{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# $F=0\\rightarrow F'=1$ 1D molasses\n", "\n", "This example covers calculating the forces in a one-dimensional optical molasses\n", "using the optical bloch equations. This example does the boring thing and\n", "checks that everything is working on the $F=0\\rightarrow F=1$ transition, which of course\n", "has no sub-Doppler effect. It is a bit more complicated than the two level molasses example,\n", "as now different kinds of polarizations and $\\hat{k}$ vectors can be used. By exploring \n", "multiple combinations, we can verify that the OBEs are working properly.\n", "\n", "It first checks the force along the $\\hat{z}$-direction. One should look to see that\n", "things agree with what one expects whether or not one puts the detuning on\n", "the lasers or on the Hamilonian. One should also look at whether the force\n", "depends on transforming the OBEs into the real/imaginary components." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pylcp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the problem\n", "\n", "We start with defining multiple laser beam polarizations. We store these in a dictionary, keyed by the polarization. In this example, we can also specify the rotating frame, and how the lasers might have a residual oscillation in that frame. The total detuning is the sum of the detuning of the lasers and hamiltonian (see the associated paper). Answers should of course be independent, but computational speed may not be." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "laser_det = 0.\n", "ham_det = -2.\n", "s = 1.25\n", "\n", "laserBeams = {}\n", "laserBeams['$\\\\sigma^+\\\\sigma^+$'] = pylcp.laserBeams([\n", " {'kvec':np.array([0., 0., 1.]), 'pol':np.array([0., 0., 1.]),\n", " 'pol_coord':'spherical', 'delta':laser_det, 's':s},\n", " {'kvec':np.array([0., 0., -1.]), 'pol':np.array([0., 0., 1.]),\n", " 'pol_coord':'spherical', 'delta':laser_det, 's':s},\n", " ], beam_type=pylcp.infinitePlaneWaveBeam)\n", "\n", "laserBeams['$\\\\sigma^+\\\\sigma^-$'] = pylcp.laserBeams([\n", " {'kvec':np.array([0., 0., 1.]), 'pol':np.array([0., 0., 1.]),\n", " 'pol_coord':'spherical', 'delta':laser_det, 's':s},\n", " {'kvec':np.array([0., 0., -1.]), 'pol':np.array([1., 0., 0.]),\n", " 'pol_coord':'spherical', 'delta':laser_det, 's':s},\n", " ], beam_type=pylcp.infinitePlaneWaveBeam)\n", "\n", "laserBeams['$\\\\pi_x\\\\pi_x$'] = pylcp.laserBeams([\n", " {'kvec':np.array([0., 0., 1.]), 'pol':np.array([1., 0., 0.]),\n", " 'pol_coord':'cartesian', 'delta':laser_det, 's':s},\n", " {'kvec':np.array([0., 0., -1.]), 'pol':np.array([1., 0., 0.]),\n", " 'pol_coord':'cartesian', 'delta':laser_det, 's':s},\n", " ], beam_type=pylcp.infinitePlaneWaveBeam)\n", "\n", "laserBeams['$\\\\pi_x\\\\pi_y$'] = pylcp.laserBeams([\n", " {'kvec':np.array([0., 0., 1.]), 'pol':np.array([1., 0., 0.]),\n", " 'pol_coord':'cartesian', 'delta':laser_det, 's':s},\n", " {'kvec':np.array([0., 0., -1.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'cartesian', 'delta':laser_det, 's':s},\n", " ], beam_type=pylcp.infinitePlaneWaveBeam)\n", "\n", "laserBeams['$\\\\sigma^+\\\\sigma^-$'].total_electric_field_gradient(np.array([0., 0., 0.]), 0.)\n", "magField = lambda R: np.zeros(R.shape)\n", "\n", "# Hamiltonian for F=0->F=1\n", "Hg, Bgq = pylcp.hamiltonians.singleF(F=0, gF=0, muB=1)\n", "He, Beq = pylcp.hamiltonians.singleF(F=1, gF=1, muB=1)\n", "dijq = pylcp.hamiltonians.dqij_two_bare_hyperfine(0, 1)\n", "ham_F0_to_F1 = pylcp.hamiltonian(Hg, He - ham_det*np.eye(3), Bgq, Beq, dijq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate the equilibrium force profile\n", "\n", "This checks to see that the rate equations and OBE agree for $F=0\\rightarrow F'=1$, two-state solution:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Working on $\\sigma^+\\sigma^+$:\n", "Completed in 42.48 s. \n", "Working on $\\sigma^+\\sigma^-$:\n", "Completed in 50.15 s. \n", "Working on $\\pi_x\\pi_x$:\n", "Completed in 49.28 s. \n", "Working on $\\pi_x\\pi_y$:\n", "Completed in 45.20 s. \n" ] } ], "source": [ "obe={}\n", "rateeq={}\n", "\n", "# Define a v axis:\n", "v = np.arange(-5.0, 5.1, 0.125)\n", "\n", "for jj, key in enumerate(laserBeams.keys()):\n", " print('Working on %s:' % key)\n", " rateeq[key] = pylcp.rateeq(laserBeams[key], magField, ham_F0_to_F1)\n", " obe[key] = pylcp.obe(laserBeams[key], magField, ham_F0_to_F1,\n", " transform_into_re_im=False, include_mag_forces=False)\n", "\n", " # Generate a rateeq model of what's going on:\n", " rateeq[key].generate_force_profile(\n", " [np.zeros(v.shape), np.zeros(v.shape), np.zeros(v.shape)],\n", " [np.zeros(v.shape), np.zeros(v.shape), v],\n", " name='molasses'\n", " )\n", "\n", " obe[key].generate_force_profile(\n", " [np.zeros(v.shape), np.zeros(v.shape), np.zeros(v.shape)],\n", " [np.zeros(v.shape), np.zeros(v.shape), v],\n", " name='molasses', deltat_tmax=2*np.pi*100, deltat_v=4, itermax=1000,\n", " progress_bar=True,\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot up the results:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, num='Optical Molasses F=0->F1', figsize=(6.5, 2.75))\n", "for jj, key in enumerate(laserBeams.keys()):\n", " ax[0].plot(obe[key].profile['molasses'].V[2],\n", " obe[key].profile['molasses'].F[2],\n", " label=key, linewidth=0.5, color='C%d'%jj)\n", " ax[0].plot(rateeq[key].profile['molasses'].V[2],\n", " rateeq[key].profile['molasses'].F[2], '--',\n", " linewidth=0.5, color='C%d'%jj)\n", "ax[0].legend(fontsize=6)\n", "ax[0].set_xlabel('$v/(\\Gamma/k)$')\n", "ax[0].set_ylabel('$f/(\\hbar k \\Gamma)$')\n", "\n", "key = '$\\\\sigma^+\\\\sigma^+$'\n", "types = ['-', '--', '-.']\n", "for q in range(3):\n", " ax[1].plot(v, obe[key].profile['molasses'].fq['g->e'][2, :, q, 0], types[q],\n", " linewidth=0.5, color='C0', label='$+k$, $q=%d$'%(q-1))\n", " ax[1].plot(v, obe[key].profile['molasses'].fq['g->e'][2, :, q, 1], types[q],\n", " linewidth=0.5, color='C1', label='$-k$, $q=%d$'%(q-1))\n", "ax[1].plot(v, obe[key].profile['molasses'].F[2], 'k-',\n", " linewidth=0.75)\n", "ax[1].legend(fontsize=6)\n", "ax[1].set_xlabel('$v/(\\Gamma/k)$')\n", "fig.subplots_adjust(left=0.08, wspace=0.15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run a simulation at resonance\n", "\n", "This allows us to see what the coherences and such are doing." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "v_i=-(ham_det+laser_det)\n", "key = '$\\\\sigma^+\\\\sigma^-$'\n", "\n", "obe[key] = pylcp.obe(laserBeams[key], magField, ham_F0_to_F1,\n", " transform_into_re_im=True)\n", "\n", "obe[key].set_initial_position_and_velocity(\n", " np.array([0., 0., 0.]), np.array([0., 0., v_i])\n", " )\n", "rho0 = np.zeros((obe[key].hamiltonian.n**2,), dtype='complex128')\n", "rho0[0] = 1.\n", "\n", "if v_i==0 or np.abs(2*np.pi*20/v_i)>500:\n", " t_max = 500\n", "else:\n", " t_max = 2*np.pi*20/np.abs(v_i)\n", "\n", "obe[key].set_initial_rho_from_rateeq()\n", "obe[key].evolve_density(t_span=[0, t_max], t_eval=np.linspace(0, t_max, 1001),)\n", "\n", "f, flaser, flaser_q, f_mag = obe[key].force(obe[key].sol.r, obe[key].sol.t,\n", " obe[key].sol.rho, return_details=True)\n", "\n", "fig, ax = plt.subplots(2, 2, num='OBE F=0->F1', figsize=(6.25, 5.5))\n", "ax[0, 0].plot(obe[key].sol.t, np.real(obe[key].sol.rho[0, 0]), label='$\\\\rho_{00}$')\n", "ax[0, 0].plot(obe[key].sol.t, np.real(obe[key].sol.rho[1, 1]), label='$\\\\rho_{11}$')\n", "ax[0, 0].plot(obe[key].sol.t, np.real(obe[key].sol.rho[2, 2]), label='$\\\\rho_{22}$')\n", "ax[0, 0].plot(obe[key].sol.t, np.real(obe[key].sol.rho[3, 3]), label='$\\\\rho_{33}$')\n", "ax[0, 0].legend(fontsize=6)\n", "\n", "ax[0, 1].plot(obe[key].sol.t, np.abs(obe[key].sol.rho[0, 1]), label='$|\\\\rho_{01}|$')\n", "ax[0, 1].plot(obe[key].sol.t, np.abs(obe[key].sol.rho[0, 2]), label='$|\\\\rho_{02}|$')\n", "ax[0, 1].plot(obe[key].sol.t, np.abs(obe[key].sol.rho[0, 3]), label='$|\\\\rho_{03}|$')\n", "ax[0, 1].plot(obe[key].sol.t, np.abs(obe[key].sol.rho[1, 3]), label='$|\\\\rho_{13}|$')\n", "ax[0, 1].legend(fontsize=6)\n", "\n", "ax[1, 0].plot(obe[key].sol.t, flaser['g->e'][2, 0], '-', linewidth=0.75)\n", "ax[1, 0].plot(obe[key].sol.t, flaser['g->e'][2, 1], '-', linewidth=0.75)\n", "ax[1, 0].plot(obe[key].sol.t, f[2], 'k-', linewidth=0.5)\n", "\n", "ax[1, 1].plot(obe[key].sol.t, obe[key].sol.v[-1], '-', label='$z$')\n", "ax[1, 1].plot(obe[key].sol.t, obe[key].sol.r[-1], '--', label='$v_z$')\n", "ax[1, 1].legend(fontsize=6);\n", "\n", "ax[0, 0].set_ylabel('$\\\\rho_{ii}$')\n", "ax[0, 1].set_ylabel('$\\\\rho_{ij}$')\n", "ax[1, 0].set_ylabel('$f/(\\hbar k \\Gamma)$')\n", "ax[1, 1].set_ylabel('$kz$; $v_z/(\\Gamma/k)$')\n", "\n", "ax[1, 0].set_xlabel('$\\Gamma t$')\n", "ax[1, 1].set_xlabel('$\\Gamma t$')\n", "\n", "fig.subplots_adjust(left=0.08, bottom=0.1, wspace=0.25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finally, calculate $\\mathbf{f}$ when $\\mathbf{k}$ is along $\\mathbf{x}$ and $\\mathbf{y}$\n", "\n", "This helps to make sure that everything is coded properly." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Working on $\\sigma^+\\sigma^+$ along x.\n", "Completed in 49.64 s. \n", "Working on $\\sigma^+\\sigma^-$ along x.\n", "Completed in 52.31 s. \n", "Working on $\\sigma^+\\sigma^+$ along y.\n", "Completed in 57.35 s. \n", "Working on $\\sigma^+\\sigma^-$ along y.\n", "Completed in 52.62 s. \n" ] } ], "source": [ "laserBeams = {}\n", "laserBeams['x'] = {}\n", "laserBeams['x']['$\\\\sigma^+\\\\sigma^+$'] = pylcp.laserBeams([\n", " {'kvec':np.array([ 1., 0., 0.]), 'pol':+1, 'delta':laser_det, 's':s},\n", " {'kvec':np.array([-1., 0., 0.]), 'pol':-1, 'delta':laser_det, 's':s},\n", " ])\n", "laserBeams['x']['$\\\\sigma^+\\\\sigma^-$'] = pylcp.laserBeams([\n", " {'kvec':np.array([ 1., 0., 0.]), 'pol':+1, 'delta':laser_det, 's':s},\n", " {'kvec':np.array([-1., 0., 0.]), 'pol':+1, 'delta':laser_det, 's':s},\n", " ])\n", "laserBeams['y'] = {}\n", "laserBeams['y']['$\\\\sigma^+\\\\sigma^+$'] = pylcp.laserBeams([\n", " {'kvec':np.array([0., 1., 0.]), 'pol':+1, 'delta':laser_det, 's':s},\n", " {'kvec':np.array([0., -1., 0.]), 'pol':-1, 'delta':laser_det, 's':s},\n", " ])\n", "laserBeams['y']['$\\\\sigma^+\\\\sigma^-$'] = pylcp.laserBeams([\n", " {'kvec':np.array([0., 1., 0.]), 'pol':+1, 'delta':laser_det, 's':s},\n", " {'kvec':np.array([0., -1., 0.]), 'pol':+1, 'delta':laser_det, 's':s},\n", " ])\n", "\n", "obe = {}\n", "rateeq = {}\n", "for coord_key in laserBeams:\n", " obe[coord_key] = {}\n", " rateeq[coord_key] = {}\n", " for pol_key in laserBeams[coord_key]:\n", " print('Working on %s along %s.' % (pol_key, coord_key))\n", " rateeq[coord_key][pol_key] = pylcp.rateeq(laserBeams[coord_key][pol_key],\n", " magField, ham_F0_to_F1)\n", " obe[coord_key][pol_key] = pylcp.obe(laserBeams[coord_key][pol_key],\n", " magField, ham_F0_to_F1,\n", " transform_into_re_im=False,\n", " include_mag_forces=True)\n", "\n", " if coord_key is 'x':\n", " V = [v, np.zeros(v.shape), np.zeros(v.shape)]\n", " elif coord_key is 'y':\n", " V = [np.zeros(v.shape), v, np.zeros(v.shape)]\n", " R = np.zeros((3,)+v.shape)\n", " # Generate a rateeq model of what's going on:\n", " rateeq[coord_key][pol_key].generate_force_profile(\n", " R, V, name='molasses'\n", " )\n", "\n", " obe[coord_key][pol_key].generate_force_profile(\n", " R, V, name='molasses', deltat_tmax=2*np.pi*100, deltat_v=4,\n", " itermax=1000, progress_bar=True\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot up these results:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "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(1, 2, num='Optical Molasses F=0->F1', figsize=(6.5, 2.75))\n", "for ii, coord_key in enumerate(laserBeams.keys()):\n", " for jj, pol_key in enumerate(laserBeams[coord_key].keys()):\n", " ax[ii].plot(obe[coord_key][pol_key].profile['molasses'].V[ii],\n", " obe[coord_key][pol_key].profile['molasses'].F[ii],\n", " label=pol_key, linewidth=0.5, color='C%d'%jj)\n", " ax[ii].plot(rateeq[coord_key][pol_key].profile['molasses'].V[ii],\n", " rateeq[coord_key][pol_key].profile['molasses'].F[ii], '--',\n", " linewidth=0.5, color='C%d'%jj)\n", "ax[1].legend(fontsize=6)\n", "ax[0].set_xlabel('$v_x/(\\Gamma/k)$')\n", "ax[1].set_xlabel('$v_y/(\\Gamma/k)$')\n", "ax[0].set_ylabel('$f/(\\hbar k \\Gamma)$')\n", "fig.subplots_adjust(left=0.08, wspace=0.15)" ] } ], "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": 4 }