{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# STIRAP\n", "\n", "This example calculates the basic STIRAP effect. It demonstrates how to modulate the intensity of a laser with time in `pylcp` to get an interesting physical effect." ] }, { "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", "This is the same as in the [last example](07_three_level_susceptibility.ipynb) in setting up the three state system, except here we add a temporal Gaussian modulation to the intensity of the laser beam. Most STIRAP literature uses $\\Omega$ rather than $I$, so remember that $I/I_{\\rm sat} = 2\\Omega^2/\\Gamma^2$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# First, define the lasers (functionalized for later):\n", "def return_three_level_lasers(Omegage, Omegare, t0, tsep, twid):\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.,\n", " 's':lambda R, t: 2*(Omegage*np.exp(-(t-t0-tsep/2)**2/2/twid**2))**2}],\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.,\n", " 's':lambda R, t: 2*(Omegare*np.exp(-(t-t0+tsep/2)**2/2/twid**2))**2}],\n", " )\n", " return laserBeams\n", "\n", "# Second, magnetic field:\n", "magField = lambda R: np.zeros(R.shape)\n", "\n", "# Now define the Hamiltonian (functionaized for later):\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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Evolve the density\n", "\n", "Let us evolve with the correct pulse order (address $r\\rightarrow e$ before $g\\rightarrow e$) and also the incorrect, opposite order. For simplicity, we choose a saturation parameter of 2 to get a $\\Omega=\\Gamma$ at the peak." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 1.41 s. \n", "Completed in 1.03 s. \n" ] } ], "source": [ "hamiltonian = return_three_level_hamiltonian(-3, 0)\n", "laserBeams = return_three_level_lasers(1, 1, 500, -125., 100)\n", "\n", "obe = pylcp.obe(laserBeams, magField, hamiltonian)\n", "obe.set_initial_rho_from_populations(np.array([1., 0., 0.]))\n", "sol1 = obe.evolve_density([0, 1000], progress_bar=True)\n", "\n", "laserBeams = return_three_level_lasers(1, 1, 500., 125., 100.)\n", "\n", "obe = pylcp.obe(laserBeams, magField, hamiltonian)\n", "obe.set_initial_rho_from_populations(np.array([1., 0., 0.]))\n", "sol2 = obe.evolve_density([0, 1000], progress_bar=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot up the state populations $\\rho_{gg}$ (blue), $\\rho_{rr}$ (orange), and $\\rho_{ee}$ (green) vs. time. We see that STIRAP is only effective in the correct order (solid), and it maintains a minium of population in $|e\\rangle>$. The incorrect order (dashed) is nearly completely ineffective at state transfer. " ] }, { "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(2, 1, figsize=(3.25, 2.))\n", "factors = [1, 1, 1e2]\n", "linespecs = ['-', '--', '-.']\n", "for ii, factor in enumerate(factors):\n", " ax[0].plot(sol1.t/1e3, factor*np.real(sol1.rho[ii, ii]),\n", " linespecs[ii], color='C%d'%ii, linewidth=0.75)\n", " ax[1].plot(sol2.t/1e3, factor*np.real(sol2.rho[ii, ii]),\n", " linespecs[ii], color='C%d'%ii, linewidth=0.75)\n", "\n", "[ax[ii].set_ylabel('$\\\\rho_{ii}$') for ii in range (2)];\n", "[ax[ii].set_xlim((0, 1)) for ii in range(2)];\n", "ax[1].set_xlabel('$\\Gamma t$')\n", "ax[0].xaxis.set_ticklabels('')\n", "ax[0].text(0.25, 0.4,'$\\\\times100$',fontsize=7, color='C2')\n", "ax[1].text(0.46, 0.075,'$\\\\times100$',fontsize=7, color='C2')\n", "fig.subplots_adjust(bottom=0.18, left=0.14)" ] } ], "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 }