examples/mb-solve-two-weak-pulse-very-few-atoms.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Two-Level: Weak Pulse through Very Few Atoms\n",
    "\n",
    "\n",
    "Time taken to solve this problem on a 2013 MacBook Pro:\n",
    "**37.3 s**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Define the Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "mb_solve_json = \"\"\"\n",
    "{\n",
    "  \"atom\": {\n",
    "    \"decays\": [\n",
    "      {\n",
    "        \"channels\": [[0, 1]],\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",
    "          \"ampl\": 1.0,\n",
    "          \"centre\": 0.0,\n",
    "          \"fwhm\": 1.0\n",
    "        },\n",
    "        \"rabi_freq_t_func\": \"gaussian\"\n",
    "      }\n",
    "    ],\n",
    "    \"num_states\": 2\n",
    "  },\n",
    "  \"t_min\": -2.0,\n",
    "  \"t_max\": 10.0,\n",
    "  \"t_steps\": 100,\n",
    "  \"z_min\": -0.2,\n",
    "  \"z_max\": 1.2,\n",
    "  \"z_steps\": 100,\n",
    "  \"z_steps_inner\": 2,\n",
    "  \"num_density_z_func\": \"square\",\n",
    "  \"num_density_z_args\": {\n",
    "    \"on\": 0.0,\n",
    "    \"off\": 1.0,\n",
    "    \"ampl\": 1.0\n",
    "  },\n",
    "  \"interaction_strengths\": [\n",
    "    0.1\n",
    "  ],\n",
    "  \"velocity_classes\": null,\n",
    "  \"method\": \"mesolve\",\n",
    "  \"opts\": {},\n",
    "  \"savefile\": \"qu/mb-solve-two-weak-pulse-very-few-atoms\"\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from maxwellbloch import mb_solve\n",
    "mb_solve_00 = mb_solve.MBSolve().from_json_str(mb_solve_json)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Solve the Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded tuple object.\n",
      "CPU times: user 2 ms, sys: 2.72 ms, total: 4.73 ms\n",
      "Wall time: 4.82 ms\n"
     ]
    }
   ],
   "source": [
    "%time Omegas_zt, states_zt = mb_solve_00.mbsolve(recalc=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Field Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "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",
    "sns.set_style('darkgrid')\n",
    "fig = plt.figure(1, figsize=(16, 6))\n",
    "ax = fig.add_subplot(111)\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_xlabel('Time ($1/\\Gamma$)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "for y in [0.0, 1.0]:\n",
    "    ax.axhline(y, c='grey', lw=1.0, ls='dotted')\n",
    "plt.colorbar(cf)\n",
    "plt.savefig('images/mb-solve-two-weak-pulse-very-few-atoms.png')"
   ]
  }
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