{ "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\n", "\n", "from functools import partial" ] }, { "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": [ "atoms = ais.create_random_ensemble(\n", " int(1e4),\n", " x_dist=partial(ais.dist.position_dist_gaussian, std=3.0e-3),\n", " y_dist=partial(ais.dist.position_dist_gaussian, std=3.0e-3),\n", " z_dist=partial(ais.dist.position_dist_gaussian, std=3.0e-3),\n", " vx_dist=partial(ais.dist.velocity_dist_from_temp, temperature=3.0e-6),\n", " vy_dist=partial(ais.dist.velocity_dist_from_temp, temperature=3.0e-6),\n", " vz_dist=partial(ais.dist.velocity_dist_for_box_pulse_velsel, pulse_duration=100e-6),\n", " 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": [ "412 of the initial 10000 atoms are detected. That's 4.12%\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_profile = 29.5e-3 / 2 # 1/e^2 beam radius in m\n", "intensity_profile = ais.IntensityProfile(\n", " r_profile=r_profile, center_rabi_freq=center_rabi_freq\n", ")" ] }, { "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(\n", " int(1e4),\n", " x_dist=partial(ais.dist.position_dist_gaussian, std=3.0e-3),\n", " y_dist=partial(ais.dist.position_dist_gaussian, std=3.0e-3),\n", " z_dist=partial(ais.dist.position_dist_gaussian, std=3.0e-3),\n", " vx_dist=partial(ais.dist.velocity_dist_from_temp, temperature=3.0e-6),\n", " vy_dist=partial(ais.dist.velocity_dist_from_temp, temperature=3.0e-6),\n", " vz_dist=partial(ais.dist.velocity_dist_for_box_pulse_velsel, pulse_duration=60e-6),\n", " seed=1,\n", " state_kets=[0, 1],\n", ")\n", "\n", "atoms2 = ais.create_random_ensemble(\n", " int(1e4),\n", " x_dist=partial(ais.dist.position_dist_gaussian, std=3.0e-3),\n", " y_dist=partial(ais.dist.position_dist_gaussian, std=3.0e-3),\n", " z_dist=partial(ais.dist.position_dist_gaussian, std=3.0e-3),\n", " vx_dist=partial(ais.dist.velocity_dist_from_temp, temperature=3.0e-6),\n", " vy_dist=partial(ais.dist.velocity_dist_from_temp, temperature=3.0e-6),\n", " vz_dist=partial(ais.dist.velocity_dist_for_box_pulse_velsel, pulse_duration=60e-6),\n", " seed=1,\n", " 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 }