity(2), destroy(2))\n",
      "sp2 = sm2.dag()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def solve(ek, e1, e2, gamma1, gamma2, kappa, n_th, E):\n",
      "    \n",
      "    eta1 = (1 - ek) * e1\n",
      "    eta2 = (1 - e1) * (1 - e2)\n",
      "    \n",
      "    H = 1j * E * (a - a.dag())\n",
      "    \n",
      "    L0 = liouvillian(H, [sqrt(kappa * (1 + n_th)) * a, sqrt(kappa * n_th) * a.dag(),\n",
      "                     sqrt(gamma1) * sm1, sqrt(gamma2) * sm2])\n",
      "    \n",
      "    L1 = - sqrt(2 * kappa * eta1 * gamma1) * \\\n",
      "            (spre(sp1 * a) - spre(a) * spost(sp1) + \n",
      "             spost(a.dag() * sm1) - spre(sm1) * spost(a.dag())) + \\\n",
      "         - sqrt(eta2 * gamma1 * gamma2) * \\\n",
      "            (spre(sp2 * sm1) - spre(sm1) * spost(sp2) + \n",
      "             spost(sp1 * sm2) - spre(sm2) * spost(sp1))\n",
      "    \n",
      "    L = L0 + L1\n",
      "    \n",
      "    rhoss = steadystate(L)\n",
      "    \n",
      "    G2_11 = correlation_4op_1t(L, rhoss, taulist, [], sp1, sp1, sm1, sm1)\n",
      "    g2_11 = G2_11 / (expect(sp1*sm1, rhoss) * expect(sp1*sm1, rhoss))\n",
      "\n",
      "    G2_22 = correlation_4op_1t(L, rhoss, taulist, [], sp2, sp2, sm2, sm2)\n",
      "    g2_22 = G2_22 / (expect(sp2*sm2, rhoss) * expect(sp2*sm2, rhoss))\n",
      "\n",
      "    G2_12 = correlation_4op_1t(L, rhoss, taulist, [], sp2, sp1, sm1, sm2)\n",
      "    g2_12 = G2_12 / (expect(sp1*sm1, rhoss) * expect(sp2*sm2, rhoss))\n",
      "    \n",
      "    G2_21 = correlation_4op_1t(L, rhoss, taulist, [], sp1, sp2, sm2, sm1)\n",
      "    g2_21 = G2_21 / (expect(sp2*sm2, rhoss) * expect(sp1*sm1, rhoss))\n",
      "    \n",
      "    return rhoss, g2_11, g2_12, g2_21, g2_22"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# thermal\n",
      "rhoss_t, g2_11_t, g2_12_t, g2_21_t, g2_22_t = solve(ek, e1, e2, gamma1, gamma2, \n",
      "                                                    kappa, n_th, 0.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# visualize the cavity state\n",
      "wigner_fock_distribution(rhoss_t.ptrace(0));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eAldjzNKqbIyZAcsyYM0mcBF1TegRZgZRFjNiIsyapvWYCOk59UA3uVk90swo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\niIuIiDiUQlxERMShFOIiIiIO9Q0MQBpSV33lFAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fafc6645f98>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(figsize=(8,4))\n",
      "\n",
      "ax.plot(taulist, g2_11_t, label=r'$g^{(2)}_{11}(\\tau)$')\n",
      "ax.plot(taulist, g2_22_t, label=r'$g^{(2)}_{22}(\\tau)$')\n",
      "ax.plot(taulist, g2_12_t, label=r'$g^{(2)}_{12}(\\tau)$')\n",
      "ax.plot(taulist, g2_21_t, label=r'$g^{(2)}_{21}(\\tau)$')\n",
      "\n",
      "ax.legend(loc=4)\n",
      "ax.set_xlabel(r'$\\tau$', fontsize=16);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QQ+9z54Kvr6lbI4zh/PXzfHrwUzac3cDYDmM5MOkAbR3bGvU9Cuo5fxIRwdG0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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fafc5ecbc50>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Similar to Fig. 12.8 in Quantum Noise, although not exactly because of different parameters."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Versions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip.ipynbtools import version_table; version_table()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>IPython</td><td>2.0.0</td></tr><tr><td>OS</td><td>posix [linux]</td></tr><tr><td>Numpy</td><td>1.8.1</td></tr><tr><td>Cython</td><td>0.20.1post0</td></tr><tr><td>QuTiP</td><td>3.0.0.dev-5a88aa8</td></tr><tr><td>SciPy</td><td>0.13.3</td></tr><tr><td>matplotlib</td><td>1.3.1</td></tr><tr><td>Python</td><td>3.4.1 (default, Jun  9 2014, 17:34:49) \n",
        "[GCC 4.8.3]</td></tr><tr><td colspan='2'>Thu Jun 26 14:13:04 2014 JST</td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<IPython.core.display.HTML at 0x7fafc67588d0>"
       ]
      }
     ],
     "prompt_number": 28
    }
   ],
   "metadata": {}
  }
 ]
}