Lecture-1-Jaynes-Cumming-model.ipynb

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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# QuTiP lecture: Vacuum Rabi oscillations in the Jaynes-Cummings model"
     ]
    },
    {
     "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": [
      "# setup the matplotlib graphics library and configure it to show \n",
      "# figures inline in the notebook\n",
      "%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": [
      "# make qutip available in the rest of the notebook\n",
      "from qutip import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Introduction\n",
      "\n",
      "The Jaynes-Cummings model is the simplest possible model of quantum mechanical light-matter interaction, describing a single two-level atom interacting with a single electromagnetic cavity mode. The Hamiltonian for this system is (in dipole interaction form)\n",
      "\n",
      "### $H = \\hbar \\omega_c a^\\dagger a + \\frac{1}{2}\\hbar\\omega_a\\sigma_z + \\hbar g(a^\\dagger + a)(\\sigma_- + \\sigma_+)$\n",
      "\n",
      "or with the rotating-wave approximation\n",
      "\n",
      "### $H_{\\rm RWA} = \\hbar \\omega_c a^\\dagger a + \\frac{1}{2}\\hbar\\omega_a\\sigma_z + \\hbar g(a^\\dagger\\sigma_- + a\\sigma_+)$\n",
      "\n",
      "where $\\omega_c$ and $\\omega_a$ are the frequencies of the cavity and atom, respectively, and $g$ is the interaction strength."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem parameters\n",
      "\n",
      "\n",
      "Here we use units where $\\hbar = 1$: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wc = 1.0  * 2 * pi  # cavity frequency\n",
      "wa = 1.0  * 2 * pi  # atom frequency\n",
      "g  = 0.05 * 2 * pi  # coupling strength\n",
      "kappa = 0.005       # cavity dissipation rate\n",
      "gamma = 0.05        # atom dissipation rate\n",
      "N = 15              # number of cavity fock states\n",
      "n_th_a = 0.0        # avg number of thermal bath excitation\n",
      "use_rwa = True\n",
      "\n",
      "tlist = np.linspace(0,25,101)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Setup the operators, the Hamiltonian and initial state"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# intial state\n",
      "psi0 = tensor(basis(N,0), basis(2,1))    # start with an excited atom\n",
      "\n",
      "# operators\n",
      "a  = tensor(destroy(N), qeye(2))\n",
      "sm = tensor(qeye(N), destroy(2))\n",
      "\n",
      "# Hamiltonian\n",
      "if use_rwa:\n",
      "    H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())\n",
      "else:\n",
      "    H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * (sm + sm.dag())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Create a list of collapse operators that describe the dissipation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c_ops = []\n",
      "\n",
      "# cavity relaxation\n",
      "rate = kappa * (1 + n_th_a)\n",
      "if rate > 0.0:\n",
      "    c_ops.append(sqrt(rate) * a)\n",
      "\n",
      "# cavity excitation, if temperature > 0\n",
      "rate = kappa * n_th_a\n",
      "if rate > 0.0:\n",
      "    c_ops.append(sqrt(rate) * a.dag())\n",
      "\n",
      "# qubit relaxation\n",
      "rate = gamma\n",
      "if rate > 0.0:\n",
      "    c_ops.append(sqrt(rate) * sm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Evolve the system\n",
      "\n",
      "Here we evolve the system with the Lindblad master equation solver, and we request that the expectation values of the operators $a^\\dagger a$ and $\\sigma_+\\sigma_-$ are returned by the solver by passing the list `[a.dag()*a, sm.dag()*sm]` as the fifth argument to the solver."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "output = mesolve(H, psi0, tlist, c_ops, [a.dag() * a, sm.dag() * sm])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Visualize the results\n",
      "\n",
      "Here we plot the excitation probabilities of the cavity and the atom (these expectation values were calculated by the `mesolve` above). We can clearly see how energy is being coherently transferred back and forth between the cavity and the atom."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_c = output.expect[0]\n",
      "n_a = output.expect[1]\n",
      "\n",
      "fig, axes = plt.subplots(1, 1, figsize=(10,6))\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')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
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        "<matplotlib.text.Text at 0x105439390>"
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      {
       "metadata": {},
       "output_type": "display_data",
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Mjkx8PzCllFJKpV/btm2ZPHmyy44XEBDA/v37XXY8b+b3xRhA10pddXskpZRSXiE8PJw8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\nb+lVtZfdMdyqYM6C1C9Wnx9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fzPMKF4aCBWGT6/Z4v2n+n/NpV7YdAeLDGxPaJEfmHDQu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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1053f7978>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Cavity wigner function\n",
      "\n",
      "In addition to the cavity's and atom's excitation probabilities, we may also be interested in for example the wigner function as a function of time. The Wigner function can give some valuable insight in the nature of the state of the resonators. \n",
      "\n",
      "To calculate the Wigner function in QuTiP, we first recalculate the evolution without specifying any expectation value operators, which will result in that the solver return a list of density matrices for the system for the given time coordinates."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "output = mesolve(H, psi0, tlist, c_ops, [])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, `output.states` contains a list of density matrices for the system for the time points specified in the list `tlist`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "output"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "Result object with mesolve data.\n",
        "--------------------------------\n",
        "states = True\n",
        "num_collapse = 0"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "type(output.states)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "list"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(output.states)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "101"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "output.states[-1] # indexing the list with -1 results in the last element in the list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "Quantum object: dims = [[15, 2], [15, 2]], shape = [30, 30], type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.496 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 4.811\\times10^{-04} & -0.015j & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.015j & 0.503 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\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 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "Quantum object: dims = [[15, 2], [15, 2]], shape = [30, 30], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[  4.96058553e-01+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j        ]\n",
        " [  0.00000000e+00+0.j           4.81112490e-04+0.j\n",
        "    0.00000000e+00-0.01549669j   0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j        ]\n",
        " [  0.00000000e+00+0.j           0.00000000e+00+0.01549669j\n",
        "    5.03460334e-01+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j        ]\n",
        " [  0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
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        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j        ]\n",
        " [  0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j        ]\n",
        " [  0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j        ]\n",
        " [  0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j        ]\n",
        " [  0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j        ]\n",
        " [  0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j        ]\n",
        " [  0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j\n",
        "    0.00000000e+00+0.j           0.00000000e+00+0.j           0.00000000e+00+0.j        ]]"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's look at the Wigner functions at the point in time when atom is in its ground state: $t = \\{0, 5, 15, 25\\}$ (see the plot above). \n",
      "\n",
      "For each of these points in time we need to:\n",
      "\n",
      " 1. Find the system density matrix for the points in time that we are interested in.\n",
      " 2. Trace out the atom and obtain the reduced density matrix for the cavity.\n",
      " 3. Calculate and visualize the Wigner function fo the reduced cavity density matrix."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# find the indices of the density matrices for the times we are interested in\n",
      "t_idx = where([tlist == t for t in [0.0, 5.0, 15.0, 25.0]])[1]\n",
      "tlist[t_idx]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "array([  0.,   5.,  15.,  25.])"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# get a list of density matrices\n",
      "rho_list = np.array(output.states, dtype=object)[t_idx]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# loop over the list of density matrices\n",
      "\n",
      "xvec = np.linspace(-3,3,200)\n",
      "\n",
      "fig, axes = plt.subplots(1,len(rho_list), sharex=True, figsize=(3*len(rho_list),3))\n",
      "\n",
      "for idx, rho in enumerate(rho_list):\n",
      "\n",
      "    # trace out the atom from the density matrix, to obtain\n",
      "    # the reduced density matrix for the cavity\n",
      "    rho_cavity = ptrace(rho, 0)\n",
      "    \n",
      "    # calculate its wigner function\n",
      "    W = wigner(rho_cavity, xvec, xvec)\n",
      "    \n",
      "    # plot its wigner function\n",
      "    axes[idx].contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-.25,.25), cmap=plt.get_cmap('RdBu'))\n",
      "\n",
      "    axes[idx].set_title(r\"$t = %.1f$\" % tlist[t_idx][idx], fontsize=16)\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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g7AG41RqtGY9B1Mr9QcSD4AZRCP9LNRd/KHU/VK6Dloo7ANM53yXgu+30qNtL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nPPkvm1Jy5wba1921rb9W+/CuAPrtz+t6y1v7ZmmwD+FIDvWGv/u7X2AcC/ghsIsJqstV8B8Dtr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\nOefqowAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105713898>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "At $t =0$, the cavity is in its ground state. At $t = 5, 15, 25$ it reaches it's maxium occupation in this Rabi-vacuum oscillation process. We can note that for $t=5$ and $t=15$ the Wigner function has negative values, indicating a truely quantum mechanical state. At $t=25$, however, the wigner function no longer has negative values and can therefore be considered a classical state."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Alternative view of the same thing"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t_idx = where([tlist == t for t in [0.0, 5.0, 10, 15, 20, 25]])[1]\n",
      "rho_list = np.array(output.states, dtype=object)[t_idx]\n",
      "\n",
      "fig_grid = (2, len(rho_list)*2)\n",
      "fig = plt.figure(figsize=(2.5*len(rho_list),5))\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');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/xUgSaRgVZ/R7Rpl6IUS4Zrv2m50qGHSwMBNC/GkAvwvA1621f8/hp7Q/ju0o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uwpXbp0kdNOO03Wrl0b68/1118v3bp1k0022UQmTJggxhj56quvfPs+ceJE6dOnj7Rr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\ny/VfsqzpMkpmKml1OE5r4R8L6fZ7N0ZUG0GbQvZ35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       "text": [
        "<matplotlib.figure.Figure at 0x106ddc160>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "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>QuTiP</td><td>3.0.1</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td>Cython</td><td>0.21</td></tr><tr><td>IPython</td><td>2.2.0</td></tr><tr><td>matplotlib</td><td>1.4.0</td></tr><tr><td>Python</td><td>3.4.1 (default, Sep 20 2014, 19:44:17) \n",
        "[GCC 4.2.1 Compatible Apple LLVM 5.1 (clang-503.0.40)]</td></tr><tr><td>Numpy</td><td>1.9.0</td></tr><tr><td>SciPy</td><td>0.14.0</td></tr><tr><td colspan='2'>Tue Sep 23 10:22:48 2014 JST</td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<IPython.core.display.HTML at 0x10ecbf208>"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}