examples/mb-solve-two-weak-square-few-atoms.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Two-Level: Weak Square through Few Atoms\n",
    "\n",
    "Time taken to solve this problem on a 2013 MacBook Pro:\n",
    "**40.3 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",
    "          \"on\": -0.5,\n",
    "          \"off\": 0.5\n",
    "        },\n",
    "        \"rabi_freq_t_func\": \"square\"\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\": 1,\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",
    "    1.0\n",
    "  ],\n",
    "  \"velocity_classes\": {},\n",
    "  \"method\": \"mesolve\",\n",
    "  \"opts\": {},\n",
    "  \"savefile\": \"qu/mb-solve-two-weak-square-few-atoms\"\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "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 2.1 ms, sys: 2.51 ms, total: 4.61 ms\n",
      "Wall time: 5.04 ms\n"
     ]
    }
   ],
   "source": [
    "%time Omegas_zt, states_zt = mb_solve_00.mbsolve(recalc=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Check the Input Pulse Profile\n",
    "\n",
    "We'll just confirm that the input pulse has the profile that we want: a Gaussian with an amplitude of $1.0 \\Gamma$ and a full-width at half maximum (FWHM) of $1.0 \\tau$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(25,0,'FWHM: 0.96')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import interpolate\n",
    "\n",
    "plt.plot(mb_solve_00.tlist, Omegas_zt[0,0].real/(2*np.pi))\n",
    "\n",
    "half_max = np.max(Omegas_zt[0,0].real/(2*np.pi))/2\n",
    "spline = interpolate.UnivariateSpline(mb_solve_00.tlist,\n",
    "                                      (Omegas_zt[0,0].real/(2*np.pi)-half_max), s=0)\n",
    "r1, r2 = spline.roots()\n",
    "\n",
    "# draw line at FWHM\n",
    "plt.hlines(y=half_max, xmin=r1, xmax=r2, linestyle='dotted')\n",
    "plt.annotate('FWHM: ' + '%0.2f'%(r2 - r1), xy=((r2+r1)/2, half_max),\n",
    "              xycoords='data',\n",
    "              xytext=(25, 0), textcoords='offset points')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Field Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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-square-few-atoms.png')"
   ]
  }
 ],
 "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": "3.5.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}