{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Adiabatic Rapid Passage\n", "\n", "This example covers an example with both laser frequency and amplitude modulation: rapid adiabatic passage. It reproduces Fig. 2 from T. Lu, X. Miao, and H. Metcalf, “Bloch theorem on the Bloch sphere” *Physical Review A* **71**, 061405(R) (2005), http://dx.doi.org/10.1103/PhysRevA.71.061405" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import solve_ivp\n", "import pylcp\n", "from pylcp.common import progressBar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code the basic Hamiltonian\n", "\n", "The Hamiltonian is a simple two-state Hamiltonian. Here, we code up a method to return the time-dependent Hamiltonian matrix to evolve it with the Schrodinger equation. We take the modulation to be the same as in Lu, *et. al.*, above: $\\Omega(t) = \\Omega_0\\sin(\\omega_m t)$ and $\\Delta=\\Delta_0\\cos(\\omega_m t)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def H(t, Delta0, Omega0, omegam):\n", " Delta = Delta0*np.cos(omegam*t)\n", " Omega = Omega0*np.sin(omegam*t)\n", " \n", " return 1/2*np.array([[Delta, Omega], [Omega, -Delta]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the problem in `pylcp`\n", "\n", "Unlike the above Hamiltonian, which is clearly time dependent, the only time dependence available to us in `pylcp` is through the fields. First, we need to remember for the amplitude modulation that $I/I_{\\rm sat} = 2\\Omega^2/\\Gamma^ = 2[\\Omega_0\\sin(\\omega_m t)]^2/\\Gamma^2$. Second, we need to frequency modulate the laser beams. Remember that if the lasers have a temporal phase $\\phi$, the frequency is $\\omega = \\frac{d\\phi}{dt}$. Thus, if the detuning $\\Delta(t)$ is specified, then $\\phi = \\int \\Delta (t)\\ dt$. `pylcp` contains a built-in integrator in order to convert the detuning to a phase, but it might not always be reliable. So you can also reproduce the detuning by modulating the phase $\\phi$. To reproduce the $\\Delta(t) = \\Delta_0\\cos(\\omega_m t)$, we need $\\phi = \\Delta_0/\\omega_m\\sin(\\omega_m t)$. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[(( 1x1), ( 1x1)) ( 1x1)]\n", " [( 1x1) (( 1x1), ( 1x1))]]\n" ] } ], "source": [ "def return_lasers(Delta0, Omega0, omegam):\n", " laserBeams = pylcp.laserBeams([\n", " {'kvec':np.array([1., 0., 0.]),\n", " 'pol':np.array([0., 0., 1.]),\n", " 'pol_coord':'cartesian',\n", " 'delta': lambda t: Delta0*np.cos(omegam*t),\n", " 'phase': 0,#lambda t: Delta0/omegam*np.sin(omegam*t),\n", " 's': lambda R, t: 2*(Omega0*np.sin(omegam*t))**2\n", " }])\n", " \n", " return laserBeams\n", "\n", "magField = lambda R: np.zeros(R.shape)\n", "\n", "# Now define the extremely simple Hamiltonian:\n", "Hg = np.array([[0.]])\n", "mugq = np.array([[[0.]], [[0.]], [[0.]]])\n", "He = np.array([[0.]])\n", "mueq = np.array([[[0.]], [[0.]], [[0.]]])\n", "dijq = np.array([[[0.]], [[1.]], [[0.]]])\n", "\n", "gamma = 1.\n", "\n", "hamiltonian = pylcp.hamiltonian(Hg, He, mugq, mueq, dijq, gamma=gamma)\n", "hamiltonian.print_structure()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Evolve a single state\n", "\n", "We solve with both the Schrodinger Equation and the OBEs. We can play with the modulation parameters ($\\Delta_0$, $\\Omega_0$, $\\omega_m$), and see how the result chanages." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "Delta0 = 5.\n", "Omega0 = 10.\n", "omegam = 1.\n", "\n", "t = np.linspace(0., np.pi/omegam, 201)\n", "sol_SE = solve_ivp(lambda t, y: -1j*H(t, Delta0, Omega0, omegam)@y, [0, np.pi/omegam],\n", " np.array([1., 0.], dtype='complex128'), t_eval=t)\n", "\n", "laserBeams = return_lasers(Delta0, Omega0, omegam)\n", "obe = pylcp.obe(laserBeams, magField, hamiltonian)\n", "obe.ev_mat['decay'] = np.zeros(obe.ev_mat['decay'].shape) # Turn off damping to compare to Schrodinger Equation.\n", "obe.set_initial_rho_from_populations(np.array([1., 0.]))\n", "sol_OBE = obe.evolve_density([0, np.pi/omegam], t_eval=t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot it up. Dashed is OBEs from `pylcp` and solid is the Schrodiner equation. Orange is the $|1\\rangle$ state; blue is the $|0\\rangle$ state." ] }, { "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": [ "fig, ax = plt.subplots(1, 1)\n", "ax.plot(sol_SE.t, np.abs(sol_SE.y[0])**2, linewidth=0.75)\n", "ax.plot(sol_SE.t, np.abs(sol_SE.y[1])**2, linewidth=0.75)\n", "ax.plot(sol_OBE.t, np.real(sol_OBE.rho[0, 0]), '--', color='C0', linewidth=1.25)\n", "ax.plot(sol_OBE.t, np.real(sol_OBE.rho[1, 1]), '--', color='C1', linewidth=1.25)\n", "ax.set_xlabel('$\\omega_m t$')\n", "ax.set_ylabel('$\\\\rho_{ii}$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reproduce Fig. 2\n", "\n", "This involves scanning over $\\Delta_0$ and $\\Omega_0$. This takes a long time, only because there is a fair amount of overhead in regenerating the optical Bloch equations on every iteration." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 8:02. \n" ] } ], "source": [ "Delta0s = np.arange(0.25, 25.1, 0.25)\n", "Omega0s = np.arange(0.25, 25.1, 0.25)\n", "t = np.linspace(0., np.pi, 201)\n", "\n", "DELTA0S, OMEGA0S = np.meshgrid(Delta0s, Omega0s)\n", "\n", "it = np.nditer([DELTA0S, OMEGA0S, None])\n", "\n", "progress = progressBar()\n", "\n", "for (Delta0, Omega0, rhogg) in it:\n", " del laserBeams\n", " \n", " # Set up new laser beams:\n", " laserBeams = return_lasers(Delta0, Omega0, omegam)\n", " \n", " # Set up OBE:\n", " obe = pylcp.obe(laserBeams, magField, hamiltonian)\n", " obe.ev_mat['decay'] = np.zeros(obe.ev_mat['decay'].shape) # Turn off damping to compare to Schrodinger Equation.\n", " obe.set_initial_rho_from_populations(np.array([1., 0.]))\n", " \n", " # Solve:\n", " sol_OBE = obe.evolve_density([0, np.pi], t_eval=t)\n", " \n", " # Save result:\n", " rhogg[...] = np.real(sol_OBE.rho[0, 0, -1])\n", " \n", " # Update progress bar:\n", " progress.update((it.iterindex+1)/it.itersize)\n", " \n", "RHOGG = it.operands[2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot it up:" ] }, { "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": [ "dDelta0 = np.mean(np.diff(Delta0s))\n", "dOmega0 = np.mean(np.diff(Omega0s))\n", "fig, ax = plt.subplots(1, 1)\n", "im = ax.imshow(RHOGG, origin='lower',\n", " extent=(np.amin(Delta0s)-dDelta0/2, np.amax(Delta0s)+dDelta0/2,\n", " np.amin(Omega0s)-dOmega0/2, np.amax(Omega0s)+dOmega0/2),\n", " aspect='auto')\n", "ax_cbar = plt.colorbar(im)\n", "ax_cbar.set_label('$\\\\rho_{gg}$')\n", "ax.set_xlabel('$\\Delta_0/\\omega_m$')\n", "ax.set_ylabel('$\\Omega_0/\\omega_m$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Add in damping\n", "\n", "These two cells are exactly the same as above, except the user must now specify $\\omega_m/\\Gamma$ ($\\Gamma=1$) and we merely comment out the line that eliminate the damping part of the OBEs." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 7:22. \n" ] } ], "source": [ "omegam = 2\n", "Delta0s = np.arange(0.25, 25.1, 0.25) # These will be normalized to the value of omegam\n", "Omega0s = np.arange(0.25, 25.1, 0.25)\n", "t = np.linspace(0., np.pi/omegam, 201)\n", "\n", "DELTA0S, OMEGA0S = np.meshgrid(Delta0s, Omega0s)\n", "\n", "it = np.nditer([DELTA0S, OMEGA0S, None])\n", "\n", "progress = progressBar()\n", "\n", "for (Delta0, Omega0, rhogg) in it:\n", " # Set up new laser beams:\n", " laserBeams = return_lasers(omegam*Delta0, omegam*Omega0, omegam)\n", " \n", " # Set up OBE:\n", " obe = pylcp.obe(laserBeams, magField, hamiltonian)\n", " obe.set_initial_rho_from_populations(np.array([1., 0.]))\n", " \n", " # Solve:\n", " sol_OBE = obe.evolve_density([0, np.pi/omegam], t_eval=t)\n", " \n", " # Save result:\n", " rhogg[...] = np.real(sol_OBE.rho[0, 0, -1])\n", " \n", " # Update progress bar:\n", " progress.update((it.iterindex+1)/it.itersize)\n", " \n", "RHOGG = it.operands[2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot it up:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dDelta0 = np.mean(np.diff(Delta0s))\n", "dOmega0 = np.mean(np.diff(Omega0s))\n", "fig, ax = plt.subplots(1, 1)\n", "im = ax.imshow(RHOGG, origin='lower',\n", " extent=(np.amin(Delta0s)-dDelta0/2, np.amax(Delta0s)+dDelta0/2,\n", " np.amin(Omega0s)-dOmega0/2, np.amax(Omega0s)+dOmega0/2),\n", " aspect='auto', clim=(0, 1))\n", "ax_cbar = plt.colorbar(im)\n", "ax_cbar.set_label('$\\\\rho_{gg}$')\n", "ax.set_xlabel('$\\Delta_0/\\omega_m$')\n", "ax.set_ylabel('$\\Omega_0/\\omega_m$');" ] } ], "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 }