{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Optical Pumping\n", "\n", "This little script tests the optical pumping from the optical Bloch equations\n", "and rate equations. It reproduces Fig. 5 of Ungar, P. J., Weiss, D. S., Riis,\n", "E., & Chu, S., \"Optical molasses and multilevel atoms: theory\", *Journal of\n", "the Optical Society of America B*, **6** (11), 2058 (1989).\n", "http://doi.org/10.1364/JOSAB.6.002058" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pylcp\n", "from pylcp.common import spherical2cart\n", "\n", "transform = False # Change the variable to transform OBEs into re/im components." ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "### Define the problem\n", "\n", "As always, we first define the laserBeams, Hamiltonian, and magnetic field. Here, we are interested in a $F=2\\rightarrow F'=3$ transition under linearly polarized light. We make three combinations of laser beams, each with linear polarization along a different axis. Note that agreement between rate equations and the optical Bloch equations will only occur with the rate equations in the case of a single laser beam. This is because the rate equations assume that thelasers are incoherent (their electric fields do not add to give twice the\n", "amplitude) whereas the optical Bloch equations do. Specifically, two coherent beams doubles the electric field which quadrupoles the intensity, so to compare the rate equations, we have to mulitply by $4$. We do that for $\\pi_y$ and $\\pi_z$ polarizations. For the $\\pi_x$ beams, we separate it into two beams.\n", "\n", "Compared to Ungar *et. al.*, the saturation parameter is defined differently. There's is defined using $\\gamma = \\Gamma/2 - i\\Delta$, which is different from ours. Namely, the ratio between the two is $(\\Gamma^2+\\Delta^2)/\\Gamma^2 = 1+\\Delta^2/\\Gamma^2$. \n", "\n", "Finally, one can put the detuning on the laser or put the detuning on the Hamiltonian (or some combination of the two). The latter appears to be faster." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[( 5x5) ( 5x7)]\n", " [( 7x5) ( 7x7)]]\n" ] } ], "source": [ "gamma = 1 # Also can demonstrate how to change gamma from 1\n", "\n", "# First the laser beams:\n", "laserBeams = {}\n", "laserBeams['$\\\\pi_z$']= pylcp.laserBeams([\n", " {'kvec': np.array([1., 0., 0.]), 'pol':np.array([0., 0., 1.]),\n", " 'pol_coord':'cartesian', 'delta':-2.73*gamma, 's':4*0.16*(1+2.73**2)}\n", " ])\n", "laserBeams['$\\\\pi_y$']= pylcp.laserBeams([\n", " {'kvec': np.array([0., 0., 1.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'cartesian', 'delta':-2.73*gamma, 's':4*0.16*(1+2.73**2)}\n", " ])\n", "laserBeams['$\\\\pi_x$']= pylcp.laserBeams([\n", " {'kvec': np.array([0., 0., 1.]), 'pol':np.array([1., 0., 0.]),\n", " 'pol_coord':'cartesian', 'delta':-2.73*gamma, 's':0.16*(1+2.73**2)},\n", " {'kvec': np.array([0., 0., -1.]), 'pol':np.array([1., 0., 0.]),\n", " 'pol_coord':'cartesian', 'delta':-2.73*gamma, 's':0.16*(1+2.73**2)}\n", " ])\n", "\n", "# Then the magnetic field:\n", "magField = lambda R: np.zeros(R.shape)\n", "\n", "# Hamiltonian for F=2->F=3\n", "H_g, muq_g = pylcp.hamiltonians.singleF(F=2, gF=1, muB=1)\n", "H_e, mue_q = pylcp.hamiltonians.singleF(F=3, gF=1, muB=1)\n", "d_q = pylcp.hamiltonians.dqij_two_bare_hyperfine(2, 3)\n", "hamiltonian = pylcp.hamiltonian()\n", "hamiltonian.add_H_0_block('g', H_g)\n", "hamiltonian.add_H_0_block('e', H_e-0.*np.eye(H_e.shape[0]))\n", "hamiltonian.add_d_q_block('g', 'e', d_q, gamma=gamma)\n", "\n", "hamiltonian.print_structure()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Evolve the density/populations\n", "Using both the `rateeq` and `obe`, we will calculate the population transfer." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 1.76 s. \n" ] } ], "source": [ "obe = {}\n", "rateeq = {}\n", "rateeq['$\\\\pi_z$'] = pylcp.rateeq(laserBeams['$\\\\pi_z$'], magField,\n", " hamiltonian)\n", "obe['$\\\\pi_z$'] = pylcp.obe(laserBeams['$\\\\pi_z$'], magField, hamiltonian,\n", " transform_into_re_im=transform)\n", "\n", "# Run the rate equations:\n", "N0 = np.zeros((rateeq['$\\\\pi_z$'].hamiltonian.n,))\n", "N0[0] = 1\n", "rateeq['$\\\\pi_z$'].set_initial_pop(N0)\n", "rateeq['$\\\\pi_z$'].evolve_populations([0, 600/gamma],\n", " max_step=1/gamma)\n", "\n", "# Run the OBEs:\n", "rho0 = np.zeros((obe['$\\\\pi_z$'].hamiltonian.n**2,))\n", "rho0[0] = 1.\n", "obe['$\\\\pi_z$'].set_initial_rho(np.real(rho0))\n", "obe['$\\\\pi_z$'].evolve_density(t_span=[0, 600/gamma],\n", " progress_bar=True)\n", "\n", "# Calculate the equilibrium populations:\n", "Neq = rateeq['$\\\\pi_z$'].equilibrium_populations(np.array([0., 0., 0.]),\n", " np.array([0., 0., 0.]), 0.)" ] }, { "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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1)\n", "for jj in range(5):\n", " ax.plot(gamma*rateeq['$\\\\pi_z$'].sol.t,\n", " rateeq['$\\\\pi_z$'].sol.y[jj, :], '--',\n", " color='C{0:d}'.format(jj),\n", " linewidth=1.0)\n", " ax.plot(gamma*obe['$\\\\pi_z$'].sol.t, np.abs(obe['$\\\\pi_z$'].sol.rho[jj, jj]), '-',\n", " color='C{0:d}'.format(jj),\n", " linewidth=0.5)\n", " ax.plot(gamma*obe['$\\\\pi_z$'].sol.t[-1], Neq[jj], '.', color='C{0:d}'.format(jj),\n", " linewidth=0.5)\n", "\n", "ax.set_xlabel('$\\\\Gamma t$')\n", "ax.set_ylabel('$\\\\rho_{ii}$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Check rotations\n", "\n", "Next, we want to check that our rotations are working properly, so we will\n", "run the same calculation for the $\\hat{z}$ going beam with $\\pi_y$ polarization. But\n", "before we even bother working with the OBE, we need to create the initial\n", "state first, which involves rotating our state." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 1.71 s. \n" ] } ], "source": [ "mug = spherical2cart(muq_g)\n", "S = -mug\n", "\n", "# What are the eigenstates of 'y'?\n", "E, U = np.linalg.eig(S[1])\n", "\n", "# Let's now define a rotation matrix that rotates us into the m_F basis alogn y:\n", "inds = np.argsort(E)\n", "E = E[inds]\n", "U = U[:, inds]\n", "Uinv = np.linalg.inv(U)\n", "\n", "# In a positive magnetic field with g_F>0, I want the lowest eigenvalue. That\n", "# corresponds to the -m_F state.\n", "psi = U[:, 0]\n", "\n", "# Now take that state and make the initial density matrix:\n", "rho0 = np.zeros((hamiltonian.n, hamiltonian.n), dtype='complex128')\n", "for ii in range(hamiltonian.ns[0]):\n", " for jj in range(hamiltonian.ns[0]):\n", " rho0[ii, jj] = psi[ii]*np.conjugate(psi[jj])\n", "\n", "#Print out the density matrix (in z-basis), and the rotated density matrix (in y-basis):\n", "#print(rho0[:5,:5])\n", "#print(Uinv@rho0[:5,:5]@U)\n", "\n", "# Evolve:\n", "obe['$\\\\pi_y$'] = pylcp.obe(laserBeams['$\\\\pi_y$'], magField, hamiltonian,\n", " transform_into_re_im=transform)\n", "obe['$\\\\pi_y$'].set_initial_rho(rho0.reshape(hamiltonian.n**2,))\n", "obe['$\\\\pi_y$'].evolve_density(t_span=[0, 600],\n", " progress_bar=True)\n", "\n", "# Now rotate the denisty matrix back to be along $y$:\n", "for jj in range(obe['$\\\\pi_y$'].sol.t.size):\n", " obe['$\\\\pi_y$'].sol.rho[:5, :5, jj] = Uinv@obe['$\\\\pi_y$'].sol.rho[:5, :5, jj]@U" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now plot it up:" ] }, { "cell_type": "code", "execution_count": 6, "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, 1)\n", "for jj in range(5):\n", " ax.plot(obe['$\\\\pi_y$'].sol.t,\n", " np.abs(obe['$\\\\pi_y$'].sol.rho[jj, jj]), '-',\n", " color='C{0:d}'.format(jj),\n", " linewidth=0.5)\n", "ax.set_xlabel('$\\\\Gamma t$')\n", "ax.set_ylabel('$\\\\rho_{ii}$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's do the same thing for $\\pi_x$, except this time we have two laser\n", "beams, with 1/4 of the intensity:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 1.97 s. \n" ] } ], "source": [ "# What are the eigenstates of 'y'?\n", "E, U = np.linalg.eig(S[0])\n", "\n", "inds = np.argsort(E)\n", "E = E[inds]\n", "U = U[:, inds]\n", "Uinv = np.linalg.inv(U)\n", "\n", "# In a positive magnetic field with g_F>0, I want the lowest eigenvalue. That\n", "# corresponds to the -m_F state.\n", "psi = U[:, 0]\n", "\n", "rho0 = np.zeros((hamiltonian.n, hamiltonian.n), dtype='complex128')\n", "for ii in range(hamiltonian.ns[0]):\n", " for jj in range(hamiltonian.ns[0]):\n", " rho0[ii, jj] = psi[ii]*np.conjugate(psi[jj])\n", "\n", "obe['$\\\\pi_x$'] = pylcp.obe(laserBeams['$\\\\pi_x$'], magField, hamiltonian,\n", " transform_into_re_im=transform)\n", "obe['$\\\\pi_x$'].set_initial_rho(rho0.reshape(hamiltonian.n**2,))\n", "obe['$\\\\pi_x$'].evolve_density(t_span=[0, 600],\n", " progress_bar=True)\n", "\n", "for jj in range(obe['$\\\\pi_x$'].sol.t.size):\n", " obe['$\\\\pi_x$'].sol.rho[:5, :5, jj] = Uinv@obe['$\\\\pi_x$'].sol.rho[:5, :5, jj]@U" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot this up too:" ] }, { "cell_type": "code", "execution_count": 8, "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, 1)\n", "for jj in range(5):\n", " ax.plot(obe['$\\\\pi_x$'].sol.t,\n", " np.abs(obe['$\\\\pi_x$'].sol.rho[jj, jj]), '-',\n", " color='C{0:d}'.format(jj),\n", " linewidth=0.5)\n", "ax.set_xlabel('$\\\\Gamma t$')\n", "ax.set_ylabel('$\\\\rho_{ii}$');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 4 }