{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP Lecture: Pulse-wise second-order optical coherences of emission from a two-level system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "K.A. Fischer, Stanford University\n", "\n", "This Jupyter notebook demonstrates how to simulate the second-order coherences of the emission from a two-level system, using QuTiP: The Quantum Toolbox in Python. The purpose is to help characterize the quality of a two-level system as a single-photon source; an ideal pulsed single-photon source has zero net second-order coherence. This notebook closely follows an example from my simulation paper, Dynamical modeling of pulsed two-photon interference, published as New J. Phys. 18 113053 (2016).\n", "\n", "For more information about QuTiP see the project web page: http://qutip.org/ " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from qutip import *" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from IPython.display import display, Math, Latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "The quantum two-level system (TLS) is the simplest possible model for quantum light-matter interaction. In the version we simulate here, the system is driven by a continuous-mode coherent state, whose dipolar interaction with the system is represented by the following Hamiltonain\n", "\n", "$$H =\\hbar \\omega_0 \\sigma^\\dagger \\sigma + \\frac{\\hbar\\Omega(t)}{2}\\left( \\sigma\\textrm{e}^{-i\\omega_dt} + \\sigma^\\dagger \\textrm{e}^{i\\omega_dt}\\right),$$\n", "\n", "where $\\omega_0$ is the system's transition frequency, $\\sigma$ is the system's atomic lowering operator, $\\omega_d$ is the coherent state's center frequency, and $\\Omega(t)$ is the coherent state's driving strength.\n", "\n", "The time-dependence can be removed to simplify the simulation by a rotating frame transformation, and is particularly simple when the driving field is resonant with the transition frequency ($\\omega_d=\\omega_0$). Then,\n", "\n", "$$H_r =\\frac{\\hbar\\Omega(t)}{2}\\left( \\sigma+ \\sigma^\\dagger \\right).$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem parameters\n", "\n", "We will explore emission from the two-level system under two different regimes: under excitation by a short pulse which gives rise to an exponential wavepacket and under excitation by a long pulse which gives rise to a Gaussian wavepacket. (Short and long are relative to the spontaneous emission time of the atomic transition.) In both cases, the driving strengths are chosen such that the expected number of photodetections is unity, i.e.\n", "\n", "$$\\gamma\\int \\langle \\sigma^\\dagger (t) \\sigma(t)\\rangle=1 .$$\n", "\n", "As a result, we can compare the statistics of the emission directly and the normalizations become trivial.\n", "\n", "Note, we use units where $\\hbar=1$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# shared parameters\n", "gamma = 1 # decay rate\n", "tlist = np.linspace(0, 13, 300)\n", "taulist = tlist\n", "\n", "# parameters for TLS with exponential shape wavepacket (short pulse)\n", "tp_e = 0.060 # Gaussian pulse parameter\n", "Om_e = 19.40 # driving strength\n", "t_offset_e = 0.405\n", "pulse_shape_e = Om_e / 2 * np.exp(-(tlist - t_offset_e) ** 2 /\n", " (2 * tp_e ** 2))\n", "\n", "# parameters for TLS with Gaussian shape wavepacket (long pulse)\n", "tp_G = 2.000 # Gaussian pulse parameter\n", "Om_G = 0.702 # driving strength\n", "t_offset_G = 5\n", "pulse_shape_G = Om_G / 2 * np.exp(-(tlist - t_offset_G) ** 2 /\n", " (2 * tp_G ** 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup the operators, Hamiltonian, and initial state" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# initial state\n", "psi0 = fock(2, 0) # ground state\n", "\n", "# operators\n", "sm = destroy(2) # atomic lowering operator\n", "n = [sm.dag()*sm] # number operator\n", "\n", "# Hamiltonian\n", "H_I = sm + sm.dag()\n", "H_e = [[H_I, pulse_shape_e]]\n", "H_G = [[H_I, pulse_shape_G]]\n", "\n", "# collapse operator that describes dissipation\n", "c_ops = [np.sqrt(gamma) * sm] # represents spontaneous emission" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate the emission flux\n", "\n", "We evolve the system with the Lindblad master equation solver, and we request that the expectation values of the number operator $\\hat{n}=\\sigma^{\\dagger} \\sigma$ are returned by the solver. If the probability of two photodetections were negligible over the course of the pulse, then $\\langle \\hat{n}(t) \\rangle$ would be the probability density of a detection occuring on an ideal detector at time $t$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n_e = mesolve(H_e, psi0, tlist, c_ops, n).expect[0]\n", "n_G = mesolve(H_G, psi0, tlist, c_ops, n).expect[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the emission flux\n", "\n", "We plot the emission flux from two different two-level systems. The flux labelled 'exponential wavepacket' was generated with a short pulse, while the flux labelled 'Gaussian wavepacket' was generated with a long pulse." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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vmtlPZnbIzDaZ2dNmVnAdXREREREREZFSdyqsk/4gcC7e+p1bgJYlKcTMmgLzgHrAh3hr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t3UNddLS+H55+F73/MHY9/6FowfX+u110VERKpTWAjDh/tArs8+g9mz4Q9/gCOPrJxMbs0aX+7t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\nTd8TqYm+I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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 333, "width": 500 } }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,5))\n", "ax.plot(tlist, n_e, 'r', label=\"exponential wavepacket\")\n", "ax.plot(tlist, n_G, 'b', label=\"Gaussian wavepacket\")\n", "ax.legend()\n", "ax.set_xlim(0, 13)\n", "ax.set_ylim(0, 1)\n", "ax.set_xlabel('Time, $t$ [$1/\\gamma$]')\n", "ax.set_ylabel('Emission flux [$\\gamma$]')\n", "ax.set_title('TLS emission shapes');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate the second-order optical coherences\n", "\n", "We are interested in exploring the second-order optical coherences of the emission from the two-level system $G^{(2)}(t,\\tau)$. If the probability of three photodetections were negligible over the course of the pulse, then $G^{(2)}(t,\\tau)$ would correspond to the probability density of a photodetection at time $t$, followed by a photodetection at time $t+\\tau$. Here, we wish to calculate time-dependent photon intensity correlations for a driven two level system with arbitrary pulse length, i.e.\n", "\n", "$$G^{(2)}(t,\\tau)= \\gamma^2 \\langle \\sigma^\\dagger(t) \\sigma^\\dagger(t+\\tau) \\sigma(t+\\tau) \\sigma(t) \\rangle.$$\n", "\n", "We identify this correlation to be of the form \n", "\n", "$$\\left< A(t)B(t+\\tau)C(t) \\right> ,$$\n", "\n", "which can be calculated with the QuTiP correlators using the master equation solver and the quantum regression theorem." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# specify relevant operators to calculate the correlation\n", "# \n", "a_op = sm.dag()\n", "b_op = sm.dag() * sm\n", "c_op = sm\n", "\n", "# calculate two-time correlations\n", "G2_t_tau_e = correlation_3op_2t(H_e, psi0, tlist, taulist, c_ops,\n", " a_op, b_op, c_op)\n", "G2_t_tau_G = correlation_3op_2t(H_G, psi0, tlist, taulist, c_ops,\n", " a_op, b_op, c_op)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize the second-order optical coherences\n", "\n", "The second-order optical coherences show dramatically different results for the exponential and Gaussian wavepackets. Looking on the axis of the first detection time, the intensity correlations are confined to the width of the pulse because this width denotes the times when the system can be re-excited after the first photodetection. While on the axis of the second detection time, the correlations decay within the sum of the pulse-width plus the decay time. For the exponential wavepacket this results in a narrow sliver of correlation, while for the Gaussian wavepacket this results in a giant blob for correlation." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WHcZPAdZS6gFoL5X0HknvMbM9JD1A0sMUAoNjJL3JzL4g6WRJp7r7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BXIsWR5QgghhBDyqDxZfkp9/n6MmqVikGILWnQq+SnVZZ/4vVkdm7Q8lLU7zU6oUA7XBOodSqkp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\nM9zVCj92r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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 282, "width": 553 } }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(9,4))\n", "\n", "ax_e = fig.add_subplot(121)\n", "p_e = ax_e.pcolor(tlist*gamma, taulist*gamma,\n", " abs(G2_t_tau_e).transpose())\n", "ax_e.set_xlim(0, 13)\n", "ax_e.set_ylim(0, 13)\n", "ax_e.set_xlabel('Time, $t$ [$1/\\gamma$]')\n", "ax_e.set_ylabel('Delay, $\\\\tau$ [$1/\\gamma$]')\n", "ax_e.set_title('$G^{(2)}(t,\\\\tau)$ for exponential wavepacket');\n", "\n", "ax_G = fig.add_subplot(122)\n", "p_G = ax_G.pcolor(tlist*gamma, taulist*gamma,\n", " abs(G2_t_tau_G).transpose())\n", "ax_G.set_xlim(0, 13)\n", "ax_G.set_ylim(0, 13)\n", "ax_G.set_xlabel('Time, $t$ [$1/\\gamma$]')\n", "ax_G.set_ylabel('Delay, $\\\\tau$ [$1/\\gamma$]')\n", "ax_G.set_title('$G^{(2)}(t,\\\\tau)$ for Gaussian wavepacket');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By integrating over $t$, we arrive at the single time correlation function that describes average correlations between pairs of photons in the wavepacket\n", "\n", "$$G^{(2)}(\\tau)= \\gamma^2 \\int \\mathop{\\textrm{d} t} \\, \\langle \\mathcal{T}_-[\\sigma^\\dagger(t) \\sigma^\\dagger(t+\\tau)] \\mathcal{T}_+[\\sigma(t+\\tau) \\sigma(t)] \\rangle,$$\n", "\n", "where the operators $\\mathcal{T}_\\pm$ indicate the time-ordering required of a physical\n", "measurement (higher times toward the center).\n", "\n", "This correlator roughly follows the shape of the wavepacket, but is much larger for the longer pulse because the system can be re-excited more times over the course of the pulse." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Zg1tvvdUhb2nX84QJE/DSSy+hWrVq6NevH8LCwnD06FGsWbMGn332Ge68806P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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 333, "width": 509 } }, "output_type": "display_data" } ], "source": [ "G2_tau_e = abs(np.trapz(G2_t_tau_e.transpose(), tlist))\n", "G2_tau_G = abs(np.trapz(G2_t_tau_G.transpose(), tlist))\n", "\n", "fig, ax = plt.subplots(figsize=(8,5))\n", "ax.plot(taulist, abs(G2_tau_e), 'r', label=\"exponential wavepacket\")\n", "ax.plot(taulist, G2_tau_G, 'b', label=\"Gaussian wavepacket\")\n", "ax.legend()\n", "ax.set_xlim(0, 13)\n", "ax.set_ylim(0, 0.07)\n", "ax.set_xlabel('Time delay, $\\\\tau$ [$1/\\gamma$]')\n", "ax.set_ylabel('$G^{(2)}(\\\\tau)$ [$\\gamma^2$]')\n", "ax.set_title('Integrated second-order coherence');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate measured degrees of second-order optical coherence\n", "\n", "The integrated second-order optical coherence is given by\n", "\n", "$$G^{(2)}[0]=\\int \\mathop{\\textrm{d} \\tau} G^{(2)}(\\tau).$$\n", "\n", "It's normalized version, referred to as the 'measured degree of second-order coherence' has the form\n", "\n", "$$g^{(2)}[0] = \\frac{G^{(2)}[0]}{\\left(\\gamma\\int \\mathop{\\textrm{d} t} \\langle \\hat{n}(t)\\rangle\\right)^2},$$\n", "\n", "which is simple for us to calculate since we set the expected number of photodetections to unity.\n", "\n", "This coherence is low (high) for the exponential (Gaussian) wavepacket, meaning it is relatively unlikely (likely) multiple photodetections will occur over the course of the pulse." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\textsf{exponential wavepacket }g^{(2)}_\\text{ME}(0) = 0.03$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\\textsf{Gaussian wavepacket }g^{(2)}_\\text{ME}(0) = 0.44$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# the factor of two comes from integration of negative taus, whose\n", "# values mirror the positive taus due to the symmetry of G2(t, tau)\n", "g20_e = 2*abs(np.trapz(G2_tau_e, taulist))\n", "g20_G = 2*abs(np.trapz(G2_tau_G, taulist))\n", "\n", "display(Math('\\\\textsf{exponential wavepacket }' + \n", " r'g^{(2)}_\\text{ME}(0) = ' + str(round(g20_e, 2))))\n", "display(Math('\\\\textsf{Gaussian wavepacket }' + \n", " r'g^{(2)}_\\text{ME}(0) = ' + str(round(g20_G, 2))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Therefore, the two-level system only acts as a good single-photon source when it is excited with a short pulse." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Connection to the Monte-Carlo wavefunction approach\n", "\n", "The measured degree of second-order coherence can also be calculated using the Monte-Carlo wavefunction approach, where the photocount distribution over the pulse duration is directly estimated. We can use the QuTiP Monte-Carlo solver to estimate this photocount distribution, $P_m(T)$. Then, we can estimate the measured degree of second-order coherence by computing \n", "\n", "$$\\hat{g}^{(2)}[0]= \\frac{\\langle m(m-1) \\rangle} {\\langle m \\rangle^2},$$\n", "\n", "where the expectations are over $P_m(T)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulate the photocount distribution" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "result_mc_e = mcsolve(H_e, psi0, tlist, c_ops, n,\n", " progress_bar=None, ntraj=1000)\n", "result_mc_G = mcsolve(H_G, psi0, tlist, c_ops, n,\n", " progress_bar=None, ntraj=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Estimate the measured degree of second-order coherence" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\textsf{exponential wavepacket }g^{(2)}_\\text{MC}[0] = 0.03$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\\textsf{Gaussian wavepacket }g^{(2)}_\\text{MC}[0] = 0.42$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# bin the collapse events to generate Pm\n", "ncollapse_e = [result_mc_e.col_times[i].size\n", " for i in range(result_mc_e.col_times.size)] \n", "ncollapse_G = [result_mc_G.col_times[i].size\n", " for i in range(result_mc_G.col_times.size)]\n", "Pm_e = np.histogram(ncollapse_e, bins=range(20), density=True)[0]\n", "Pm_G = np.histogram(ncollapse_G, bins=range(20), density=True)[0]\n", "\n", "# calculate the measured degree of second-order coherence\n", "g20_mc_e = sum([p * m * (m - 1) for m,p in enumerate(Pm_e)])\n", "g20_mc_G = sum([p * m * (m - 1) for m,p in enumerate(Pm_G)])\n", "\n", "display(Math('\\\\textsf{exponential wavepacket }' + \n", " r'g^{(2)}_\\text{MC}[0] = ' + str(round(g20_mc_e, 2))))\n", "display(Math('\\\\textsf{Gaussian wavepacket }' + \n", " r'g^{(2)}_\\text{MC}[0] = ' + str(round(g20_mc_G, 2))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Which is in excellent agreement with the values calculated using the quantum regression theorem and the master equation solver." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Versions" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "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 22:15:15 2017 MDT
" ], "text/plain": [ "" ] }, "execution_count": 15, "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": "3.4.3" }, "name": "G2(t,tau) Kevin Fischer" }, "nbformat": 4, "nbformat_minor": 1 }