{ "metadata": { "name": "", "signature": "sha256:c9c9896f112ba5b52f70936df3acb3b05a7facc5902008a21e822aae33ab4741" }, "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), 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 *\n", "\n", "from IPython.display import Image" ], "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, as illustrated in the figure below. If there atom excitation rate $\\Gamma$ 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." ] }, { "cell_type": "code", "collapsed": false, "input": [ "Image(filename='images/schematic-lasing-model.png')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "png": 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Qg65B6F6vl1mzZtG/P/7s7Ibs4E4Dk+9iZGVgZNac3jztNHZ8880iZyxmAhrEOaF7PB7m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\njAW6REi0tFB1441MamtLn0u87LJTptt12TJqm5p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"prompt_number": 3, "text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coherent dynamics in this model is described by the Hamiltonian\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", "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: \n", "\n", "1. $\\kappa$ relaxation and thermal excitations of the cavity, \n", "2. $\\Gamma$ atomic excitation rate (pumping process).\n", "\n", "The Lindblad master equation for the model is:\n", "\n", "$\\frac{d}{dt}\\rho = -i[H, \\rho] + \\Gamma\\left(\\sigma_+\\rho\\sigma_- - \\frac{1}{2}\\sigma_-\\sigma_+\\rho - \\frac{1}{2}\\rho\\sigma_-\\sigma_+\\right)\n", "+ \\kappa (1 + n_{\\rm th}) \\left(a\\rho a^\\dagger - \\frac{1}{2}a^\\dagger a\\rho - \\frac{1}{2}\\rho a^\\dagger a\\right)\n", "+ \\kappa n_{\\rm th} \\left(a^\\dagger\\rho a - \\frac{1}{2}a a^\\dagger \\rho - \\frac{1}{2}\\rho a a^\\dagger\\right)$\n", "\n", "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 = np.linspace(0, 150, 101)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "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": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "H" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "Quantum object: dims = [[50, 2], [50, 2]], shape = [100, 100], type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.314 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 6.283 & 0.314 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.314 & 6.283 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.314 & 0.0 & 0.0 & 12.566 & 0.444 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.444 & 12.566 & \\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 & 301.593 & 2.177 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 2.177 & 301.593 & 0.0 & 0.0 & 2.199\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 307.876 & 2.199 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 2.199 & 307.876 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 2.199 & 0.0 & 0.0 & 314.159\\\\\\end{array}\\right)\\end{equation*}" ], "metadata": {}, "output_type": "pyout", "prompt_number": 7, "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": 7 }, { "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": 8 }, { "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": 9 }, { "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 = plt.subplots(1, 1, figsize=(8,6))\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": [ { "metadata": {}, "output_type": "display_data", "png": 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Xr16hP3PixAlER0dDr9dDr9dj8ODBmDBhAubNmwcAGDFiBADg1VdfxebNm+Hm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\nzcRnAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 10 }, { "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": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 2, figsize=(12,6))\n", "\n", "xvec = np.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=plt.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": [ { "metadata": {}, "output_type": "display_data", "png": 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PEwSKffMEdXYt+rZ5dQtqr+1n4h6tKc846sFi2hzxPGUHm7rXec51agoj6XMd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\nNmWtTmgDeovHWJRVrRPenWDyU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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cavity fock-state distribution and Wigner function as a function of time" ] }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = np.linspace(0, 25, 5)\n", "output = mesolve(H, psi0, tlist, c_ops, [], options=Odeoptions(nsteps=5000))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "rho_ss_sublist = output.states\n", "\n", "xvec = np.linspace(-5,5,200)\n", "\n", "fig, axes = plt.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=plt.get_cmap('RdBu'))\n", " axes[0,idx].set_title(r'$t = %.1f$' % tlist[idx])\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": [ { "metadata": {}, "output_type": "display_data", "png": 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2Y/sqaES8upqAu0javgnauhb6bbdrw7Emu/skZ30ViSYpo11gr4w1CBnt+obm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\nvb19xDJXXHGFjh49Kkk6evSoLrvssnMCD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"text": [ "" ] } ], "prompt_number": 15 }, { "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", " # cavity photon number\n", " n_cavity = expect(a.dag() * a, rho_ss)\n", " \n", " # cavity second order coherence function\n", " g2_cavity = expect(a.dag() * a.dag() * a * a, rho_ss) / (n_cavity ** 2)\n", "\n", " return n_cavity, g2_cavity" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "Gamma_max = 2 * (4*g**2) / kappa\n", "Gamma_vec = np.linspace(0.1, Gamma_max, 50)\n", "\n", "n_avg_vec = []\n", "g2_vec = []\n", "\n", "for Gamma in Gamma_vec:\n", " n_avg, g2 = calulcate_avg_photons(N, Gamma)\n", " n_avg_vec.append(n_avg)\n", " g2_vec.append(g2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.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.set_xlim(0, 2);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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UlCoFrVvDwoXQq5ftNCIiIvldOLg7atQot97H0RaFx48fZ+fOncTGxhIZGQnA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\nZGSosbHR22ECbjFvwlcxb8IXtLS0qKGhQampqS7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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 1, figsize=(12,6))\n", "\n", "axes.plot(Gamma_vec * kappa / (4*g**2), g2_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'$g^{(2)}(0)$', fontsize=18)\n", "axes.set_xlim(0, 2)\n", "axes.text(0.1, 1.1, \"Lasing regime\", fontsize=16)\n", "axes.text(1.5, 1.8, \"Thermal regime\", fontsize=16);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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T9e6775bq/aVBKAfg6L791hwCMSrK6koAADej3EK5MyKUA3BkSUnSW29Jr70m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\nAQAAyBUXF6e4uLib3o9Dj74iSQkJCer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EREREUcamnIiIiIgoytiUExERERFFGZtyIiIi\nIqIo+wdhfz7Nsc2PAgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 19 }, { "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": 20 }, { "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": 21 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 2, figsize=(16,6))\n", "\n", "xvec = np.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=plt.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_xlabel(r'$n$', fontsize=18)\n", "axes[0].set_ylabel(r'Occupation probability', fontsize=18)\n", "axes[0].set_ylim(0, 1)\n", "axes[0].set_xlim(0, N);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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CV10nHV/5PEHgV6XO04pePchKD7FSA6wiv97Lq4dX2YKr2kKrGFi1dWHqMiGEEDIj/Lsy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UCojcfV9San86WHnm91dZsEU2WlkGkwVa4fMO0R5LEKxJGjT+JILtLlYj3CXKS5U+niXol7eSsX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\n5cuXO3fccYevzbXXXuusXLmytnzCCSc4+/btCx1r+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"text": [ "" ] } ], "prompt_number": 22 }, { "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": 23 }, { "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": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 2, figsize=(16,6))\n", "\n", "xvec = np.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=plt.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_xlabel(r'$n$', fontsize=18)\n", "axes[0].set_ylabel(r'Occupation probability', fontsize=18)\n", "axes[0].set_ylim(0, 1)\n", "axes[0].set_xlim(0, N);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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+VzpH0B3Zsqy3TTo2azW3Wcj1z9VKyN1ecdoKuH649V83WuH1voZDbitTl2th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\n6H7lK1/RwQcfrG3btmnMmDFatGiRnnvuOd1+++0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"text": [ "" ] } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Too large pumping rate $\\Gamma$ kills the lasing process: reversed threshold." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Software version" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
SoftwareVersion
IPython2.0.0
OSposix [linux]
Python3.4.1 (default, Jun 9 2014, 17:34:49) \n", "[GCC 4.8.3]
QuTiP3.0.0.dev-5a88aa8
Numpy1.8.1
matplotlib1.3.1
Cython0.20.1post0
SciPy0.13.3
Thu Jun 26 14:28:35 2014 JST
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 27, "text": [ "" ] } ], "prompt_number": 27 } ], "metadata": {} } ] }