{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP Example: Birth and Death of Photons in a Cavity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "J.R. Johansson and P.D. Nation\n", "\n", "For more information about QuTiP see [http://qutip.org](http://qutip.org)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from qutip import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we aim to reproduce the experimental results from:\n", "\n", "
\n", " Gleyzes et al., \"Quantum jumps of light recording the birth and death of a photon in a cavity\", [Nature **446**, 297 (2007)](http://dx.doi.org/10.1038/nature05589).\n", "
\n", "\n", "In particular, we will simulate the creation and annihilation of photons inside the optical cavity due to the thermal environment when the initial cavity is a single-photon Fock state $ |1\\rangle$, as presented in Fig. 3 from the article." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## System Setup" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "N=5\n", "a=destroy(N) \n", "H=a.dag()*a # Simple oscillator Hamiltonian\n", "psi0=basis(N,1) # Initial Fock state with one photon\n", "kappa=1.0/0.129 # Coupling rate to heat bath\n", "nth= 0.063 # Temperature with =0.063\n", "\n", "# Build collapse operators for the thermal bath\n", "c_ops = []\n", "c_ops.append(np.sqrt(kappa * (1 + nth)) * a)\n", "c_ops.append(np.sqrt(kappa * nth) * a.dag())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Run Simulation" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10.1%. Run time: 0.71s. Est. time left: 00:00:00:06\n", "20.0%. Run time: 1.59s. Est. time left: 00:00:00:06\n", "30.1%. Run time: 2.41s. Est. time left: 00:00:00:05\n", "40.0%. Run time: 3.04s. Est. time left: 00:00:00:04\n", "50.0%. Run time: 3.70s. Est. time left: 00:00:00:03\n", "60.1%. Run time: 4.32s. Est. time left: 00:00:00:02\n", "70.0%. Run time: 4.98s. Est. time left: 00:00:00:02\n", "80.1%. Run time: 5.66s. Est. time left: 00:00:00:01\n", "90.0%. Run time: 6.29s. Est. time left: 00:00:00:00\n", "100.0%. Run time: 6.94s. Est. time left: 00:00:00:00\n", "Total run time: 6.99s\n" ] } ], "source": [ "ntraj = [1,5,15,904] # number of MC trajectories\n", "tlist = np.linspace(0,0.8,100)\n", "mc = mcsolve(H,psi0,tlist,c_ops,[a.dag()*a],ntraj)\n", "me = mesolve(H,psi0,tlist,c_ops, [a.dag()*a])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot Results" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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TnYiISAwpwYuIiMSQEryIiEgMFeQ4+FQffvghFRUVuQ5DREQkWyKt1VLwCb5f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\nZ/BKKaWUOkK7SPAicqmIbBGRbSJyfwPrRUSeDqzfICJntka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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8, 8), frameon=False)\n", "plt.subplots_adjust(hspace=0.0)\n", "\n", "# Results for a single trajectory\n", "ax1 = plt.subplot(4,1,1)\n", "ax1.xaxis.tick_top()\n", "ax1.plot(tlist,mc.expect[0][0],'b',lw=2)\n", "ax1.set_xticks([0,0.2,0.4,0.6])\n", "ax1.set_yticks([0,0.5,1])\n", "ax1.set_ylim([-0.1,1.1])\n", "ax1.set_ylabel(r'$\\langle P_{1}(t)\\rangle$')\n", "\n", "# Results for five trajectories\n", "ax2 = plt.subplot(4,1,2)\n", "ax2.plot(tlist,mc.expect[1][0],'b',lw=2)\n", "ax2.set_yticks([0,0.5,1])\n", "ax2.set_ylim([-0.1,1.1])\n", "ax2.set_ylabel(r'$\\langle P_{1}(t)\\rangle$')\n", "\n", "# Results for fifteen trajectories\n", "ax3 = plt.subplot(4,1,3)\n", "ax3.plot(tlist,mc.expect[2][0],'b',lw=2)\n", "ax3.plot(tlist,me.expect[0],'r--',lw=2)\n", "ax3.set_yticks([0,0.5,1])\n", "ax3.set_ylim([-0.1,1.1])\n", "ax3.set_ylabel(r'$\\langle P_{1}(t)\\rangle$')\n", "\n", "# Results for 904 trajectories\n", "ax4 = plt.subplot(4,1,4)\n", "ax4.plot(tlist,mc.expect[3][0],'b',lw=2)\n", "ax4.plot(tlist,me.expect[0],'r--',lw=2)\n", "plt.xticks([0,0.2,0.4,0.6])\n", "plt.yticks([0,0.5,1])\n", "ax4.set_xlim([0,0.8])\n", "ax4.set_ylim([-0.1,1.1])\n", "ax4.set_xlabel(r'Time (s)')\n", "ax4.set_ylabel(r'$\\langle P_{1}(t)\\rangle$')\n", "\n", "xticklabels = ax2.get_xticklabels()+ax3.get_xticklabels()\n", "plt.setp(xticklabels, visible=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Versions" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.3.0.dev0+6e5b1d43
Numpy1.13.1
SciPy0.19.1
matplotlib2.0.2
Cython0.25.2
Number of CPUs2
BLAS InfoINTEL MKL
IPython6.1.0
Python3.6.2 |Anaconda custom (x86_64)| (default, Jul 20 2017, 13:14:59) \n", "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
OSposix [darwin]
Thu Jul 20 22:08:20 2017 MDT
" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }