{ "metadata": { "name": "Lecture-Quantum-Monte-Carlo-Trajectories" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP lecture: Quantum Monte-Carlo Trajectories" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Author: J.R. Johansson, robert@riken.jp\n", "\n", "http://dml.riken.jp/~rob/\n", "\n", "Latest version of this ipython notebook lecture is available at: http://github.com/jrjohansson/qutip-lectures\n", "\n", "The example in this lecture is based on an example by P.D. Nation." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# setup the matplotlib graphics library and configure it to show figures inline in the notebook\n", "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", "For more information, type 'help(pylab)'.\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# make qutip available in the rest of the notebook\n", "from qutip import *\n", "\n", "#qutip.settings.qutip_graphics=False\n", "#qutip.settings.qutip_gui=False" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "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", "
\n", "$\\frac{d}{dt}\\left|\\psi(t)\\right> = - \\frac{i}{\\hbar} H_{\\rm eff} \\left|\\psi(t)\\right>$\n", "
\n", "\n", "where the Hamiltonian is an effective Hamiltonian that, in addition to the system Hamiltonian $H(t)$, alos contains a non-Hermitian contribution due to the interaction with the environment:\n", "\n", "
\n", "$H_{\\rm eff}(t) = H(t) - \\frac{i\\hbar}{2}\\sum_n c_n^\\dagger c_n$\n", "
\n", "\n", "... incomplete ...\n", "\n", "$\\delta p = \\delta t \\sum_n \\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>$\n", "\n", "$\\left|\\psi(t+\\delta t)\\right> = c_n \\left|\\psi(t)\\right>/\\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>^{1/2}$ " ] }, { "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:\n", "\n", "" ] }, { "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 =0.063\n", "\n", "tlist = linspace(0,0.6,100)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "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": 4 }, { "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": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Run 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)\n", "\n", "# get expectation values from mc data (need extra index since ntraj is list)\n", "ex1 = mc.expect[0][0] # for ntraj=1\n", "ex5 = mc.expect[1][0] # for ntraj=5\n", "ex15 = mc.expect[2][0] # for ntraj=15\n", "ex904 = mc.expect[3][0] # for ntraj=904" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "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": 32 }, { "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 = 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].plot(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(linspace(0, 2, 5))\n", " axes[idx].set_ylim([0, 1.5])\n", " axes[idx].set_ylabel(r'$\\left$', 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(MaxNLocator(4))\n", "axes[3].set_xlabel('Time (sec)',fontsize=14)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 36, "text": [ "" ] }, { "output_type": "display_data", "png": 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joVKpUFBQgMOHD+tsPVtbW+PTTz/FO++8g507dyIvLw9FRUWIiYnBRx99BEA4KyWVSmFp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zExMbalWw3DMFasWGE8+uijhmEYRm5urtGnTx9jw4YNRnR0tOHi4mL8/PPPdnFdaZnZ4OBgY+PG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\n/JdzceGPtg/yTuhMD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} ], "prompt_number": 36 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 } ], "metadata": {} } ] }