{ "metadata": { "name": "Lecture-1-Jaynes-Cumming-model" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "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\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" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# setup the matplotlib graphics library and configure it to show \n", "# 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 *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction\n", "\n", "The Jaynes-Cumming 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 = 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", "figure(figsize=(8,5))\n", "plot(tlist, n_c, label=\"Cavity\")\n", "plot(tlist, n_a, label=\"Atom excited state\")\n", "legend()\n", "xlabel('Time')\n", "ylabel('Occupation probability')\n", "title('Vacuum Rabi oscillations')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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7lkqVKqkfM2nSJF6/fs306dN5/PgxFSpUICYmBlPT/9W70cZhCXGJcbj+4sqj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} ], "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 recalculte 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": [ { "output_type": "pyout", "prompt_number": 9, "text": [ "Odedata 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": [ { "output_type": "pyout", "prompt_number": 10, "text": [ "list" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "len(output.states)" ], "language": "python", "metadata": {}, "outputs": [ { "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": [ "\\begin{equation}\\text{Quantum object: dims = [[15, 2], [15, 2]], shape = [30, 30], type = oper, isHerm = True}\\\\[1em]\\begin{pmatrix}0.49605855334 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.000481112489832 & -0.0154966903108j & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0154966903108j & 0.50346033417 & 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{pmatrix}\\end{equation}" ], "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", " 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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: $t = \\\\{5, 15, 25\\\\}$ (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": [ { "output_type": "pyout", "prompt_number": 13, "text": [ "array([ 0., 5., 15., 25.])" ] } ], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "# get a list density matrices\n", "rho_list = array(output.states)[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 = linspace(-3,3,200)\n", "\n", "fig, axes = 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=get_cmap('RdBu'))\n", "\n", " axes[idx].set_title(r\"$t = %.1f$\" % tlist[t_idx][idx], fontsize=16)\n", " " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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W7sD6SWODhFRkD/Gb/HlxGfJajdffX3b49a+rhE+O70/tbgK+4Tmd+1PrtL3H7Mjy/Dlh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} ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "At $t =0$, the cavity is in it's 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 = array(output.states)[t_idx]\n", "\n", "fig_grid = (2, len(rho_list)*2)\n", "fig = 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 = subplot2grid(fig_grid, (0, 2*idx), colspan=2)\n", " ax.contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-.25,.25), cmap=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 stateLecture-1-Jaynes-Cumming-model\n", "Delete\n", "\n", "ax = 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": [ { "output_type": "pyout", "prompt_number": 16, "text": [ "" ] }, { "output_type": "display_data", "png": 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jUeo8t6Y483EdbQ2IXFN9zuv5/buizH1sjChbFrpWujgvVI13KENGnEROkS/G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\nd2odktkLuBhAxYUVqVygMge7HaRo9qJah2QQadPC2LFy9sbLC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} ], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }