{ "metadata": { "name": "Lecture-4-Correlation-Functions" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP lecture: Correlation functions \n", "\n", "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": [ "%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": [ "from qutip import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## First-order coherence function\n", "\n", "\n", "Consider an oscillator that is interacting with a thermal environment. If the oscillator initially is in a coherent state, it will gradually decay to a thermal (incoherent) state. The amount of coherence can be quantified using the first-order optical coherence function\n", "\n", "
\n", " $g^{(1)}(\\tau) = \\langle a^\\dagger(\\tau)a(0)\\rangle/\\sqrt{\\langle a^\\dagger(\\tau)a(\\tau)\\rangle\\langle a^\\dagger(0)a(0)\\rangle}$\n", "
\n", "\n", "For a coherent state $|g^{(1)}(\\tau)| = 1$, and for a completely incoherent (thermal) state $g^{(1)}(\\tau) = 0$. \n", "\n", "The following code calculates and plots $g^{(1)}(\\tau)$ as a function of $\\tau$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Decay of a coherent state to an incoherent (thermal) state" ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 15\n", "taulist = linspace(0,10.0,200)\n", "a = destroy(N)\n", "H = 2*pi*a.dag()*a\n", "\n", "# collapse operator\n", "G1 = 0.75\n", "n_th = 2.00 # bath temperature in terms of excitation number\n", "c_ops = [sqrt(G1*(1+n_th)) * a, sqrt(G1*n_th) * a.dag()]\n", "\n", "# start with a coherent state\n", "rho0 = coherent_dm(N, 2.0)\n", "\n", "# first calculate the occupation number as a function of time\n", "n = mesolve(H, rho0, taulist, c_ops, [a.dag() * a]).expect[0]\n", "\n", "# calculate the correlation function G1 and normalize with n to obtain g1\n", "G1 = correlation(H, rho0, None, taulist, c_ops, a.dag(), a)\n", "g1 = G1 / sqrt(n[0] * n)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(2, 1, sharex=True, figsize=(12,6))\n", "\n", "axes[0].plot(taulist, real(g1), 'b', label=r'First-order coherence function $g^{(1)}(\\tau)$')\n", "axes[1].plot(taulist, real(n), 'r', label=r'occupation number $n(\\tau)$')\n", "axes[0].legend()\n", "axes[1].legend()\n", "axes[1].set_xlabel(r'$\\tau$')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 4, "text": [ "" ] }, { "output_type": "display_data", "png": 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LmDFDNhFxtrAw2T570iTn92UrpYBRoySFyNGBMiBbzX/9teTLHzvm+PadISsL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\nqJBGjGgdoEeMkKKjra4YAAB8j7AMWKWqygzhaBmgDx82Kww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} ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Leggett-Garg inequality\n", "\n", "Definition: Given an observable $Q(t)$ that is bound below and above by $|Q(t)| \\leq 1$, the assumptions of \n", "\n", " * macroscopic realism\n", " * noninvasive measurements\n", "\n", "implies that\n", "\n", "
\n", "$L(t_1, t_2) = \\langle Q(t_1)Q(0)\\rangle + \\langle Q(t_1+t_2)Q(t_1)\\rangle - \\langle Q(t_1+t_2)Q(0)\\rangle \\leq 1$\n", "
\n", "\n", "If $Q$ is at a steady state at the initial time of measurement, we can set $\\tau = t_1 = t_2$ and the Leggett-Garg inequality then reads\n", "\n", "
\n", "$L(\\tau) = 2\\langle Q(\\tau)Q(0)\\rangle - \\langle Q(2\\tau)Q(0)\\rangle \\leq 1$\n", "
\n", "\n", "\n", "### References\n", "\n", "* [A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)](http://dx.doi.org/10.1103/PhysRevLett.54.857)\n", "* [A. J. Leggett, J. Phys. Condens. Matter 14, R415 (2002)](http://dx.doi.org/10.1088/0953-8984/14/15/201)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def leggett_garg(c_mat):\n", " \"\"\"\n", " For a given correlation matrix c_mat = , calculate the Leggett-Garg correlation.\n", " \"\"\"\n", " \n", " N, M = shape(c_mat)\n", "\n", " lg_mat = zeros([N/2,M/2], dtype=complex)\n", " lg_vec = zeros(N/2, dtype=complex)\n", "\n", " # c_mat(i, j) = \n", " # LG = + - \n", "\n", " for i in range(N/2):\n", " lg_vec[i] = 2*c_mat[0, i] - c_mat[0, 2*i];\n", " \n", " for j in range(M/2):\n", " lg_mat[i, j] = c_mat[0, i] + c_mat[i, j] - c_mat[0, i+j];\n", "\n", "\n", " return lg_mat, lg_vec" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Leggett-Garg inequality for two coupled resonators (optomechanical system)\n", "\n", "\n", "References:\n", "\n", " * [N. Lambert, J.R. Johansson, F. Nori, Phys. Rev. B 82, 245421 (2011)](http://dx.doi.org/10.1103/PhysRevB.84.245421)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "wc = 1.0 * 2 * pi # cavity frequency\n", "wa = 1.0 * 2 * pi # resonator frequency\n", "g = 0.3 * 2 * pi # coupling strength\n", "kappa = 0.075 # cavity dissipation rate\n", "gamma = 0.005 # resonator dissipation rate\n", "Na = Nc = 3 # number of cavity fock states\n", "n_th = 0.0 # avg number of thermal bath excitation\n", "\n", "tlist = linspace(0, 7.5, 251)\n", "tlist_sub = tlist[0:(len(tlist)/2)]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "# start with an excited resonator\n", "rho0 = tensor(fock_dm(Na,0), fock_dm(Nc,1)) \n", "\n", "a = tensor(qeye(Nc), destroy(Na))\n", "c = tensor(destroy(Nc), qeye(Na))\n", "\n", "na = a.dag() * a\n", "nc = c.dag() * c\n", "\n", "H = wa * na + wc * nc - g * (a + a.dag()) * (c + c.dag())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "# measurement operator on resonator\n", "Q = na # photon number resolving detector\n", "#Q = tensor(qeye(Nc), 2 * fock_dm(Na, 1) - qeye(Na)) # fock-state |1> detector\n", "#Q = tensor(qeye(Nc), qeye(Na) - 2 * fock_dm(Na, 0)) # click or no-click detector" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "c_op_list = []\n", "\n", "rate = kappa * (1 + n_th)\n", "if rate > 0.0:\n", " c_op_list.append(sqrt(rate) * c)\n", "\n", "rate = kappa * n_th\n", "if rate > 0.0:\n", " c_op_list.append(sqrt(rate) * c.dag())\n", "\n", "rate = gamma * (1 + n_th)\n", "if rate > 0.0:\n", " c_op_list.append(sqrt(rate) * a)\n", " \n", "rate = gamma * n_th\n", "if rate > 0.0:\n", " c_op_list.append(sqrt(rate) * a.dag())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate the correlation function $\\langle Q(t_1+t_2)Q(t_1)\\rangle$\n", "\n", "Using the regression theorem, and QuTiP function `correlation`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "corr_mat = correlation(H, rho0, tlist, tlist, c_op_list, Q, Q)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate the Leggett-Garg correlation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "LG_tt, LG_t = leggett_garg(corr_mat)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot results" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 2, figsize=(12,4))\n", "\n", "axes[0].pcolor(tlist,tlist,abs(corr_mat),edgecolors='none')\n", "axes[0].set_xlabel(r'$t_1 + t_2$')\n", "axes[0].set_ylabel(r'$t_1$')\n", "axes[0].autoscale(tight=True)\n", "\n", "axes[1].pcolor(tlist_sub,tlist_sub,abs(LG_tt),edgecolors='none')\n", "axes[1].set_xlabel(r'$t_1$')\n", "axes[1].set_ylabel(r'$t_2$')\n", "axes[1].autoscale(tight=True)\n", "\n", "fig, axes = subplots(1, 1, figsize=(12,4))\n", "axes.plot(tlist_sub, diag(real(LG_tt)), label=r'$\\tau = t_1 = t_2$')\n", "axes.plot(tlist_sub, ones(shape(tlist_sub)), 'k', label=r'quantum boundary')\n", "axes.fill_between(tlist_sub, diag(LG_tt), 1, where=(diag(LG_tt)>1), color=\"green\", alpha=0.5)\n", "axes.set_xlim([0, max(tlist_sub)])\n", "axes.legend(loc=0)\n", "axes.set_xlabel(r'$\\tau$', fontsize=18)\n", "axes.set_ylabel(r'LG($\\tau$)', fontsize=18)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 13, "text": [ "" ] }, { "output_type": "display_data", "png": 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TIdPXd3NBNq5HcfYVvBK3KQwEmUKPOfasjCVeZN55bEuZ9OUcTSi0g25sB+9JkSZe+R9C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\nEngpkIQYgGr7BHcjpxKl+zUYb/l/yrjBtYcDMs8yym2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AZ/nw26UNJzk12xcWtw8xbbFj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zZsFDD1kdjXiCsDCTfG/Zkv7R73Qn38nJlCkTx48fJ3/+/GkOzpmUfNtnwAA4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\nyJEj4VJRs2bNiI6O5ty5c06N09PpXHYOncuOEx0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} ], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 } ], "metadata": {} } ] }