{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Example: Effect of wavefront aberrations in atom interferometry" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, we reproduce two plots from the paper https://link.springer.com/article/10.1007/s00340-015-6138-5.\n", "\n", "The simulation will require the following objects and parameters\n", "* `Wavefront`: contains the wavefront aberrations of the interferometry lasers\n", "* `AtomicEnsemble`: an ensemble of atoms which different trajectories or phase space vectors\n", "* `Detector`: determines which atoms contribute to the signal\n", "* times of the three interferometer pulses\n", "* effective wavevector" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import aisim as ais" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Loading and preparing wavefront data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wavefront aberration in multiples of $\\lambda$ = 780 nm. \n", "\n", "Load Zernike coefficients from file:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "coeff_window = np.loadtxt('data/wf_window.txt')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Creating `Wavefront` objects and removing piston, tip and tilt from the data:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "r_beam = 11e-3 # radius of the available wavefront data in m\n", "\n", "wf = ais.Wavefront(r_beam, coeff_window)\n", "for n in [0,1,2]:\n", " wf.coeff[n] = 0" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "wf.plot()\n", "fig, ax = wf.plot_coeff()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Creating an atomic ensemble\n", "\n", "Due to the large number of parameters determining an atomic ensemble, dictionaries are used:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "pos_params = {\n", " 'std_rho' : 3.0e-3, # cloud radius in m\n", " 'std_z' : 0, # ignore z dimension, its not relevant here\n", " 'n_rho' : 20, # within each standard deviation of the distribution we use 20 points\n", " 'n_theta' : 36, # using a resolution of 10°\n", " 'n_z' : 1, # use one value for the distribution along z\n", " 'm_std_rho' : 3, # use 3 standard deviations of the distribution, i.e. atoms up to 9 mm away from the center\n", " 'm_std_z' : 0, # ignore z dimension, its not relevant here \n", "}\n", "\n", "vel_params = {\n", " 'std_rho' : ais.vel_from_temp(3e-6), # velocity spread in m/s from a temperature of 3 uK\n", " 'std_z' : 0, # ignore z dimension, its not relevant here\n", " 'n_rho' : 20, # within each standard deviation of the distribution we use 20 points\n", " 'n_theta' : 36, # using a resolution of 10°\n", " 'n_z' : 1, # use one value for the distribution along z\n", " 'm_std_rho' : 3, # use 3 standard deviations of the distribution\n", " 'm_std_z' : 0, # ignore z dimension, its not relevant here \n", "}\n", "\n", "atoms = ais.create_ensemble_from_grids(pos_params, vel_params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the grid and the weights:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "x = atoms.initial_position[:, 0]\n", "y = atoms.initial_position[:, 1]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y / mm')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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8KC4kZTB0kanTy3MLcAvwUUlPBY4Efhv4CPCEGMoJQ9dG5gLSH+Zdqz4KTaNeHjP7MaOel01xzBk2MRuIC8jw6KM344ulByD1RXbxSEOJo8NLF5mV6zYu/YLMUlqDXmX6NH9v7DbdZSnSDcBnzewHsYwLzRCmL4DyGqnT78GYIUWmi6C8n1FZ/LWMpjK4rPTalL4KSl9LvFeZpjdpaec+9NrGdSepFqPBgacw6tn5B+DTZvbtVtZEpg+CkqphuYCkp81NWtI1qmN/J0EZ7+BQRoJyDKNalJcAV5jZOxpZm4DSBCVXY3ExyUeI8CLntVtmf5eQ562MqmbvAT4FfN7MHpK0C/AtMzuotdWRKElQUnoiqY85RGKJcKj8RY72VEWXKSD3Al5rZrdPv2lmj0o6vpGVK0CqPEis46+6VxPrt685/ZIgolK1j5KuV51K2fcs+OzmsOb0i1KeFiEpqXGWQiiRnd5HyGtaksh4YVtLShGTrhPouIDUI/S5CuWxzCOXyKxcYVtbcocyVYSYjWuIghJTKGevUcjj5CiwbFvo2bmXp090FZQSxQPC5Eea7Mc9mGpi57D6gAvKHEoJXZaRWkxWhTbnJWYY2vRYuShKUCT9JfCbwIPAt4FTzOyHFdttB+4DHgEervoBVdQVlNLFJMYEwy4o4Yk9xqdEUenSbRyDK4B3jieq/gDwTuDP5mx7pJndk860bpRYb7DKItI0bGvjsSxKsIYIG2e/X6LATMgiKGZ2+dTLq4HX5bAjBCUKSNsityGGRal+y6Iu4dCJ3JJHzO+S2wDg94Evz/nMgMslbRkvNVoUpYjJ9rOOe9y/LnYss6WUhhubrucx1r7bHjMV0TwUSVcC+1R89G4z+8J4m3cDDwOfnbObI8xsp6RnAldIusXMrppzvKhrG5d6I6WuNyil4bZlWQiyyNOImWwNXThXdYwUZOvlkfRG4DTgVWb2QI3tzwDuN7MPLdu2ay9P7AsRs2tx1UOcZbTNqUCcJPk0JY8hmqWopKykYxglYV8+T0wk7Q7sYmb3jf8+GnhvaFv6Nn1janvriE6f6lVyVRbXqYwdgteSq9t4G/BTwPfHb11tZqdJejbwKTNbL+nngYvGnz8JON/Mzqyz/5JGG0OZT7a6N8eQvZg2hX7TND0npcyTEkJUiqpDiU1JglKSmPgUB48nRFFb2/MYM+nblDa2FBXyDJnUq9071aTyrNoKTJfBgTG6oUO1PReUgKR46qd4Ig4hzKlj+2SbXDmgUPmNknJYHvJ0IPWYja4xe9NcwVASsXVoEw7GGN6Qq7ap6XE95AlM38ZoNC0lD7m/mOT0puaFCiXkqnIJvgtKJuqKSY6kX59o0h3bh2kbQs7qFrMwbx4e8jQgtSvbdUh9G9e9bldy38Khpt3k0wwhBJoQqpDTQ56OlNQo6pCzfqGN2MQOXVL0vtQJgZrYEoPYbdEFZQ65BKRtkVpKupybed/t2nVZxwMpxXNqYkcJ43OaUMJo4+Log5iEGF082c/k2CGSsTkbfJ1jtzlnMX5T2+tXgiAuwj2UAJT01GiTJ2ibW2izTR+oSozWzTOFTKrmPEZb3EPJzMQz6JqAnewrNCG8oFB0HWXd9DzX3W/X75ZUht8VF5SO9DXEicWyhOwy5m1T1+66BYJd8zWhmb6+pQh4GzzkaUhfL3aX7tC227chRNK2bo9RlwI0D4GqcQ+lgq5PyUWEDHHa7m/yvZDb527IMWlzfuftpy5duq5z4h7KHGLcIKEbVOqRtF23i03IUbM59j9LCSX8TXEPZQVo001aymRAsyyzK0d9R5PvtvUo2x4jtRC5hxKRnONwuvaINCVlSNSkjH5ZfmPari7Vum28iaYeT1uPJaVn5YISidhPoLbkSMQ2vWlCVtOGro6d7KuUMK80POTpGSnzJqEK3oZI1+7xrpR63nPNen8G8IfA3eO33mVmmyq2OwY4G9iV0eTVZyUzsgWlTDXQdn9t3e/SaOLJVHkcIbyaFN3KJQ06nJAz5PnoojV2JO0KfBw4CtgBXCPpYjO7KZWBTUjRJZhrvyXSND+yjJD5lLak7kWKQckhzzpgm5ndZmYPAhcAJ2a2KQshMvYxM/653P/c3dp1z2kqkYhZP1WXnB7KBklvADYDf2pmP5j5fD/gjqnXO4DD5+0s9lKkVaSYaiBVQVUK97mu8IROzE7vP9bvWmZTqsra3B5OlrWNgXOA9zFaDP19wIcZLZr+uF1UfHfu9HJmthHYCKMZ21qY3IgSQpwQx2hTkp+70aYkdC9RE/oYAkUTFDN7dZ3tJH0S+FLFRzuAA6Ze7w/sDGBa8aQYpdqWvjXwJsy7gXPkU/pKlhyKpH2nXr4GuLFis2uAgyU9V9JuwEnAxSnsC0nOCXRyVEqmpmkBX6hK26rvlZZTyUGuHMoHJR3GKITZDrwZYHptYzN7WNIG4DJG3cbnmtnWTPY2ooQG0+XGCLV9CeehithhTEk5ldRk8VDM7PVm9kIzO8TMTjCzO8fv7zSz9VPbbTKzXzCzg+oulL4qxCjPzzXYsA83CuS3sw/eppfet2TeUy7msPNQDTpF4VsVoXtu6h6zbdi5KJ8yvV1XciZ+Q+OC0oFQN0GMsSahyf107kJbweoidE3H/DQNgUq9HiUXtjlTlDA/SqmUXK+Ro5gwJy4ohRN6jtF5+2rTQEtKyLYVlVTzoKwKLiiZSD0BzqKbp8RCttTzubQltOBP9tlXXFAyUNINsYw+N+5pUnWjz9tHm/lx+njuXVAKpskQ/D6JVCzaFq3FKnaLtZ+ScUEpjMmTqel8Hsv2uSrk6hJPPSVFqdfUu40TkvoJFbNnqKSEbCnEGvPTp/PpHkoiSnR3S0zG1j1+6vMZMuwpsS2EwgWlIJrOMBazYeYWkxLpQwFiblxQCqBpRn+ojTEUbT2b3EMbhoALykBZ5UbdhZCisorXwJOyAyNk71Cb767iTdSWvk1NUAf3UBIRovsvVN6k9GRsycTKXQ0ljHVBSch0jUmpeZOY0wikPuY8QghqydN05sQFZUCsWuNdRNfq15A5kDYPkL7igjIAQlfWxvx+SlbhBi6NXEuR/j3wvPHLPYEfmtlhFdttB+4DHgEeNrO1yYwcILHFxG9gJ9ecsr9rZoeNReSfgQsXbH7keNuVFJPUUxzk+G6O/YYg5EJvJf/OJmTtNpYk4HeAV+a0o1T6MM9sTlIshLVsvtc2NvTxXNcldw7l14G7zOxbcz434HJJW8ZLjTpjViXJ15UQ44H8PNcny1KkZvaF8d8nA59bsJsjzGynpGcCV0i6xcyumnO85Gsb94k+JVOd/pJtKVJJTwJeC7x4wT52jv//nqSLgHVApaCkXtu4T8Suu1j1J3jpM9GnJGfI82rgFjPbUfWhpN0l7TH5Gzia6iVLnQ74TRAO9wLzCspJzIQ7kp4tadP45bOAf5N0PfBfwCVmdmliG7MypB6BLr8l5rwonkcJS7ZeHjN7U8V7O4H1479vAw5NbFZxDKUh51g1cEKonppYM7INidy9PE5kvPGPGIowl44LyoAJVdnqCVmnLi4oK4oLQXuGlNsKjU+w5PSCRXmQEHmYpvtw8ajGPRRnZUi1oNcq44LirBTuWcTFBWXAxI71/eZ0ZvEcysAJkVtwnLq4h+I4TjBcUJyVw7t94+Ehj7OSuHjEwT0Ux3GC4YLiLMTDA6cJHvI4SylFPOZVy5ZinwMyG97kZmvXrrXNmzfnNsOZwcVgOEjaUrUShXsoTjJcPIaP51AcxwmGC4rjOMFwQXEcJxguKI7jBMMFxXGcYAyy21jS3cDtue0IzF7APbmNiIT/tv7xHDPbe/bNQQrKEJG0uarffwj4bxsOHvI4jhMMFxTHcYLhgtIfNuY2ICL+2waC51AcxwmGeyiO4wTDBcVxnGC4oPQISWdI+o6k68b/1ue2qQuSjpH0TUnbJJ2e257QSNou6YbxtVqJ+TQ8h9IjJJ0B3G9mH8ptS1ck7QrcChwF7ACuAU42s5uyGhYQSduBtWY2xMK2StxDcXKxDthmZreZ2YPABcCJmW1yOuKC0j82SPqGpHMl/WxuYzqwH3DH1Osd4/eGhAGXS9oi6dTcxqTABaUwJF0p6caKfycC5wAHAYcBdwIfzmpsN1Tx3tDi7yPM7EXAscBbJL0st0Gx8SkgC8PMXl1nO0mfBL4U2ZyY7AAOmHq9P7Azky1RMLOd4/+/J+kiRmHeVXmtiot7KD1C0r5TL18D3JjLlgBcAxws6bmSdgNOAi7ObFMwJO0uaY/J38DR9Pt61cI9lH7xQUmHMQoNtgNvzmtOe8zsYUkbgMuAXYFzzWxrZrNC8izgIkkwus/ON7NL85oUH+82dhwnGB7yOI4TDBcUx3GC4YLiOE4wXFAcxwmGC4rjOMFwQXGSIelvJB2R2w4nHt5t7CRD0nXAi83skdy2OHFwD8XphKRfHQ9WfMq4OnSrpF+u2O6XgFtnxUTSeZLOkfQVSbdJevl44OPNks6b2u5+SR8YD7S7UtI6Sf86/s4J8X+pUwf3UJzOSHo/8BTgqcAOM/uLim3eBvzQzM6def+88XdPBk4A/g44AtjKqDz/D8zsOkkGrDezL4/HxewOHAc8H/hbMzss1u9z6uOl904I3svo5v9f4K1ztvkN4JQ5n33RzEzSDcBdZnYDgKStwBrgOuBBYFK6fgPwEzN7aPydNSF+hNMdD3mcEDwDeDqwByNv43FIehqw52T0bQU/Gf//6NTfk9eTh95D9pg7/f/bmdn0Nk5mXFCcEGwE/hz4LPCBis+PBL6S1CInC67sTickvQF42MzOH88T+3VJrzSzf5na7Fjgn/JY6KTEk7JOdCRdCxxuZg/ltsWJiwuK4zjB8ByK4zjBcEFxHCcYLiiO4wTDBcVxnGC4oDiOEwwXFMdxgvF/kEe37bvpWh0AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.scatter(1e3*x, 1e3*y)\n", "ax.set_aspect('equal', 'box')\n", "ax.set_xlabel('x / mm')\n", "ax.set_ylabel('y / mm')" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'weights')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.scatter(1e3*x, atoms.weights)\n", "ax.set_xlabel('x / mm')\n", "ax.set_ylabel('weights')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setting up the detector\n", "\n", "We want to calculate the dependency of the phase shift caused by wavefront aberrations on the detection area. For this reason, we set up a Detector with varying detection radius within a for-loop." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "t_det = 778e-3 # time of the detection in s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation the bias in gravity from wavefront aberrations\n", "\n", "For the simulation we need the objects created above and the timing of the interferometer sequence." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "T = 260e-3 # interferometer time in s\n", "t1 = 130e-3 # time of first pulse in s\n", "t2 = t1 + T\n", "t3 = t2 + T" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "awfs = []\n", "r_dets = np.linspace(2e-3, 10e-3, 10)\n", "for r_det in r_dets:\n", " # creating detector with new detection radius\n", " det = ais.PolarDetector(t_det, r_det=r_det)\n", " \n", " det_atoms = det.detected_atoms(atoms)\n", " \n", " # calculate the imprinted phase for each \"test atom\" at each pulse. This is the computationally heavy part\n", " phi1 = 2 * np.pi * wf.get_value(det_atoms.calc_position(t1))\n", " phi2 = 2 * np.pi * wf.get_value(det_atoms.calc_position(t2))\n", " phi3 = 2 * np.pi * wf.get_value(det_atoms.calc_position(t3))\n", "\n", " # calculate a complex amplitude factor for the Mach-Zehnder sequence and\n", " # weight their contribution to the signal\n", " awf = np.exp(1j * (phi1 - 2*phi2 + phi3))\n", " weighted_awf = np.sum(det_atoms.weights * awf) / np.sum(det_atoms.weights) \n", "\n", " awfs.append(weighted_awf)\n", " \n", "g = ais.phase_to_grav(np.angle(awfs), T=260e-3, keff=1.610574779769e6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We load the measured gravity data from a file and compare it to the simulation results." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "data = np.loadtxt('data/wf_grav_data.csv', skiprows=1, delimiter=',')\n", "r_det_data = data[:, 0]\n", "grav = data[:, 1]\n", "graverr = data[:, 2]" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(1e3*r_dets, 1e9*g, label='Simulation')\n", "ax.errorbar(1e3*r_det_data, 1e9*grav, yerr=1e9*graverr, fmt='o', label='data')\n", "ax.set_xlabel('Detection radius / mm')\n", "ax.set_ylabel('Gravity bias / $nm/s^2$');\n", "ax.set_ylim([-35, -5])\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that a different simulation software with different simulation parameters was used in the aformentioned paper, so some differences are to be expected." ] } ], "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }