{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Reproduce: Schmidt et al., Phys. Rev. B 82, 100507(R) (2010)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "J.R. Johansson, robert@riken.jp, http://dml.riken.jp/~rob/" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction\n", "\n", "This notebook reproduces some of the results in [S. Schmidt et al., Phys. Rev. B 82, 100507(R) (2010)](http://dx.doi.org/10.1103/PhysRevB.82.100507) using QuTiP." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem parameters\n", "\n", "\n", "Here we use units where $\\hbar = 1$: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 21 # number of cavity fock states\n", "nn = N-1\n", "\n", "wc = ones(2) * 1.00 * 2 * pi # cavity frequency\n", "wa = ones(2) * 1.00 * 2 * pi # atom frequency\n", "J = 0.01 * 2 * pi # coupling strength: cavity-cavity\n", "\n", "# localization threshold is 2.8 * sqrt(nn) * J\n", "gc = 2.8 * sqrt(nn) * J\n", "\n", "g = ones(2) * gc * 2.0 # coupling strength: atom-cavity\n", "kappa = ones(2) * 0.01 * J/(2*pi) # cavity dissipation rate\n", "gamma = ones(2) * 0.01 * J/(2*pi) # atom dissipation rate\n", "\n", "n_th = 0.0 # avg number of thermal bath excitation\n", "\n", "T = 10 / (J/(2*pi))\n", "tlist = linspace(0, T, 1001)" ], "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": [ "# start with a fock state witn nn photons in cavity #1\n", "psi0 = tensor(basis(N,nn), basis(2,0), basis(N,0), basis(2,0))\n", "#psi0 = tensor(coherent(N,sqrt(nn)), basis(2,0), basis(N,0), basis(2,0))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "# cavity annihilation operator\n", "C = [tensor(destroy(N), qeye(2), qeye(N), qeye(2)), tensor(qeye(N), qeye(2), destroy(N), qeye(2))]\n", "\n", "# atomic annihilation operator\n", "A = [tensor(qeye(N), destroy(2), qeye(N), qeye(2)), tensor(qeye(N), qeye(2), qeye(N), destroy(2))]\n", "\n", "# number operators\n", "NA = array([a.dag() * a for a in A])\n", "NC = array([c.dag() * c for c in C])\n", "\n", "# polariton operators\n", "P = NA + NC" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# Jaynes-Cumming Hamiltonian for system 0\n", "H0c = wc[0] * C[0].dag() * C[0] \n", "H0a = wa[0] * A[0].dag() * A[0]\n", "H0int = g[0] * (A[0].dag() * C[0] + A[0] * C[0].dag())\n", "H0 = H0c + H0a + H0int\n", "\n", "# Jaynes-Cumming Hamiltonian for system 1\n", "H1c = wc[1] * C[1].dag() * C[1]\n", "H1a = wa[1] * A[1].dag() * A[1] \n", "H1int = g[1] * (A[1].dag() * C[1] + A[1] * C[1].dag())\n", "H1 = H1c + H1a + H1int\n", "\n", "# cavity-cavity interaction\n", "Hint = J * (C[0].dag() * C[1] + C[0] * C[1].dag())\n", "\n", "H = H0 + H1 + Hint" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "H" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "$\\text{Quantum object: dims = [[21, 2, 21, 2], [21, 2, 21, 2]], shape = [1764, 1764], type = oper, isHerm = True}\\\\[1em]\\begin{pmatrix}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 6.283 & 1.574 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.574 & 6.283 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 12.566 & 2.225 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 2.225 & 12.566 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 251.327 & 6.859 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 6.859 & 251.327 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 257.611 & 7.037 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 7.037 & 257.611 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 263.894\\\\\\end{pmatrix}$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "Quantum object: dims = [[21, 2, 21, 2], [21, 2, 21, 2]], shape = [1764, 1764], type = oper, isherm = True\n", "Qobj data =\n", "[[ 0. 0. 0. ..., 0. 0. 0. ]\n", " [ 0. 6.28318531 1.5735585 ..., 0. 0. 0. ]\n", " [ 0. 1.5735585 6.28318531 ..., 0. 0. 0. ]\n", " ..., \n", " [ 0. 0. 0. ..., 257.61059759\n", " 7.03716754 0. ]\n", " [ 0. 0. 0. ..., 7.03716754\n", " 257.61059759 0. ]\n", " [ 0. 0. 0. ..., 0. 0.\n", " 263.8937829 ]]" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "energy_level_diagram([H0c + H1c, H0a + H1a, H0int + H1int, Hint], 23);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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3btZr+QC4A4UJhFEgENCYMWP017/+Veeff778fr+iotjoAdyA71QgjDwej+bO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\ncEDNmzeXz+czHQUAGhwK00UqKyvVv39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"text": [ "" ] } ], "prompt_number": 8 }, { "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", "for i in [0,1]:\n", " rate = kappa[i] * (1 + n_th)\n", " if rate > 0.0:\n", " c_ops.append(sqrt(rate) * C[i])\n", "\n", "# cavity excitation, if temperature > 0\n", "for i in [0,1]:\n", " rate = kappa[i] * n_th\n", " if rate > 0.0:\n", " c_ops.append(sqrt(rate) * C[i].dag())\n", "\n", "# atom relaxation\n", "for i in [0,1]:\n", " rate = gamma[i]\n", " if rate > 0.0:\n", " c_ops.append(sqrt(rate) * A[i])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "print(\"Number of collapse operators = %d\" % len(c_ops))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Number of collapse operators = 4\n" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Evolve the system\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "opts = Odeoptions()\n", "output = mesolve(H, psi0, tlist, c_ops, list(hstack([NA,NC,P,NC[1]-NC[0],NC[1]+NC[0]])), options=opts)\n", "#output = mcsolve_f90(H, psi0, tlist, c_ops, list(hstack([NA,NC,P,NC[1]-NC[0],NC[1]+NC[0]])), ntraj=100)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualize the results\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "M = 2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 2, sharex=True, figsize=(12,4))\n", "\n", "for m in range(M):\n", " axes[0].plot(tlist, real(output.expect[m]), label=\"Atom #%d\" % m)\n", "\n", "axes[0].legend(loc=0)\n", "axes[0].set_xlabel('Time')\n", "axes[0].set_title('Atomic Occupation probability')\n", "\n", "for m in range(M):\n", " axes[1].plot(tlist, real(output.expect[M+m]), label=\"Cavity #%d\" % m)\n", "\n", "axes[1].legend(loc=0)\n", "axes[1].set_xlabel('Time')\n", "axes[1].set_title('Cavity Occupation probability');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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TAIDdu3ejb9++sLe319gOEamk1xkaGmLSpEkICwsDAMTGxiIxMREjR47UWo5B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\n", "text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "For $g > g_c$, the energy is localized in one cavity-atom system. See Fig. 2 in Schmidt et al." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(M, 2, sharex=True, figsize=(12,2*M))\n", "\n", "for m in range(M):\n", " axes[m,0].plot(tlist, real(output.expect[m]), 'b', label=\"Atom #%d\" % m)\n", " axes[m,0].legend(loc=0)\n", " axes[m,0].set_ylim(0,1)\n", "\n", " axes[m,1].plot(tlist, real(output.expect[M+m]), 'g', label=\"Cavity #%d\" % m)\n", " axes[m,1].legend(loc=0)\n", "\n", " if m == 0:\n", " axes[m,0].set_xlabel('Time')\n", " axes[m,1].set_xlabel('Time')\n", " axes[m,0].set_title('Atomic Occupation probability')\n", " axes[m,1].set_title('Cavity Occupation probability')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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mplbhXg28/75V2f5qYmLChbUUjS1vT6sK8uQUISmPrLkVFRV5Bqny44n28sreExX1rQyR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\nc3YWI/SAGMFWjuYDg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GaMMcYYY8wIDpQZY4wxxhgzggNlxhhjjDHGjOBAmTHGGGOMMSM4\nUGaMMcYYY8wIDpQZY4wxxhgz4v8DYiZV6m95uQ8AAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "\"\"\"\n", "Plot polaritons\n", "\"\"\"\n", "fig, axes = subplots(M, 1, sharex=True, sharey=True, figsize=(12,2*M))\n", "\n", "for m in range(M):\n", " axes[m].plot(tlist, real(output.expect[2*M+m]), label=\"Polariton system #%d\" % m)\n", " axes[m].legend(loc=0)\n", "\n", " if m == 0:\n", " axes[m].set_xlabel('Time')\n", " axes[m].set_title('Polariton Occupation probability')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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QAICfnx/i4uKQn5+PjRs3Ii0tDQCQlpaGDRs2uCQYIiIiIqLu1OqZ48ZMJhPuuOMOHD58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\nshojbFAajgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "\"\"\"\n", "Plot photon imbalance\n", "\"\"\"\n", "\n", "n = output.expect[3*M] / output.expect[3*M+1]\n", "\n", "fig, axes = subplots(1, 1, sharex=True, sharey=True, figsize=(12,2*M))\n", "\n", "axes.plot(tlist * J, n, label=\"Photon imbalance\")\n", "axes.set_xlabel('Time')\n", "axes.set_ylim(-1.1, 1.1)\n", "axes.set_title('Photon imbalance');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Large photon imbalance ($\\sim - 1$) shows that the energy is localized in one cavity-atom system." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 } ], "metadata": {} } ] }