{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Example: Rabi oscillations with a Gaussian beam and thermal atoms\n", "\n", "We simulate the decay of Rabi oscillation in the presence of thermal motion. Note that at the moment this only includes the motion within the $x$-$y$ plane, as well as in the $z$ direction. The parameters that we use here are roughly the ones that are achieved with the atom interferometer [GAIN](https://www.physics.hu-berlin.de/en/qom/research/ai).\n", "\n", "The simulation will require the following objects and parameters\n", "* `IntensityProfile`: contains information about the Gaussian beams\n", "* `Wavevectors`: the wavevectors are important for the incorporation of the Doppler shift along $z$\n", "* `AtomicEnsemble`: an ensemble of atoms which different trajectors or phase space vectors\n", "* `Detector`: determines which atoms contribute to the signal\n", "* `t`: time of flight before the lasers are turned on" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import aisim as ais" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Detector\n", "\n", "Setting up da detector with a fixed detection radius and time." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "t_det = 778e-3 # time of the detection in s\n", "r_det = 5e-3 # size of detected region in x-y plane\n", "\n", "det = ais.SphericalDetector(t_det, r_det=r_det) # set detection region" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Atomic cloud and state vectors\n", "\n", "Here we use a Monte-Carlo method by randomly drawing positions and velocities from a distribution. We initialize all atoms in the excited state, represented by a state vector `[0, 1]`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "pos_params = {\n", " \"mean_x\": 0.0,\n", " \"std_x\": 3.0e-3, # cloud radius in m\n", " \"mean_y\": 0.0,\n", " \"std_y\": 3.0e-3, # cloud radius in m\n", " \"mean_z\": 0.0,\n", " \"std_z\": 0.0, # ignore z dimension, its not relevant here\n", "}\n", "vel_params = {\n", " \"mean_vx\": 0.0,\n", " \"std_vx\": ais.convert.vel_from_temp(\n", " 3.0e-6\n", " ), # cloud velocity spread in m/s at tempearture of 3 uK\n", " \"mean_vy\": 0.0,\n", " \"std_vy\": ais.convert.vel_from_temp(\n", " 3.0e-6\n", " ), # cloud velocity spread in m/s at tempearture of 3 uK\n", " \"mean_vz\": 0.0,\n", " \"std_vz\": ais.convert.vel_from_temp(\n", " 160e-9\n", " ), # after velocity selection, velocity in z direction is 160 nK\n", "}\n", "\n", "atoms = ais.create_random_ensemble_from_gaussian_distribution(\n", " pos_params, vel_params, int(1e4), state_kets=[0, 1], seed=1\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We visualize the spread of the atomic ensemble and its convolution with the detector." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y / mm')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x0 = atoms.initial_position[:, 0]\n", "y0 = atoms.initial_position[:, 1]\n", "\n", "x_det = atoms.calc_position(t_det)[:, 0]\n", "y_det = atoms.calc_position(t_det)[:, 1]\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(1e3 * x_det, 1e3 * y_det, label=\"cloud at detection\")\n", "ax.scatter(1e3 * x0, 1e3 * y0, label=\"initial cloud\")\n", "angle = np.linspace(0, 2 * np.pi, 100)\n", "ax.plot(\n", " 1e3 * r_det * np.cos(angle),\n", " 1e3 * r_det * np.sin(angle),\n", " c=\"C2\",\n", " label=\"detection region\",\n", ")\n", "\n", "ax.set_aspect(\"equal\", \"box\")\n", "\n", "ax.set_xlabel(\"x / mm\")\n", "ax.set_ylabel(\"y / mm\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "452 of the initial 10000 atoms are detected. That's 4.52%\n" ] } ], "source": [ "n_init = len(atoms)\n", "atoms = det.detected_atoms(atoms)\n", "\n", "print(\n", " \"{} of the initial {} atoms are detected. That's {}%\".format(\n", " len(atoms), n_init, len(atoms) / n_init * 100\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Intensity profile\n", "\n", "We set up an intensity profile of the interferometry laser, defined by the center Rabi frequency" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "center_rabi_freq = 2 * np.pi * 12.5e3 # center Rabi frequency in Hz\n", "r_beam = 29.5e-3 / 2 # 1/e^2 beam radius in m\n", "intensity_profile = ais.IntensityProfile(r_beam, center_rabi_freq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Wave vectors\n", "\n", "We set up the two wavevectors used to drive the Raman transitions:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "wave_vectors = ais.Wavevectors(k1=2 * np.pi / 780e-9, k2=-2 * np.pi / 780e-9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation\n", "\n", "First, we freely propagate the atomic ensemble to the time when we start the Rabi oscillations by applying a light pulse. We save the resulting `AtomicEnsemble` in two objects since we want to perform two different simulations with this ensemble." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "atoms1 = ais.create_random_ensemble_from_gaussian_distribution(\n", " pos_params, vel_params, int(1e4), state_kets=[0, 1]\n", ")\n", "atoms2 = ais.create_random_ensemble_from_gaussian_distribution(\n", " pos_params, vel_params, int(1e4), state_kets=[0, 1]\n", ")\n", "\n", "atoms1 = det.detected_atoms(atoms1)\n", "atoms2 = det.detected_atoms(atoms2)\n", "\n", "free_prop = ais.FreePropagator(129e-3)\n", "\n", "atoms1 = free_prop.propagate(atoms1)\n", "atoms2 = free_prop.propagate(atoms2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The current position of the atoms is stored in `atoms.positions` and the `time` attribute has changed accordingly:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now simulate the effect of the pulse length in two different ways. First, we neglect the motion of the atoms in the $z$ direction, then we incorporate the Doppler effect caused by the finite temperature in $z$. We first set up two different propagators for this:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "prop1 = ais.TwoLevelTransitionPropagator(\n", " time_delta=1e-6, intensity_profile=intensity_profile\n", ")\n", "prop2 = ais.TwoLevelTransitionPropagator(\n", " time_delta=1e-6, intensity_profile=intensity_profile, wave_vectors=wave_vectors\n", ")" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": true }, "outputs": [], "source": [ "state_occupation1 = []\n", "state_occupation2 = []\n", "taus = np.arange(200) * 1e-6\n", "for tau in taus:\n", " # acting on the states in `atom` at each run\n", " atoms1 = prop1.propagate(atoms1)\n", " atoms2 = prop2.propagate(atoms2)\n", " # mean occupation of the excited state\n", " state_occupation1.append(np.mean(atoms1.state_occupation(state=1)))\n", " state_occupation2.append(np.mean(atoms2.state_occupation(state=1)))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(1e6 * taus, state_occupation1, label=\"w/o Doppler shift\")\n", "ax.plot(1e6 * taus, state_occupation2, label=\"with Doppler shift\")\n", "ax.set_xlabel(\"Pulse duration / μs\")\n", "ax.set_ylabel(\"Occupation of excited state\")\n", "ax.legend()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "aisim", "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": "3.13.0" } }, "nbformat": 4, "nbformat_minor": 2 }