{ "cells": [ { "cell_type": "markdown", "source": [ "# Cavity QED" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "ZPGenerator is designed to facilitate the construction of more complicated sources from elementary building blocks. A good example of this is found in cavity quantum electrodynamics (QED) where the emission properties of an emitter can be modified by coupling it to an optical cavity mode. By combining a TwoLevelEmitter object with a CavityEmitter object, and adding a Jaynes-Cummings coupling, we obtain a new emitter object that is a textbook example of cavity QED. This new emitter, called the PurcellEmitter, is used to make the PurcellSource that can be constructed using the purcell() class method of the Source class. In this notebook, we will take a look at this source type and what we can learn from it.\n", "\n", "For information about the model underlying the purcell() catalogue source, please see [Sources](sources_catalogue.ipynb). For information about how to construct complex systems from scratch, see [Constructing Components](component_construction.ipynb)." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## The Purcell source" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 2, "outputs": [], "source": [ "from zpgenerator import *\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:12:04.899659Z", "start_time": "2024-02-09T14:12:03.954758Z" } } }, { "cell_type": "markdown", "source": [ "A two-level emitter coupled to a single cavity mode via a Jaynes-Cummings type interaction is available as a catalogue source component using the Source.purcell() class method to construct a PurcellSource object. Let's make a purcell() source and look at the default parameters." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 3, "outputs": [ { "data": { "text/plain": "{'coupling': 5.0,\n 'area': 3.141592653589793,\n 'phase': 0,\n 'delay': 0,\n 'emitter/resonance': 0.0,\n 'emitter/decay': 0.1,\n 'emitter/dephasing': 0.0,\n 'cavity/resonance': 0.0,\n 'cavity/dephasing': 0.0,\n 'cavity/decay': 99.99999999999999,\n 'efficiency': 1}" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "source = Source.purcell()\n", "source.default_parameters" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:12:04.917143Z", "start_time": "2024-02-09T14:12:04.900097Z" } } }, { "cell_type": "markdown", "source": [ "By default, we can see that the emitter decay rate is $\\gamma=0.1$, the cavity-coupling rate is $g=5.0$, and the cavity decay rate is $\\kappa=100$. Together, using the formula $4g^2/\\kappa\\gamma$, this implies a canonical Purcell factor of 10, which we can verify using the method canonical_purcell_factor():" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 4, "outputs": [ { "data": { "text/plain": "10.0" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "source.canonical_purcell_factor()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:12:04.940699Z", "start_time": "2024-02-09T14:12:04.919218Z" } } }, { "cell_type": "markdown", "source": [ "In practice, the actual Purcell enhancement is not exactly equal to the canonical Purcell factor because there is always a finite amount of Purcell saturation due to the finite proximity to the emitter-cavity strong coupling regime. In addition, dephasing or emitter-cavity detuning can further reduce the effective Purcell enhancement. To see what the effective Purcell enhancement is, we can use the effective_purcell_factor() method." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 5, "outputs": [ { "data": { "text/plain": "9.891196834817015" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "source.effective_purcell_factor()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:12:04.941173Z", "start_time": "2024-02-09T14:12:04.924188Z" } } }, { "cell_type": "markdown", "source": [ "Since the dephasing and detuning are zero, this inhibition is due to Purcell saturation. How close the source are to the strong coupling regime is indicated by the regime factor $2g/\\kappa$, which can be accessed using the regime() method of the PurcellSource class." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 6, "outputs": [ { "data": { "text/plain": "0.10000000000000002" }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "source.regime()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:12:04.941267Z", "start_time": "2024-02-09T14:12:04.937297Z" } } }, { "cell_type": "markdown", "source": [ "Since the regime factor is much less than 1, this indicates we are in the weak-coupling regime where the canonical Purcell enhancement gives quite an accurate representation of the enhanced decay rate. This is why we observe an effective enhancement of 9.89 that is very close to 10. In this regime, the source behaves very similar to the two_level() source. Looking at the lifetime, we can see that it appears to be a simple exponential decay:" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 7, "outputs": [ { "data": { "text/plain": "
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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source.plot_lifetime(scale=10, start=-1, end=6, label='Purcell source').show()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:12:05.342180Z", "start_time": "2024-02-09T14:12:04.937426Z" } } }, { "cell_type": "markdown", "source": [ "## Using Purcell keywords" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "To help easily set up a Purcell source with the right characteristics, the class method has three keywords: 'purcell_factor', 'regime', and 'timescale'. Together, these three keywords fix the important decay rate and cavity coupling that determines the qualitative behaviour of the system. Using these keyword parameters, let's now make a purcell() source with a Purcell factor of 10, a timescale of 1, and that is excited by a Gaussian pulse. To see the impact of the regime keyword, we can plot the lifetime for three different regimes: strong coupling, critical coupling, and weak coupling." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 8, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pulse = Pulse.gaussian()\n", "source = Source.purcell(pulse=pulse, purcell_factor=10, timescale=1)\n", "for x in [[2, 'strong'], [1, 'critical'], [0.1, 'weak']]:\n", " plot = source.plot_lifetime(parameters={'regime': x[0]}, end=20, label=x[1])\n", "plot.show()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:12:05.654239Z", "start_time": "2024-02-09T14:12:05.343940Z" } } }, { "cell_type": "markdown", "source": [ "For a fixed source timescale, we can see that moving into the strong coupling regime will actually reduce the Purcell enhancement, which is again a manifestation of Purcell saturation. In addition, there is a pronounced revival in the emission due to the vacuum Rabi oscillations induced between the emitter and cavity. Each of these regimes also give rise to different source quality in terms of brightness, single-photon purity, and indistinguishability. Using the methods available from the SourceComponent class, we can easily explore these different characteristics." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 9, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regime_list = np.logspace(-1, 1.5, 40)\n", "beta_list = [source.beta(parameters={'regime': x}) for x in regime_list]\n", "g2_list = [source.g2(parameters={'regime': x}) for x in regime_list]\n", "plt.semilogx(regime_list, beta_list, label='Brightness')\n", "plt.semilogx(regime_list, g2_list, label='g2')\n", "plt.ylim([0, 1])\n", "plt.legend()\n", "plt.xlabel('Coupling regime, $2g/\\kappa$')\n", "plt.ylabel('Figure of Merit')\n", "plt.show()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:12:08.945968Z", "start_time": "2024-02-09T14:12:05.655180Z" } } }, { "cell_type": "markdown", "source": [ "From this plot, we can clearly see the effect of Purcell saturation on the source brightness. As we move into the strong coupling regime, the vacuum Rabi oscillations prolong the interaction between the light and the emitter, allowing for more time for the light to escape via spontaneous emission and thus reducing the amount of light collection from the cavity mode. However, we can also see a very interesting effect on the single-photon purity. Moving toward the strong coupling regime can substantially suppress multi-photon emission." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## Overcoming dephasing" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "In addition to providing an enhanced collection efficiency, the acceleration of emission due to the cavity can also improve indistinguishability. The presence of the cavity will open a new decay channel that can extract photons from the emitter before interactions with the environment can degrade the quantum coherence of the emitter. To see this effect, let's look at adding a 'dephasing' value to the emitter in our PurcellSource object. To make a nice comparison, we must fix the emitter decay rate relative to the dephasing rate. To do this, we can specify the `timescale' to be 1/purcell_factor so that $\\gamma = 1$.\n", "\n", "Let's consider a pure dephasing rate of $\\gamma^\\star = 2\\gamma$ and use a Gaussian excitation pulse with a width of $\\tau = 0.004/\\gamma$. For example, if the bare lifetime of the emitter was 1 nanosecond, the pulse width is 4 picoseconds. Now, we can loop over a changing Purcell factor and generate the source figures of merit." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 10, "outputs": [], "source": [ "source = Source.purcell(pulse=Pulse.gaussian({'width': 0.004}),\n", " regime=0.1, parameters={'emitter/dephasing': 2})\n", "purcell_list = np.logspace(-1, 1.5, 20)\n", "M_list = [source.hom(parameters={'purcell_factor': x, 'timescale': 1/x},\n", " pseudo_limit=0.1)['M'] for x in purcell_list]\n", "g2_list = [source.g2(parameters={'purcell_factor': x, 'timescale': 1/x},\n", " pseudo_limit=0.1) for x in purcell_list]\n", "beta_list = [source.beta(parameters={'purcell_factor': x, 'timescale': 1/x}) for x in purcell_list]" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:13:15.332563Z", "start_time": "2024-02-09T14:12:08.948569Z" } } }, { "cell_type": "markdown", "source": [ "Plotting this, we have:" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 11, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogx(purcell_list, M_list, label='Mean wavepacket overlap')\n", "plt.semilogx(purcell_list, beta_list, label='Brightness')\n", "plt.semilogx(purcell_list, g2_list, label='$g^{(2)}$')\n", "plt.ylim([0, 1])\n", "plt.legend()\n", "plt.xlabel('Canonical purcell factor, $4g^2/\\kappa\\gamma$')\n", "plt.ylabel('Figure of Merit')\n", "plt.show()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2024-02-09T14:13:15.469149Z", "start_time": "2024-02-09T14:13:15.337517Z" } } }, { "cell_type": "markdown", "source": [ "From this plot, we can see that increasing the Purcell factor improves the mean wavepacket overlap, which quantifies indistinguishability, in addition to improving the source brightness. Without a cavity, we would expect a mean wavepacket overlap of at most $M = \\gamma/(\\gamma+\\gamma^\\star) = 1/3$. With a cavity, we can exceed 80%. However, for a fixed pulse width, we can also see that the multiphoton emission is increased. This is because the Purcell effect decreases the effective lifetime of the source and makes it more likely that the pulse will cause re-excitation. This increasing $g^{(2)}$ causes the mean wavepacket overlap to saturate instead of increasing arbitrarily to 1.\n", "\n", "The $g^{(2)}$ problem can be compensated by decreasing the pulse width. However, this requires a more intense laser pulse, which in turn makes it more difficult to filter out the single photon. In summary, the presence of a cavity can help improve indistinguishability and brightness, but in practice it cannot arbitrarily improve the source figures of merit." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [], "metadata": { "collapsed": false } } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }