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 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Two-Level: Sech Pulse 2π — Self-Induced Transparency"
   ]
  },
  {
   "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/tpogden/phd-thesis))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "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\": 2.0,\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\": 120,\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-2pi\"\n",
    "}\n",
    "\"\"\" % (t_width)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from maxwellbloch import mb_solve\n",
    "\n",
    "mb_solve_00 = 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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\n",
    "    \"The input pulse area is {0}\".format(\n",
    "        np.trapezoid(mb_solve_00.Omegas_zt[0, 0, :].real, mb_solve_00.tlist) / np.pi\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve the Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%time Omegas_zt, states_zt = mb_solve_00.mbsolve(recalc=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_style(\"darkgrid\")\n",
    "\n",
    "fig = plt.figure(1, figsize=(16, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "cmap_range = np.linspace(0.0, 1.0, 11)\n",
    "cf = ax.contourf(\n",
    "    mb_solve_00.tlist,\n",
    "    mb_solve_00.zlist,\n",
    "    np.abs(mb_solve_00.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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(16, 4))\n",
    "ax.plot(mb_solve_00.zlist, mb_solve_00.fields_area()[0] / np.pi, clip_on=False)\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 $2 \\pi$ sech pulse passes through, slowed but with shape unaltered. This is **self-induced transparency.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Movie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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 = 30 # frames per second\n",
    "# ATOMS_ALPHA = 0.2 # Atom indicator transparency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# FNAME = \"images/mb-solve-two-sech-2pi\"\n",
    "# FNAME_JSON = FNAME + '.json'\n",
    "# with open(FNAME_JSON, \"w\") as f:\n",
    "#     f.write(mb_solve_json)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# FNAME_MP4 = FNAME + '.mp4'\n",
    "# !make-gif-ffmpeg.sh -f $FNAME_MP4 --in-fps $FPS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from IPython.display import Image\n",
    "# Image(url=FNAME_MP4 +'.gif', format='gif')"
   ]
  }
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