examples/mb-solve-lambda-weak-pulse-cloud-atoms-some-coupling-store.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Λ-Type Three-Level: Weak Pulse with Time-Dependent Coupling in a Cloud — Storage and Retrieval\n",
    "\n",
    "Time taken to solve this problem on a 2013 MacBook Pro:\n",
    "**2h 32min 15s**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mb_solve_json = \"\"\"\n",
    "{\n",
    "  \"atom\": {\n",
    "    \"decays\": [\n",
    "      { \"channels\": [[0,1], [1,2]], \n",
    "        \"rate\": 0.0\n",
    "      }\n",
    "    ],\n",
    "    \"energies\": [],\n",
    "    \"fields\": [\n",
    "      {\n",
    "        \"coupled_levels\": [[0, 1]],\n",
    "        \"detuning\": 0.0,\n",
    "        \"detuning_positive\": true,\n",
    "        \"label\": \"probe\",\n",
    "        \"rabi_freq\": 1.0e-3,\n",
    "        \"rabi_freq_t_args\": \n",
    "          {\n",
    "             \"ampl\": 1.0,\n",
    "             \"centre\": 0.0,\n",
    "             \"fwhm\": 1.0\n",
    "          },\n",
    "        \"rabi_freq_t_func\": \"gaussian\"\n",
    "      },\n",
    "      {\n",
    "        \"coupled_levels\": [[1, 2]],\n",
    "        \"detuning\": 0.0,\n",
    "        \"detuning_positive\": false,\n",
    "        \"label\": \"coupling\",\n",
    "        \"rabi_freq\": 5.0,\n",
    "        \"rabi_freq_t_args\": \n",
    "        {\n",
    "          \"ampl\": 1.0,\n",
    "          \"fwhm\": 0.2,\n",
    "          \"off\": 4.0, \n",
    "          \"on\": 6.0\n",
    "          },\n",
    "        \"rabi_freq_t_func\": \"ramp_offon\"\n",
    "      }\n",
    "    ],\n",
    "    \"num_states\": 3\n",
    "  },\n",
    "  \"t_min\": -2.0,\n",
    "  \"t_max\": 12.0,\n",
    "  \"t_steps\": 140,\n",
    "  \"z_min\": -0.2,\n",
    "  \"z_max\": 1.2,\n",
    "  \"z_steps\": 140,\n",
    "  \"z_steps_inner\": 50,\n",
    "  \"num_density_z_func\": \"gaussian\",\n",
    "  \"num_density_z_args\": {\n",
    "    \"ampl\": 1.0,\n",
    "    \"fwhm\": 0.5,\n",
    "    \"centre\": 0.5\n",
    "  },\n",
    "  \"interaction_strengths\": [1.0e3, 1.0e3],\n",
    "  \"velocity_classes\": null,\n",
    "  \"method\": \"mesolve\",\n",
    "  \"opts\": {},\n",
    "  \"savefile\": \"qu/mb-solve-lambda-weak-pulse-cloud-atoms-some-coupling-store\" \n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from maxwellbloch import mb_solve\n",
    "mb_solve_00 = mb_solve.MBSolve().from_json_str(mb_solve_json)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve the Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded tuple object.\n",
      "CPU times: user 2.77 ms, sys: 7.44 ms, total: 10.2 ms\n",
      "Wall time: 12.1 ms\n"
     ]
    }
   ],
   "source": [
    "%time Omegas_zt, states_zt = mb_solve_00.mbsolve(recalc=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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WQvcBAABA6hk9epDdSwDgYoR+Qzw6bszxmnr+hd2PdHZ06I2Gem147mlJSjj4AwAApIMd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\nMSKzZs0a7JwAAADAQepX6f/MZz6TJDnjjDNyxhlnpLm5OUmyadOmPrf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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bd8bef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "fig = plt.figure(1, figsize=(16, 12))\n",
    "\n",
    "# Probe \n",
    "ax = fig.add_subplot(211)\n",
    "cmap_range = np.linspace(0.0, 1.0e-3, 11)\n",
    "cf = ax.contourf(mb_solve_00.tlist, mb_solve_00.zlist, \n",
    "                 np.abs(mb_solve_00.Omegas_zt[0]/(2*np.pi)), \n",
    "                 cmap_range, cmap=plt.cm.Blues)\n",
    "ax.set_title('Rabi Frequency ($\\Gamma / 2\\pi $)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "ax.text(0.02, 0.95, 'Probe',\n",
    "        verticalalignment='top', horizontalalignment='left',\n",
    "        transform=ax.transAxes, color='grey', fontsize=16)\n",
    "plt.colorbar(cf)\n",
    "\n",
    "# Coupling\n",
    "ax = fig.add_subplot(212)\n",
    "cmap_range = np.linspace(0.0, 8.0, 11)\n",
    "cf = ax.contourf(mb_solve_00.tlist, mb_solve_00.zlist, \n",
    "                 np.abs(mb_solve_00.Omegas_zt[1]/(2*np.pi)), \n",
    "                 cmap_range, cmap=plt.cm.Greens)\n",
    "ax.set_xlabel('Time ($1/\\Gamma$)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "ax.text(0.02, 0.95, 'Coupling',\n",
    "        verticalalignment='top', horizontalalignment='left',\n",
    "        transform=ax.transAxes, color='grey', fontsize=16)\n",
    "plt.colorbar(cf)\n",
    "\n",
    "# Both\n",
    "for ax in fig.axes:\n",
    "    for y in [0.0, 1.0]:\n",
    "        ax.axhline(y, c='grey', lw=1.0, ls='dotted')\n",
    "plt.tight_layout()\n",
    "plt.savefig('images/mb-solve-lambda-weak-pulse-cloud-atoms-some-coupling-store.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysis\n",
    "\n",
    "From my [thesis](https://github.com/tommyogden/phd-thesis), §4.3.3.\n",
    "\n",
    "> We see that the effect is that the pulse envelope vanishes as the coupling field is ramped down, but returns dramatically, with the same profile, as the coupling field is ramped back up. It appears as though the light has been ‘stopped’ by the medium before being allowed to continue on its way.\n",
    "\n",
    "> We can understand this behaviour by considering the propagation of the dark state polariton in this system. Ramping down the driving field envelope once the pulse is in the medium equates to rotating the mixing angle $\\theta \\rightarrow \\pi/2$ such that it is coherently mapped on to the spin wave. At a time later we ramp up the driving field, rotating the mixing angle back to its previous position, and the field continues on its way.\n",
    "\n",
    "> Although the storage and retrieval of dark-state polaritons is often described as ‘stopping light’, we must be careful to note that it is really a coherent transfer of energy to the medium. No elecromagnetic field envelope remains at the limit $\\theta = \\pi/2$, so the light itself is not ‘stopped’, it has been transferred into a spin excitation.\n",
    "\n",
    ">It is important to consider the limitations of these techniques. First, for eit and associated slow light effect, the duration of the pulse tw must be greater than the reciprocal of the eit bandwidth, so that spectrally\n",
    "it propagates in the transparency window. Second, for storage of the entire pulse to be possible, the spatial extent of the pulse must be compressed below the length $L$ of the medium, which is possible only if the medium has a sufficiently large optical depth such that $NgL \\gg 1$. "
   ]
  }
 ],
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