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   "cell_type": "markdown",
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   "source": [
    "# Two-Level: Weak Square Pulse with Decay"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define and Solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mb_solve_json = \"\"\"\n",
    "{\n",
    "  \"atom\": {\n",
    "    \"decays\": [\n",
    "      {\n",
    "        \"channels\": [[0, 1]],\n",
    "        \"rate\": 1.0\n",
    "      }\n",
    "    ],\n",
    "    \"energies\": [],\n",
    "    \"fields\": [\n",
    "      {\n",
    "        \"coupled_levels\": [[0, 1]],\n",
    "        \"detuning\": 0.0,\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\": 20,\n",
    "  \"interaction_strengths\": [\n",
    "    1.0\n",
    "  ]\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from maxwellbloch import mb_solve\n",
    "\n",
    "mbs = mb_solve.MBSolve().from_json_str(mb_solve_json)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Omegas_zt, states_zt = mbs.mbsolve()"
   ]
  },
  {
   "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\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import interpolate\n",
    "\n",
    "plt.plot(mbs.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(\n",
    "    mbs.tlist, (Omegas_zt[0, 0].real / (2 * np.pi) - half_max), s=0\n",
    ")\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(\n",
    "    \"FWHM: \" + \"%0.2f\" % (r2 - r1),\n",
    "    xy=((r2 + r1) / 2, half_max),\n",
    "    xycoords=\"data\",\n",
    "    xytext=(25, 0),\n",
    "    textcoords=\"offset points\",\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Field Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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(\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);"
   ]
  }
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