{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two-Level: Sech Pulse 4π — Pulse Breakup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the Problem\n",
    "\n",
    "First we need to define a sech pulse with the area we want. We'll fix the width of the pulse and the area to find the right amplitude.\n",
    "\n",
    "The full-width at half maximum (FWHM) $t_s$ of the sech pulse is related to the FWHM of a Gaussian by a factor of $1/2.6339157938$. (See §3.2.2 of my [PhD thesis](https://github.com/tommyogden/phd-thesis))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_width 0.3796628587572578\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "SECH_FWHM_CONV = 1.0 / 2.6339157938\n",
    "t_width = 1.0 * SECH_FWHM_CONV  # [τ]\n",
    "print(\"t_width\", t_width)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mb_solve_json = \"\"\"\n",
    "{\n",
    "  \"atom\": {\n",
    "    \"fields\": [\n",
    "      {\n",
    "        \"coupled_levels\": [[0, 1]],\n",
    "        \"rabi_freq_t_args\": {\n",
    "          \"n_pi\": 4.0,\n",
    "          \"centre\": 0.0,\n",
    "          \"width\": %f\n",
    "        },\n",
    "        \"rabi_freq_t_func\": \"sech\"\n",
    "      }\n",
    "    ],\n",
    "    \"num_states\": 2\n",
    "  },\n",
    "  \"t_min\": -2.0,\n",
    "  \"t_max\": 10.0,\n",
    "  \"t_steps\": 240,\n",
    "  \"z_min\": -0.5,\n",
    "  \"z_max\": 1.5,\n",
    "  \"z_steps\": 100,\n",
    "  \"interaction_strengths\": [\n",
    "    10.0\n",
    "  ],\n",
    "  \"savefile\": \"mbs-two-sech-4pi\"\n",
    "}\n",
    "\"\"\" % (t_width)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from maxwellbloch import mb_solve\n",
    "\n",
    "mbs = mb_solve.MBSolve().from_json_str(mb_solve_json)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll just check that the pulse area is what we want."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The input pulse area is 3.986854595865458\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    \"The input pulse area is {0}\".format(\n",
    "        np.trapezoid(mbs.Omegas_zt[0, 0, :].real, mbs.tlist) / np.pi\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "Omegas_zt, states_zt = mbs.mbsolve(recalc=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "import seaborn as sns\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, 3.0, 11)\n",
    "cf = ax.contourf(\n",
    "    mbs.tlist,\n",
    "    mbs.zlist,\n",
    "    np.abs(mbs.Omegas_zt[0] / (2 * np.pi)),\n",
    "    cmap_range,\n",
    "    cmap=plt.cm.Blues,\n",
    ")\n",
    "ax.set_title(r\"Rabi Frequency ($\\Gamma / 2\\pi $)\")\n",
    "ax.set_xlabel(r\"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);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Pulse Area ($\\\\pi$)')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(16, 5))\n",
    "ax.plot(mbs.zlist, mbs.fields_area()[0] / np.pi)\n",
    "ax.set_ylim([0.0, 8.0])\n",
    "ax.set_xlabel(\"Distance ($L$)\")\n",
    "ax.set_ylabel(r\"Pulse Area ($\\pi$)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysis\n",
    "\n",
    "The $4 \\pi$ sech pulse breaks up into two $2 \\pi$ pulses, which travel at a speed according to their width."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Movie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# C = 0.1 # speed of light\n",
    "# Y_MIN = 0.0 # Y-axis min\n",
    "# Y_MAX = 4.0 # y-axis max\n",
    "# ZOOM = 2 # level of linear interpolation\n",
    "# FPS = 60 # frames per second\n",
    "# ATOMS_ALPHA = 0.2 # Atom indicator transparency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# FNAME = \"images/mb-solve-two-sech-4pi\"\n",
    "# FNAME_JSON = FNAME + '.json'\n",
    "# with open(FNAME_JSON, \"w\") as f:\n",
    "#     f.write(mb_solve_json)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !make-mp4-fixed-frame.py -f $FNAME_JSON -c $C --fps $FPS --y-min $Y_MIN --y-max $Y_MAX \\\n",
    "#     --zoom $ZOOM --atoms-alpha $ATOMS_ALPHA #--peak-line --c-line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# FNAME_MP4 = FNAME + '.mp4'\n",
    "# !make-gif-ffmpeg.sh -f $FNAME_MP4 --in-fps $FPS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from IPython.display import Image\n",
    "# Image(url=FNAME_MP4 +'.gif', format='gif')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "maxwellbloch",
   "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": "3.14.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}