docs/examples/mbs-vee-sech-sqrt8pi-sqrt8pi-collision.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "# V-Type Three-Level: Solitons form Simulton\n",
    "\n",
    "In this example, a soliton is put in on both the probe and the coupling fields."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "sech_fwhm_conv = 1./2.6339157938\n",
    "t_width = 1.0*sech_fwhm_conv # [τ]\n",
    "\n",
    "print('t_width', t_width)\n",
    "\n",
    "n_1 = np.sqrt(8) # For a pulse area of nπ    \n",
    "ampl_1 = n_1/t_width/(2*np.pi) # Pulse amplitude [2π Γ]\n",
    "\n",
    "print('ampl_1', ampl_1)\n",
    "\n",
    "n_2 = np.sqrt(8) # For a pulse area of nπ    \n",
    "ampl_2 = n_2/t_width/(2*np.pi) # Pulse amplitude [2π Γ]\n",
    "\n",
    "print('ampl_2', ampl_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.sqrt(n_1**2 + n_2**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mb_solve_json = \"\"\"\n",
    "{{\n",
    "  \"atom\": {{\n",
    "    \"fields\": [\n",
    "      {{\n",
    "        \"coupled_levels\": [[0, 1]],\n",
    "        \"label\": \"probe\",\n",
    "        \"rabi_freq\": 1.0,\n",
    "        \"rabi_freq_t_args\": \n",
    "          {{\n",
    "             \"ampl\": {ampl_1},\n",
    "             \"centre\": 0.0,\n",
    "             \"width\": {t_width}\n",
    "          }},\n",
    "        \"rabi_freq_t_func\": \"sech\"\n",
    "      }},\n",
    "      {{\n",
    "        \"coupled_levels\": [[0, 2]],\n",
    "        \"label\": \"coupling\",\n",
    "        \"rabi_freq\": 1.0,\n",
    "        \"rabi_freq_t_args\": \n",
    "          {{\n",
    "             \"ampl\": {ampl_2},\n",
    "             \"centre\": 3.0,\n",
    "             \"width\": {t_width}\n",
    "          }},\n",
    "        \"rabi_freq_t_func\": \"sech\"\n",
    "      }}\n",
    "    ],\n",
    "    \"num_states\": 3\n",
    "  }},\n",
    "  \"t_min\": -2.0,\n",
    "  \"t_max\": 14.0,\n",
    "  \"t_steps\": 200,\n",
    "  \"z_min\": -0.5,\n",
    "  \"z_max\": 1.5,\n",
    "  \"z_steps\": 500,\n",
    "  \"z_steps_inner\": 1,\n",
    "  \"interaction_strengths\": [50.0, 10.0],\n",
    "  \"savefile\": \"mbs-vee-sech-sqrt8pi-sqrt8pi-collision\"\n",
    "}}\n",
    "\"\"\".format(ampl_1=ampl_1, t_width=t_width, ampl_2=ampl_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from maxwellbloch import mb_solve\n",
    "mb_solve_00 = mb_solve.MBSolve().from_json_str(mb_solve_json)\n",
    "\n",
    "%time Omegas_zt, states_zt = mb_solve_00.mbsolve(recalc=False, pbar_chunk_size=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_style('darkgrid')\n",
    "fig = plt.figure(1, figsize=(16, 12))\n",
    "\n",
    "# Probe \n",
    "ax = fig.add_subplot(211)\n",
    "# cmap_range = np.linspace(0.0, 0.8, 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, \n",
    "                 cmap=plt.cm.Blues)\n",
    "ax.set_title('Rabi Frequency ($\\Gamma / 2\\pi $)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "ax.text(0.02, 0.95, 'Probe',\n",
    "        verticalalignment='top', horizontalalignment='left',\n",
    "        transform=ax.transAxes, color='grey', fontsize=16)\n",
    "plt.colorbar(cf)\n",
    "\n",
    "# Coupling\n",
    "ax = fig.add_subplot(212)\n",
    "# cmap_range = np.linspace(0.0, 0.8, 11)\n",
    "cf = ax.contourf(mb_solve_00.tlist, mb_solve_00.zlist, \n",
    "                 np.abs(mb_solve_00.Omegas_zt[1]/(2*np.pi)), \n",
    "#                  cmap_range, \n",
    "                 cmap=plt.cm.Greens)\n",
    "ax.set_xlabel('Time ($1/\\Gamma$)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "ax.text(0.02, 0.95, 'Coupling',\n",
    "        verticalalignment='top', horizontalalignment='left',\n",
    "        transform=ax.transAxes, color='grey', fontsize=16)\n",
    "plt.colorbar(cf)\n",
    "\n",
    "# Both\n",
    "for ax in fig.axes:\n",
    "    for y in [0.0, 1.0]:\n",
    "        ax.axhline(y, c='grey', lw=1.0, ls='dotted')\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "total_area = np.sqrt(mb_solve_00.fields_area()[0]**2 + mb_solve_00.fields_area()[1]**2)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(16, 4))\n",
    "ax.plot(mb_solve_00.zlist, mb_solve_00.fields_area()[0]/np.pi, label='Probe', clip_on=False)\n",
    "ax.plot(mb_solve_00.zlist, mb_solve_00.fields_area()[1]/np.pi, label='Coupling', clip_on=False)\n",
    "ax.plot(mb_solve_00.zlist, total_area/np.pi, label='Total', ls='dashed', clip_on=False)\n",
    "ax.legend()\n",
    "ax.set_ylim([0.0, 4.0])\n",
    "ax.set_xlabel('Distance ($L$)')\n",
    "ax.set_ylabel('Pulse Area ($\\pi$)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fields_area_abs = np.trapz(np.abs(mb_solve_00.Omegas_zt), mb_solve_00.tlist, axis=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Animation"
   ]
  },
  {
   "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 = 3.0 # 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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "FNAME = \"mbs-vee-sech-sqrt8pi-sqrt8pi-collision\"\n",
    "FNAME_JSON = FNAME + '.json'\n",
    "with open(FNAME_JSON, \"w\") as f:\n",
    "    f.write(mb_solve_json)"
   ]
  }
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