{ "metadata": { "name": "Lecture-2B-Single-Atom-Lasing" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP lecture: Single-Atom-Lasing" ] }, { "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 and model\n", "\n", "Consider a single atom coupled to a single cavity mode. If there atom excitation rate exceeds the relaxation rate, a population inversion can occur in the atom, and if coupled to the cavity the atom can then act as a photon pump on the cavity.\n", "\n", "
\n", "\n", "The coherent dynamics in this model is described by the Hamiltonian\n", "\n", "
\n", "$H = \\hbar \\omega_0 a^\\dagger a + \\frac{1}{2}\\hbar\\omega_a\\sigma_z + \\hbar g\\sigma_x(a^\\dagger + a)$\n", "
\n", " \n", "where $\\omega_0$ is the cavity energy splitting, $\\omega_a$ is the atom energy splitting and $g$ is the atom-cavity interaction strength.\n", "\n", "In addition to the coherent dynamics the following incoherent processes are also present: 1) $\\kappa$ relaxation and thermal excitations of the cavity, $\\Gamma$ atomic excitation rate (pumping process).\n", "\n", "The Lindblad master equation for the model is:\n", "\n", "
\n", "$\\frac{d}{dt}\\rho = -i[H, \\rho] + \\Gamma\\left(\\sigma_+\\rho\\sigma_- - \\frac{1}{2}\\sigma_-\\sigma_+\\rho - \\frac{1}{2}\\rho\\sigma_-\\sigma_+\\right)$\n", "\n", "$+ \\kappa (1 + n_{\\rm th}) \\left(a\\rho a^\\dagger - \\frac{1}{2}a^\\dagger a\\rho - \\frac{1}{2}\\rho a^\\dagger a\\right)$\n", "\n", "$+ \\kappa n_{\\rm th} \\left(a^\\dagger\\rho a - \\frac{1}{2}a a^\\dagger \\rho - \\frac{1}{2}\\rho a a^\\dagger\\right)$\n", "
\n", "\n", "\n", "in units where $\\hbar = 1$.\n", "\n", "References:\n", "\n", " * [Yi Mu, C.M. Savage, Phys. Rev. A 46, 5944 (1992)](http://dx.doi.org/10.1103/PhysRevA.46.5944)\n", "\n", " * [D.A. Rodrigues, J. Imbers, A.D. Armour, Phys. Rev. Lett. 98, 067204 (2007)](http://dx.doi.org/10.1103/PhysRevLett.98.067204)\n", "\n", " * [S. Ashhab, J.R. Johansson, A.M. Zagoskin, F. Nori, New J. Phys. 11, 023030 (2009)](http://dx.doi.org/10.1088/1367-2630/11/2/023030)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem parameters" ] }, { "cell_type": "code", "collapsed": false, "input": [ "w0 = 1.0 * 2 * pi # cavity frequency\n", "wa = 1.0 * 2 * pi # atom frequency\n", "g = 0.05 * 2 * pi # coupling strength\n", "\n", "kappa = 0.04 # cavity dissipation rate\n", "gamma = 0.00 # atom dissipation rate\n", "Gamma = 0.35 # atom pump rate\n", "\n", "N = 50 # number of cavity fock states\n", "n_th_a = 0.0 # avg number of thermal bath excitation\n", "\n", "tlist = linspace(0, 150, 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(2,0)) # start without excitations\n", "\n", "# operators\n", "a = tensor(destroy(N), qeye(2))\n", "sm = tensor(qeye(N), destroy(2))\n", "sx = tensor(qeye(N), sigmax())\n", "\n", "# Hamiltonian\n", "H = w0 * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * sx" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "H" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "\\begin{equation}\\text{Quantum object: dims = [[50, 2], [50, 2]], shape = [100, 100], type = oper, isHerm = True}\\\\[1em]\\begin{pmatrix}0.0 & 0.0 & 0.0 & 0.314159265359 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 6.28318530718 & 0.314159265359 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.314159265359 & 6.28318530718 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.314159265359 & 0.0 & 0.0 & 12.5663706144 & 0.444288293816 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.444288293816 & 12.5663706144 & \\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 & 301.592894745 & 2.17655923708 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 2.17655923708 & 301.592894745 & 0.0 & 0.0 & 2.19911485751\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 307.876080052 & 2.19911485751 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 2.19911485751 & 307.876080052 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 2.19911485751 & 0.0 & 0.0 & 314.159265359\\\\\\end{pmatrix}\\end{equation}" ], "output_type": "pyout", "prompt_number": 5, "text": [ "Quantum object: dims = [[50, 2], [50, 2]], shape = [100, 100], type = oper, isherm = True\n", "Qobj data =\n", "[[ 0. 0. 0. ..., 0. 0. 0. ]\n", " [ 0. 6.28318531 0.31415927 ..., 0. 0. 0. ]\n", " [ 0. 0.31415927 6.28318531 ..., 0. 0. 0. ]\n", " ..., \n", " [ 0. 0. 0. ..., 307.87608005\n", " 2.19911486 0. ]\n", " [ 0. 0. 0. ..., 2.19911486\n", " 307.87608005 0. ]\n", " [ 0. 0. 0. ..., 0. 0.\n", " 314.15926536]]" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Create a list of collapse operators that describe the dissipation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# collapse operators\n", "c_ops = []\n", "\n", "rate = kappa * (1 + n_th_a)\n", "if rate > 0.0:\n", " c_ops.append(sqrt(rate) * a)\n", "\n", "rate = kappa * n_th_a\n", "if rate > 0.0:\n", " c_ops.append(sqrt(rate) * a.dag())\n", "\n", "rate = gamma\n", "if rate > 0.0:\n", " c_ops.append(sqrt(rate) * sm)\n", "\n", "rate = Gamma\n", "if rate > 0.0:\n", " c_ops.append(sqrt(rate) * sm.dag())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "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": [ "opt = Odeoptions(nsteps=2000) # allow extra time-steps \n", "output = mesolve(H, psi0, tlist, c_ops, [a.dag() * a, sm.dag() * sm], options=opt)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "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)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "n_c = output.expect[0]\n", "n_a = output.expect[1]\n", "\n", "fig, axes = subplots(1, 1, sharex=True, figsize=(12,8))\n", "\n", "axes.plot(tlist, n_c, label=\"Cavity\")\n", "axes.plot(tlist, n_a, label=\"Atom excited state\")\n", "axes.set_xlim(0, 150)\n", "axes.legend(loc=0)\n", "axes.set_xlabel('Time')\n", "axes.set_ylabel('Occupation probability')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "output_type": "display_data", "png": 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C7vPP4dpr4cwzg/uuiiFJUsFzpFkqpPbvhwcfhPbtg6XkJkywMEuSFBZHmqVC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\nw04jSZKUP3Lqnbluoz1u3Dh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klVyONBdiL70UTM2wMEuSJBVeUS3NN954I9WrV6dhw4ZZ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\nhGYAAACgFf8P0vhuu4AJhl8AAAAASUVORK5CYII=\n" } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Steady state: cavity fock-state distribution and wigner function" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rho_ss = steadystate(H, c_ops)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 2, figsize=(16,6))\n", "\n", "xvec = linspace(-5,5,200)\n", "\n", "rho_cavity = ptrace(rho_ss, 0)\n", "W = wigner(rho_cavity, xvec, xvec)\n", "wlim = abs(W).max()\n", "\n", "axes[1].contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-wlim,wlim), cmap=get_cmap('RdBu'))\n", "axes[1].set_xlabel(r'Im $\\alpha$', fontsize=18)\n", "axes[1].set_ylabel(r'Re $\\alpha$', fontsize=18)\n", "\n", "axes[0].bar(arange(0, N), real(rho_cavity.diag()), color=\"blue\", alpha=0.6)\n", "axes[0].set_ylim(0, 1)\n", "axes[0].set_xlim(0, N)\n", "axes[0].set_xlabel('Fock number', fontsize=18)\n", "axes[0].set_ylabel('Occupation probability', fontsize=18)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 10, "text": [ "" ] }, { "output_type": "display_data", "png": 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Fte5YHfCLByGEkDrh50p1plVoF4rMFmn+NC1R2SoiWzQa6yKxFNjmKCu3LmIr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\nRESS9D+QwTCbDhHEgQAAAABJRU5ErkJggg==\n" } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cavity fock-state distribution and Wigner function as a function of time" ] }, { "cell_type": "code", "collapsed": false, "input": [ "opt = Odeoptions(nsteps=5000) # allow extra time-steps \n", "output = mesolve(H, psi0, linspace(0, 25, 5), c_ops, [], options=opt)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "rho_ss_sublist = output.states\n", "\n", "xvec = linspace(-5,5,200)\n", "\n", "fig, axes = subplots(2, len(rho_ss_sublist), figsize=(3*len(rho_ss_sublist), 6))\n", "\n", "for idx, rho_ss in enumerate(rho_ss_sublist):\n", "\n", " # trace out the cavity density matrix\n", " rho_ss_cavity = ptrace(rho_ss, 0)\n", " \n", " # calculate its wigner function\n", " W = wigner(rho_ss_cavity, xvec, xvec)\n", " \n", " # plot its wigner function\n", " wlim = abs(W).max()\n", " axes[0,idx].contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-wlim,wlim), cmap=get_cmap('RdBu'))\n", "\n", " # plot its fock-state distribution\n", " axes[1,idx].bar(arange(0, N), real(rho_ss_cavity.diag()), color=\"blue\", alpha=0.8)\n", " axes[1,idx].set_ylim(0, 1)\n", " axes[1,idx].set_xlim(0, 15)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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IxZsHQ8YfMeLbMy4CWTOqAZeZI4NcgNclZL50z10sYXQBowxkJmBMqy4HxWyV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\nMGZfmg9/+MP43ve+d5TjfOtb3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UuXBuKdl7xq1pj8dEuzM1uPZmcmyOfaoDRr\njLfd0izNukGz/iuEx7ReNmtMcB4f2NJsyJgAPHEXAAAAAApYXp/KCAAAAACYHoMZAAAAAPiMwQwA\nAAAAfMZgBgAAAAA+YzADAAAAAJ8xmAEAAACAzxjMAAAAAMBn/wtOIFIlzjfvKgAAAABJRU5ErkJg\ngg==\n" } ], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Steady state average photon occupation in cavity as a function of pump rate\n", "\n", "References:\n", "\n", " * [S. Ashhab, J.R. Johansson, A.M. Zagoskin, F. Nori, New J. Phys. 11, 023030 (2009)](http://dx.doi.org/10.1088/1367-2630/11/2/023030)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def calulcate_avg_photons(N, Gamma):\n", " \n", " # collapse operators\n", " c_ops = []\n", "\n", " rate = kappa * (1 + n_th_a)\n", " if rate > 0.0:\n", " c_ops.append(sqrt(rate) * a)\n", "\n", " rate = kappa * n_th_a\n", " if rate > 0.0:\n", " c_ops.append(sqrt(rate) * a.dag())\n", "\n", " rate = gamma\n", " if rate > 0.0:\n", " c_ops.append(sqrt(rate) * sm)\n", "\n", " rate = Gamma\n", " if rate > 0.0:\n", " c_ops.append(sqrt(rate) * sm.dag())\n", " \n", " # Ground state and steady state for the Hamiltonian: H = H0 + g * H1\n", " rho_ss = steadystate(H, c_ops)\n", " \n", " n_cavity = expect(a.dag() * a, rho_ss)\n", "\n", " return n_cavity" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "Gamma_max = 2 * (4*g**2) / kappa\n", "Gamma_vec = linspace(0.0, Gamma_max, 50)\n", "\n", "n_avg_vec = [calulcate_avg_photons(N, Gamma) for Gamma in Gamma_vec]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 1, figsize=(12,6))\n", "\n", "axes.plot(Gamma_vec * kappa / (4*g**2), n_avg_vec, color=\"blue\", alpha=0.6, label=\"numerical\")\n", "\n", "axes.set_xlabel(r'$\\Gamma\\kappa/(4g^2)$', fontsize=18)\n", "axes.set_ylabel(r'Occupation probability $\\langle n \\rangle$', fontsize=18)\n", "axes.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 15, "text": [ "" ] }, { "output_type": "display_data", "png": 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FD7BixQqWL1/O4cOHyc3Nvez60KFDnX0Jv7VhAzRsaDqF+IMbbwSHA1JToVYt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\nAB70fyVhi9ND3V5sAAAAAElFTkSuQmCC\n" } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we see that lasing is suppressed for $\\Gamma\\kappa/(4g^2) > 1$. \n", "\n", "\n", "Let's look at the fock-state distribution at $\\Gamma\\kappa/(4g^2) = 0.5$ (lasing regime) and $\\Gamma\\kappa/(4g^2) = 1.5$ (suppressed regime):" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Case 1: $\\Gamma\\kappa/(4g^2) = 0.5$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Gamma = 0.5 * (4*g**2) / kappa" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "c_ops = [sqrt(kappa * (1 + n_th_a)) * a, sqrt(kappa * n_th_a) * a.dag(), sqrt(gamma) * sm, sqrt(Gamma) * sm.dag()]\n", "\n", "rho_ss = steadystate(H, c_ops)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 2, figsize=(16,6))\n", "\n", "xvec = linspace(-10,10,200)\n", "\n", "rho_cavity = ptrace(rho_ss, 0)\n", "W = wigner(rho_cavity, xvec, xvec)\n", "wlim = abs(W).max()\n", "axes[1].contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-wlim,wlim), cmap=get_cmap('RdBu'))\n", "\n", "axes[0].bar(arange(0, N), real(rho_cavity.diag()), color=\"blue\", alpha=0.6)\n", "axes[0].set_ylim(0, 1)\n", "axes[0].set_xlim(0, N)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 18, "text": [ "(0, 50)" ] }, { "output_type": "display_data", "png": 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irl27NrjPP/7jP+JDH/oQAOBbv/Vb8eY3vxlf/vKX8eCDD+7g6RJCCCGEzGdJ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\nrkJggg==\n" } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Case 2: $\\Gamma\\kappa/(4g^2) = 1.5$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Gamma = 1.5 * (4*g**2) / kappa" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "c_ops = [sqrt(kappa * (1 + n_th_a)) * a, sqrt(kappa * n_th_a) * a.dag(), sqrt(gamma) * sm, sqrt(Gamma) * sm.dag()]\n", "\n", "rho_ss = steadystate(H, c_ops)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 2, figsize=(16,6))\n", "\n", "xvec = linspace(-10,10,200)\n", "\n", "rho_cavity = ptrace(rho_ss, 0)\n", "W = wigner(rho_cavity, xvec, xvec)\n", "wlim = abs(W).max()\n", "axes[1].contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-wlim,wlim), cmap=get_cmap('RdBu'))\n", "\n", "axes[0].bar(arange(0, N), real(rho_cavity.diag()), color=\"blue\", alpha=0.6)\n", "axes[0].set_ylim(0, 1)\n", "axes[0].set_xlim(0, N)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 21, "text": [ "(0, 50)" ] }, { "output_type": "display_data", "png": 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YKK0uRtpfw85eu/41Vj15tiVTY65Ug7g3PeXI9bzY/FHzPTHVUbO6brI6alp0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\nowAAAACAviOMAgAAAAD67v8DQXIvRAT19fQAAAAASUVORK5CYII=\n" } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Too large pumping rate $\\Gamma$ kills the lasing process: reversed threshold." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 } ], "metadata": {} } ] }