{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The bichromatic force\n", "\n", "This example covers calculating the forces involved in the bichormatic force, or in the stimulated emission of light into two travelling wavepackets. It attempts to replicate Fig. 1 of J. Söding, R. Grimm, Y. Ovchinnikov, P. Bouyer, and C. Salomon, Short-Distance Atomic Beam Deceleration with a Stimulated Light Force”, *Phys. Rev. Lett.* **78**, 1420 (1997) http://dx.doi.org/10.1103/PhysRevLett.78.1420" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import animation\n", "import pylcp\n", "from IPython.display import HTML" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the problem\n", "\n", "As always, the first step is to define the laser beams, magnetic field, and Hamiltonian. The two level Hamiltonian here is the same as many others, like that in the [rapid adiabatic passage](../basics/04_adiabatic_passage.ipynb) and [two-level molasses](../molasses/00_two_level_1D_molasses.ipynb) examples.\n", "\n", "Because we are dealing with a two state system addressable only with $\\pi$ light, we keep the geometry pretty straight forward by having all lasers move along $\\hat{x}$. Note that because we have positive and negative frequencies about resonance, we will put the detuning on the lasers themselves, since the average detuning is zero.\n", "\n", "The last thing to think about is the beat phase of the lasers. I follow the phase convention of L. Aldridge, *The Bichromatic Force in Multi-Level Systems*, Ph.D. thesis, 2016." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Make a method to return the lasers:\n", "def return_lasers(delta, s):\n", " return pylcp.laserBeams([\n", " {'kvec':np.array([1., 0., 0.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'spherical', 'delta':delta, 's':s, 'phase':-np.pi/8},\n", " {'kvec':np.array([1., 0., 0.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'spherical', 'delta':-delta, 's':s, 'phase':np.pi/8},\n", " {'kvec':np.array([-1., 0., 0.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'spherical', 'delta':delta, 's':s, 'phase':np.pi/8},\n", " {'kvec':np.array([-1., 0., 0.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'spherical', 'delta':-delta, 's':s, 'phase':-np.pi/8},\n", " ], beam_type=pylcp.infinitePlaneWaveBeam)\n", "\n", "\n", "# Standard two-level Hamiltonian:\n", "Hg = np.array([[0.]])\n", "He = np.array([[0.]])\n", "mu_q = np.zeros((3, 1, 1))\n", "d_q = np.zeros((3, 1, 1))\n", "d_q[1, 0, 0] = 1.\n", "\n", "hamiltonian = pylcp.hamiltonian(Hg, He, mu_q, mu_q, d_q)\n", "\n", "magField = lambda R: np.zeros(R.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Examine the phase\n", "\n", "Let's specifically compare our electric field with Eq. 2.6 in L. Aldridge, *The Bichromatic Force in Multi-Level Systems*, Ph.D. thesis, 2016. To do this, we first make the `laserBeams`, then divide them into the $+\\hat{k}$ (rightward) and $-\\hat{z}$ (leftward) going components." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "delta = 39.\n", "intensity = 2*39**2\n", "\n", "laserBeams = return_lasers(delta, intensity)\n", "laserBeams_rightward = pylcp.laserBeams(laserBeams.beam_vector[:2])\n", "laserBeams_leftward = pylcp.laserBeams(laserBeams.beam_vector[2:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set up the figure for the animation. We want to capture the output, hence the `%%capture` statement in this cell. The output is just the figure we will draw the animation into." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "%%capture\n", "fig, ax = plt.subplots(1, 1)\n", "line_thr, = ax.plot([], [], lw=1.0)\n", "line_exp, = ax.plot([], [], lw=0.75, color='k', linestyle='--')\n", "\n", "ax.set_ylim((-350, 350));\n", "ax.set_xlim((-4*np.pi, 4*np.pi))\n", "ax.set_xlabel('$kx$')\n", "ax.set_ylabel('$E/E_0$')\n", "x = np.linspace(-4*np.pi, 4*np.pi, 1001)\n", "\n", "def init():\n", " line_thr.set_data([], [])\n", " line_exp.set_data([], [])\n", " return (line_thr, line_exp)\n", "\n", "def animate(i):\n", " t = i/50*(np.pi/delta)\n", " #ax.plot(x, np.real(laserBeams_rightward.total_electric_field(np.array([x,]+[np.zeros(x.shape)]*2), t))[1])\n", " #ax.plot(x, np.real(laserBeams_leftward.total_electric_field(np.array([x,]+[np.zeros(x.shape)]*2), t))[1])\n", " line_thr.set_data(x, np.real(laserBeams.total_electric_field(np.array([x,]+[np.zeros(x.shape)]*2), t))[1])\n", " line_exp.set_data(x, 4*np.sqrt(2*intensity)*np.real(np.cos(x)*np.cos(delta*t)*np.cos(np.pi/8)+1j*np.sin(x)*np.sin(delta*t)*np.sin(np.pi/8)))\n", " \n", " return (line_thr, line_exp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now make the animation. The dashed lines are the expectation from Aldridge, and the solid is the result from `pylcp`." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "anim = animation.FuncAnimation(fig, animate, init_func=init,\n", " frames=100, interval=20, \n", " blit=True)\n", "\n", "HTML(anim.to_html5_video())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generate a force profile\n", "\n", "Using the same parameters as Fig. 1 of the PRL. We also use the same time-ending criteria as Aldridge." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 35:44. \n", "Completed in 33:30. \n", "Completed in 45:44. \n" ] } ], "source": [ "delta = 39\n", "intensities = [2*39**2, 2*43**2, 2*47**2]\n", "\n", "v = np.arange(-50., 50.1, 0.5)\n", "\n", "obe ={}\n", "for intensity in intensities:\n", " laserBeams = return_lasers(delta, intensity)\n", " \n", " obe[intensity] = pylcp.obe(laserBeams, magField, hamiltonian, transform_into_re_im=True)\n", " obe[intensity].generate_force_profile(\n", " np.zeros((3,) + v.shape),\n", " [v, np.zeros(v.shape), np.zeros(v.shape)],\n", " name='molasses', progress_bar=True,\n", " deltat_func=lambda r, v: 2*np.pi*(np.amin([10., 1./(np.linalg.norm(v)+1e-9)]) + 200./delta),\n", " itermax=3, rel=1e-4, abs=1e-6\n", " )" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 3, figsize=(3.25, 1.5))\n", "for ii, intensity in enumerate(intensities):\n", " ax[ii].plot(v, obe[intensity].profile['molasses'].F[0], linewidth=0.5)\n", " ax[ii].set_ylim(-1, 16)\n", " ax[ii].set_xlim(-30, 30)\n", "\n", "for ii in range(1, 3):\n", " ax[ii].yaxis.set_ticklabels('')\n", " \n", "ax[0].set_ylabel('$f/\\hbar k \\Gamma$')\n", "ax[1].set_xlabel('$v/(\\Gamma/k)$')\n", "fig.subplots_adjust(bottom=0.25)" ] } ], "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 }