Lecture-6-Quantum-Monte-Carlo-Trajectories.ipynb

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    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# QuTiP lecture: Quantum Monte-Carlo Trajectories"
     ]
    },
    {
     "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).\n",
      "\n",
      "The example in this lecture is based on an example by P.D. Nation."
     ]
    },
    {
     "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": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Introduction to the Quantum Monte-Carlo trajectory method\n",
      "\n",
      "The Quantum Monte-Carlo trajectory method is an equation of motion for a single realization of the state vector $\\left|\\psi(t)\\right>$ for a quantum system that interacts with its environment. The dynamics of the wave function is given by the Schrodinger equation,\n",
      "\n",
      "<center>\n",
      "$\\displaystyle\\frac{d}{dt}\\left|\\psi(t)\\right> = - \\frac{i}{\\hbar} H_{\\rm eff} \\left|\\psi(t)\\right>$\n",
      "</center>\n",
      "\n",
      "where the Hamiltonian is an effective Hamiltonian that, in addition to the system Hamiltonian $H(t)$, also contains a non-Hermitian contribution due to the interaction with the environment:\n",
      "\n",
      "<center>\n",
      "$\\displaystyle H_{\\rm eff}(t) = H(t) - \\frac{i\\hbar}{2}\\sum_n c_n^\\dagger c_n$\n",
      "</center>\n",
      "\n",
      "Since the effective Hamiltonian is non-Hermitian, the norm of the wavefunction is decreasing with time, which to first order in a small time step $\\delta t$ is given by $\\langle\\psi(t+\\delta t)|\\psi(t+\\delta t)\\rangle \\approx 1 - \\delta p\\;\\;\\;$, where \n",
      "\n",
      "<center>\n",
      "$\\displaystyle \\delta p = \\delta t \\sum_n \\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>$\n",
      "</center>\n",
      "\n",
      "The decreasing norm is used to determine when so-called quantum jumps are to be imposed on the dynamics, where we compare $\\delta p$ to a random number in the range [0, 1]. If the norm has decreased below the randomly chosen number, we apply a \"quantum jump\", so that the new wavefunction at $t+\\delta t$ is given by\n",
      "\n",
      "<center>\n",
      "$\\left|\\psi(t+\\delta t)\\right> = c_n \\left|\\psi(t)\\right>/\\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>^{1/2}$ \n",
      "</center>\n",
      "\n",
      "for a randomly chosen collapse operator $c_n$, weighted so the probability that the collapse being described by the nth collapse operator is given by\n",
      "    \n",
      "<center>\n",
      "$\\displaystyle P_n = \\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>/{\\delta p}$ \n",
      "</center>\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Decay of a single-photon Fock state in a cavity\n",
      "\n",
      "This is a Monte-Carlo simulation showing the decay of a cavity Fock state $\\left|1\\right>$ in a thermal environment with an average occupation number of $n=0.063$ .\n",
      "\n",
      "Here, the coupling strength is given by the inverse of the cavity ring-down time $T_c = 0.129$ .\n",
      "\n",
      "The parameters chosen here correspond to those from S. Gleyzes, et al., Nature 446, 297 (2007), and we will carry out a simulation that corresponds to these experimental results from that paper:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image\n",
      "Image(filename='images/exdecay.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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AANKsA6eDtRMsJgQBACBNAACANCFNAACkCWkCACDNhpGmTSWTZ1p9m90IaQIAglOaTnOa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\n/D94tChUqA+XLgAAAABJRU5ErkJggg==\n",
       "prompt_number": 4,
       "text": [
        "<IPython.core.display.Image at 0x7fadedd3a780>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem parameters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 4               # number of basis states to consider\n",
      "kappa = 1.0/0.129   # coupling to heat bath\n",
      "nth = 0.063         # temperature with <n>=0.063\n",
      "\n",
      "tlist = np.linspace(0,0.6,100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Create operators, Hamiltonian and initial state\n",
      "\n",
      "Here we create QuTiP `Qobj` representations of the operators and state that are involved in this problem."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = destroy(N)      # cavity destruction operator\n",
      "H = a.dag() * a     # harmonic oscillator Hamiltonian\n",
      "psi0 = basis(N,1)   # initial Fock state with one photon: |1>"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Create a list of collapse operators that describe the dissipation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# collapse operator list\n",
      "c_op_list = []\n",
      "\n",
      "# decay operator\n",
      "c_op_list.append(sqrt(kappa * (1 + nth)) * a)\n",
      "\n",
      "# excitation operator\n",
      "c_op_list.append(sqrt(kappa * nth) * a.dag())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Monte-Carlo simulation\n",
      "\n",
      "Here we start the Monte-Carlo simulation, and we request expectation values of photon number operators with 1, 5, 15, and 904 trajectories (compare with experimental results above)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ntraj = [1, 5, 15, 904] # list of number of trajectories to avg. over\n",
      "\n",
      "mc = mcsolve(H, psi0, tlist, c_op_list, [a.dag()*a], ntraj)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10.1%. Run time:   1.86s. Est. time left: 00:00:00:16\n",
        "20.0%. Run time:   3.07s. Est. time left: 00:00:00:12\n",
        "30.1%. Run time:   4.32s. Est. time left: 00:00:00:10\n",
        "40.0%. Run time:   5.55s. Est. time left: 00:00:00:08\n",
        "50.0%. Run time:   6.84s. Est. time left: 00:00:00:06\n",
        "60.1%. Run time:   8.18s. Est. time left: 00:00:00:05\n",
        "70.0%. Run time:   9.47s. Est. time left: 00:00:00:04\n",
        "80.1%. Run time:  10.70s. Est. time left: 00:00:00:02\n",
        "90.0%. Run time:  12.39s. Est. time left: 00:00:00:01\n",
        "100.0%. Run time:  14.25s. Est. time left: 00:00:00:00\n",
        "Total run time:  14.29s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The expectation values of $a^\\dagger a$ are now available in array ``mc.expect[idx][0]`` where ``idx`` takes values in ``[0,1,2,3]`` corresponding to the averages of ``1, 5, 15, 904`` Monte Carlo trajectories, as specified above. Below we plot the array ``mc.expect[idx][0]`` vs. ``tlist`` for each index ``idx``."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Lindblad master-equation simulation and steady state\n",
      "\n",
      "For comparison with the averages of single quantum trajectories provided by the Monte-Carlo solver we here also calculate the dynamics of the Lindblad master equation, which should agree with the Monte-Carlo simultions for infinite number of trajectories."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# run master equation to get ensemble average expectation values\n",
      "me = mesolve(H, psi0, tlist, c_op_list, [a.dag()*a])\n",
      "\n",
      "# calulate final state using steadystate solver\n",
      "final_state = steadystate(H, c_op_list) # find steady-state\n",
      "fexpt = expect(a.dag()*a, final_state)  # find expectation value for particle number"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Plot the results"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.font_manager\n",
      "leg_prop = matplotlib.font_manager.FontProperties(size=10)\n",
      "\n",
      "fig, axes = plt.subplots(4, 1, sharex=True, figsize=(8,12))\n",
      "\n",
      "fig.subplots_adjust(hspace=0.1) # reduce space between plots\n",
      "\n",
      "for idx, n in enumerate(ntraj):\n",
      "\n",
      "    axes[idx].step(tlist, mc.expect[idx][0], 'b', lw=2)\n",
      "    axes[idx].plot(tlist, me.expect[0], 'r--', lw=1.5)\n",
      "    axes[idx].axhline(y=fexpt, color='k', lw=1.5)\n",
      "    \n",
      "    axes[idx].set_yticks(np.linspace(0, 2, 5))\n",
      "    axes[idx].set_ylim([0, 1.5])\n",
      "    axes[idx].set_ylabel(r'$\\left<N\\right>$', fontsize=14)\n",
      "    \n",
      "    if idx == 0:\n",
      "        axes[idx].set_title(\"Ensemble Averaging of Monte Carlo Trajectories\")\n",
      "        axes[idx].legend(('Single trajectory', 'master equation', 'steady state'), prop=leg_prop)\n",
      "    else:\n",
      "        axes[idx].legend(('%d trajectories' % n, 'master equation', 'steady state'), prop=leg_prop)\n",
      "        \n",
      "\n",
      "axes[3].xaxis.set_major_locator(plt.MaxNLocator(4))\n",
      "axes[3].set_xlabel('Time (sec)',fontsize=14);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dOwcrKyuMHj262lPsFa+fE5HYX6D852VsbKzUca8u8DV5xhgzRNHR6h/Vta8D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sgbDFce/oaLjEwodnZKIiIiTuX2Rd5otH5toJRPGcPjKaPh/HnnJCUiIuIC3L7IJyWVjceXP0rN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\nXksoOfQig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       "text": [
        "<matplotlib.figure.Figure at 0x7fadec456ef0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 3,
     "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>3.0.0.dev-5a88aa8</td></tr><tr><td>Numpy</td><td>1.8.1</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>IPython</td><td>2.0.0</td></tr><tr><td>SciPy</td><td>0.13.3</td></tr><tr><td>matplotlib</td><td>1.3.1</td></tr><tr><td>Cython</td><td>0.20.1post0</td></tr><tr><td>OS</td><td>posix [linux]</td></tr><tr><td colspan='2'>Thu Jun 26 15:01:46 2014 JST</td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<IPython.core.display.HTML at 0x7fadec1e5d30>"
       ]
      }
     ],
     "prompt_number": 13
    }
   ],
   "metadata": {}
  }
 ]
}