{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Three-level susceptibility & EIT\n", "\n", "This example demonstrates damped Rabi flopping as calculated with the optical\n", "Bloch equations for a three level system and calculates the three-level susceptibility\n", "to demonstrate EIT. It the first example with a three-manifold sytem, so we will focus on \n", "the construction of the Hamiltonian. \n", "\n", "State notation used within:\n", "```\n", " ---- |e>\n", "\n", "\n", "\n", " ---- |r>\n", " ---- |g>\n", "\n", "```\n", "The three level detuning $\\delta$ and two level detuning $\\Delta$ are the standard detunings for a $\\Lambda$ system." ] }, { "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", "### Hamiltonian\n", "\n", "To construct the three-manifold Hamiltonian, we add the blocks to Hamiltonian one at a time. The order in which they are added is important, as the manifolds are assumed to be in increasing energy order, even though their field-independent elements should already be placed in the appropriate rotating frames, implying that those elements should not contain optical-frequency components.\n", "\n", "Our three manifold system is really quite simple, with each manifold containing a single state. Detunings are placed on the $|r\\rangle$ and $|e\\rangle$ states. Finally, the states are connected through $\\pi$-polarized light. We write a method to return the Hamiltonian given the specified detunings." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[( 1x1) None ( 1x1)]\n", " [None ( 1x1) ( 1x1)]\n", " [( 1x1) ( 1x1) ( 1x1)]]\n" ] } ], "source": [ "Delta = -2; delta = 0.\n", "\n", "H0 = np.array([[1.]])\n", "mu_q = np.zeros((3, 1, 1))\n", "d_q = np.zeros((3, 1, 1))\n", "d_q[1, 0, 0,] = 1/np.sqrt(2)\n", "\n", "def return_three_level_hamiltonian(Delta, delta):\n", " hamiltonian = pylcp.hamiltonian()\n", " hamiltonian.add_H_0_block('g', 0.*H0)\n", " hamiltonian.add_H_0_block('r', delta*H0)\n", " hamiltonian.add_H_0_block('e', -Delta*H0)\n", " hamiltonian.add_d_q_block('g','e', d_q)\n", " hamiltonian.add_d_q_block('r','e', d_q)\n", "\n", " return hamiltonian\n", "\n", "hamiltonian = return_three_level_hamiltonian(Delta, delta)\n", "hamiltonian.print_structure()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lasers and magnetic fields\n", "\n", "Here, a method returns the lasers for a given intensity. Note that function returns a dictionary of two lasers, one addressing the $|g\\rangle \\rightarrow |e\\rangle$ transition and the other the $|r\\rangle \\rightarrow |e\\rangle$ transition. Finally, we assume a constant zero magnitude magnetic field." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# First, define the lasers (functionalized for later):\n", "Ige = 4; Ire = 4;\n", "def return_three_level_lasers(Ige, Ire):\n", " laserBeams = {}\n", " laserBeams['g->e'] = pylcp.laserBeams(\n", " [{'kvec':np.array([1., 0., 0.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'spherical', 'delta':0., 's':Ige}],\n", " beam_type=pylcp.infinitePlaneWaveBeam\n", " )\n", " laserBeams['r->e'] = pylcp.laserBeams(\n", " [{'kvec':np.array([1., 0., 0.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'spherical', 'delta':0., 's':Ire}], \n", " beam_type=pylcp.infinitePlaneWaveBeam\n", " )\n", " return laserBeams\n", "\n", "laserBeams = return_three_level_lasers(Ige, Ire)\n", "\n", "# Second, magnetic field:\n", "magField = lambda R: np.zeros(R.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Damped Rabi oscillations\n", "\n", "We first evolve the optical Bloch equations to see damped Rabi oscillations in the three-level system." ] }, { "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": [ "obe = pylcp.obe(laserBeams, magField, hamiltonian,\n", " transform_into_re_im=True)\n", "obe.set_initial_rho_from_populations(np.array([0., 1., 0.]))\n", "obe.evolve_density([0, 100])\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6.5, 2.75))\n", "ax[0].plot(obe.sol.t/2/np.pi, np.real(obe.sol.rho[0, 0]), linewidth=0.5, label='$\\\\rho_{gg}$')\n", "ax[0].plot(obe.sol.t/2/np.pi, np.real(obe.sol.rho[1, 1]), linewidth=0.5, label='$\\\\rho_{rr}$')\n", "ax[0].plot(obe.sol.t/2/np.pi, np.real(obe.sol.rho[2, 2]), linewidth=0.5, label='$\\\\rho_{ee}$')\n", "ax[0].plot(obe.sol.t/2/np.pi, np.real(obe.sol.rho[0, 0]+obe.sol.rho[1, 1]+obe.sol.rho[2, 2]), 'k--', linewidth=0.5)\n", "ax[0].legend(fontsize=7)\n", "ax[0].set_xlabel('$\\Gamma t$')\n", "ax[0].set_ylabel('$\\\\rho_{ii}$')\n", "\n", "ax[1].plot(obe.sol.t/2/np.pi, np.real(obe.sol.rho[0, 1]), linewidth=0.5,\n", " label='Re$[\\\\rho_{gr}]$')\n", "ax[1].plot(obe.sol.t/2/np.pi, np.imag(obe.sol.rho[0, 1]), linewidth=0.5,\n", " label='Im$[\\\\rho_{gr}]$')\n", "ax[1].plot(obe.sol.t/2/np.pi, np.abs(obe.sol.rho[0, 1]), 'k-',\n", " label='$|\\\\rho_{gr}|$')\n", "ax[1].plot(obe.sol.t/2/np.pi, np.abs(obe.sol.rho[0, 2]), linewidth=0.5, label='$|\\\\rho_{ge}|$')\n", "ax[1].plot(obe.sol.t/2/np.pi, np.abs(obe.sol.rho[1, 2]), linewidth=0.5, label='$|\\\\rho_{re}|$')\n", "ax[1].legend(fontsize=7)\n", "ax[1].set_xlabel('$\\Gamma t$')\n", "\n", "fig.subplots_adjust(wspace=0.15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Susceptibility and EIT\n", "\n", "To see EIT, we want to compute the susceptibility of the laser addressed to the $|r\\rangle \\rightarrow |e\\rangle$ transition, which is proportional to $\\rho_{re}$. We will use our methods returning the appropriate lasers and Hamiltonian to loop through several three level detunings $\\delta$ and two level detunings $\\Delta$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "Deltas = np.array([-5., -1., -0.1])\n", "deltas = np.arange(-7., 7., 0.1)\n", "delta_random = np.random.choice(deltas)\n", "\n", "it = np.nditer(np.meshgrid(Deltas, deltas)+ [None,])\n", "\n", "laserBeams = return_three_level_lasers(1, 0.1)\n", "for Delta, delta, rhore in it:\n", " hamiltonian = return_three_level_hamiltonian(Delta, delta)\n", " obe = pylcp.obe(laserBeams, magField, hamiltonian,\n", " transform_into_re_im=True)\n", " obe.set_initial_rho_from_populations([0, 1, 0])\n", " obe.evolve_density([0, 2*np.pi*5])\n", "\n", " rhore[...] = np.abs(obe.sol.rho[1, 2, -1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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(3, 1, figsize=(3.25, 2.75))\n", " \n", "for ii, row in enumerate(it.operands[2].T):\n", " ax[ii].plot(deltas, 1e2*row**2, linewidth=0.75)\n", " ax[ii].set_xlim(-7, 7)\n", " if ii<2:\n", " ax[ii].xaxis.set_ticklabels('')\n", "ax[1].set_ylabel('$10^2|\\\\rho_{re}|^2$')\n", "ax[-1].set_xlabel('$\\delta/\\Gamma$')\n", "\n", "fig.subplots_adjust(bottom=0.15, left=0.13)" ] } ], "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 }