examples/mb-solve-two-sech-4pi.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two-Level: Sech Pulse 4π — Pulse Breakup\n",
    "\n",
    "Time taken to solve this problem on a 2013 MacBook Pro:\n",
    "**1min 17s**"
   ]
  },
  {
   "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)).\n",
    "\n",
    "We then obtain the amplitude $a$ we need from\n",
    "\n",
    "$$\n",
    "a = \\frac{n}{2 \\pi ~ t_s}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_width 0.3796628587572578\n",
      "ampl 1.6768028730843334\n"
     ]
    }
   ],
   "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 = 4.0 # For a pulse area of nπ    \n",
    "ampl = n/t_width/(2*np.pi) # Pulse amplitude [2π Γ]\n",
    "\n",
    "print('ampl', ampl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "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\": 1.6768028730843334,\n",
    "        \"rabi_freq_t_args\": {\n",
    "          \"ampl\": 1.0,\n",
    "          \"centre\": 0.0,\n",
    "          \"width\": 0.3796628587572578\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\": 200,\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",
    "    10.0\n",
    "  ],\n",
    "  \"velocity_classes\": {},\n",
    "  \"method\": \"mesolve\",\n",
    "  \"opts\": {},\n",
    "  \"savefile\": \"qu/mb-solve-two-sech-4pi\"\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from maxwellbloch import mb_solve\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": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The input pulse area is 3.9868546216125154\n"
     ]
    }
   ],
   "source": [
    "print('The input pulse area is {0}'.format(np.trapz(mb_solve_00.Omegas_zt[0,0,:].real, \n",
    "                                                    mb_solve_00.tlist)/np.pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded tuple object.\n",
      "CPU times: user 3.42 ms, sys: 8.12 ms, total: 11.5 ms\n",
      "Wall time: 13.5 ms\n"
     ]
    }
   ],
   "source": [
    "%time Omegas_zt, states_zt = mb_solve_00.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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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "\n",
    "import numpy as np\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(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-sech-4pi.png')"
   ]
  },
  {
   "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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\n",
      "text/plain": [
       "<Figure size 1152x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(16, 5))\n",
    "ax.plot(mb_solve_00.zlist, mb_solve_00.fields_area()[0]/np.pi)\n",
    "ax.set_ylim([0.0, 8.0])\n",
    "ax.set_xlabel('Distance ($L$)')\n",
    "ax.set_ylabel('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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Namespace(atoms_alpha='0.2', c_line=False, file='images/mb-solve-two-sech-4pi.json', fps='60', peak_line=False, save_path='./', speed_of_light='0.1', y_max='4.0', y_min='0.0', zoom='2')\n",
      "Loaded tuple object.\n",
      "Saving MP4\n",
      "./images/mb-solve-two-sech-4pi.mp4\n",
      "Figure(1200x400)\n"
     ]
    }
   ],
   "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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converting images/mb-solve-two-sech-4pi.mp4 to gif format\n",
      "Input Scale: 900\n",
      "Input FPS: 60\n",
      "Output Scale: 900\n",
      "Output FPS: 30\n",
      "/Users/tommy/.miniconda3/envs/mb-0.4.0/bin/make-gif-ffmpeg.sh: line 59: Y: command not found\n",
      "ffmpeg version 3.2.4 Copyright (c) 2000-2017 the FFmpeg developers\n",
      "  built with Apple LLVM version 8.0.0 (clang-800.0.42.1)\n",
      "  configuration: --prefix=/usr/local/Cellar/ffmpeg/3.2.4 --enable-shared --enable-pthreads --enable-gpl --enable-version3 --enable-hardcoded-tables --enable-avresample --cc=clang --host-cflags= --host-ldflags= --enable-libmp3lame --enable-libx264 --enable-libxvid --enable-opencl --disable-lzma --enable-vda\n",
      "  libavutil      55. 34.101 / 55. 34.101\n",
      "  libavcodec     57. 64.101 / 57. 64.101\n",
      "  libavformat    57. 56.101 / 57. 56.101\n",
      "  libavdevice    57.  1.100 / 57.  1.100\n",
      "  libavfilter     6. 65.100 /  6. 65.100\n",
      "  libavresample   3.  1.  0 /  3.  1.  0\n",
      "  libswscale      4.  2.100 /  4.  2.100\n",
      "  libswresample   2.  3.100 /  2.  3.100\n",
      "  libpostproc    54.  1.100 / 54.  1.100\n",
      "Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'images/mb-solve-two-sech-4pi.mp4':\n",
      "  Metadata:\n",
      "    major_brand     : isom\n",
      "    minor_version   : 512\n",
      "    compatible_brands: isomiso2avc1mp41\n",
      "    artist          : Me\n",
      "    encoder         : Lavf57.56.101\n",
      "  Duration: 00:00:08.03, start: 0.000000, bitrate: 857 kb/s\n",
      "    Stream #0:0(und): Video: h264 (High) (avc1 / 0x31637661), yuv420p, 1200x400, 851 kb/s, 60 fps, 60 tbr, 15360 tbn, 120 tbc (default)\n",
      "    Metadata:\n",
      "      handler_name    : VideoHandler\n",
      "Output #0, image2, to 'palette.png':\n",
      "  Metadata:\n",
      "    major_brand     : isom\n",
      "    minor_version   : 512\n",
      "    compatible_brands: isomiso2avc1mp41\n",
      "    artist          : Me\n",
      "    encoder         : Lavf57.56.101\n",
      "    Stream #0:0(und): Video: png, rgba, 16x16 [SAR 1:1 DAR 1:1], q=2-31, 200 kb/s, 60 fps, 60 tbn, 60 tbc (default)\n",
      "    Metadata:\n",
      "      handler_name    : VideoHandler\n",
      "      encoder         : Lavc57.64.101 png\n",
      "Stream mapping:\n",
      "  Stream #0:0 -> #0:0 (h264 (native) -> png (native))\n",
      "Press [q] to stop, [?] for help\n",
      "\u001b[1;32m[Parsed_palettegen_2 @ 0x7fc4b0408da0] \u001b[0m255(+1) colors generated out of 73578 colors; ratio=0.003466\n",
      "\u001b[1;32m[Parsed_palettegen_2 @ 0x7fc4b0408da0] \u001b[0m\u001b[0;33mDupped color: FFFEFCFE\n",
      "    Last message repeated 1 times\n",
      "frame=    1 fps=0.6 q=-0.0 Lsize=N/A time=00:00:00.01 bitrate=N/A speed=0.0104x    \n",
      "video:1kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: unknown\n",
      "Outputting to .gif\n",
      "ffmpeg version 3.2.4 Copyright (c) 2000-2017 the FFmpeg developers\n",
      "  built with Apple LLVM version 8.0.0 (clang-800.0.42.1)\n",
      "  configuration: --prefix=/usr/local/Cellar/ffmpeg/3.2.4 --enable-shared --enable-pthreads --enable-gpl --enable-version3 --enable-hardcoded-tables --enable-avresample --cc=clang --host-cflags= --host-ldflags= --enable-libmp3lame --enable-libx264 --enable-libxvid --enable-opencl --disable-lzma --enable-vda\n",
      "  libavutil      55. 34.101 / 55. 34.101\n",
      "  libavcodec     57. 64.101 / 57. 64.101\n",
      "  libavformat    57. 56.101 / 57. 56.101\n",
      "  libavdevice    57.  1.100 / 57.  1.100\n",
      "  libavfilter     6. 65.100 /  6. 65.100\n",
      "  libavresample   3.  1.  0 /  3.  1.  0\n",
      "  libswscale      4.  2.100 /  4.  2.100\n",
      "  libswresample   2.  3.100 /  2.  3.100\n",
      "  libpostproc    54.  1.100 / 54.  1.100\n",
      "Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'images/mb-solve-two-sech-4pi.mp4':\n",
      "  Metadata:\n",
      "    major_brand     : isom\n",
      "    minor_version   : 512\n",
      "    compatible_brands: isomiso2avc1mp41\n",
      "    artist          : Me\n",
      "    encoder         : Lavf57.56.101\n",
      "  Duration: 00:00:08.03, start: 0.000000, bitrate: 857 kb/s\n",
      "    Stream #0:0(und): Video: h264 (High) (avc1 / 0x31637661), yuv420p, 1200x400, 851 kb/s, 60 fps, 60 tbr, 15360 tbn, 120 tbc (default)\n",
      "    Metadata:\n",
      "      handler_name    : VideoHandler\n",
      "Input #1, png_pipe, from 'palette.png':\n",
      "  Duration: N/A, bitrate: N/A\n",
      "    Stream #1:0: Video: png, rgba(pc), 16x16 [SAR 1:1 DAR 1:1], 25 tbr, 25 tbn, 25 tbc\n",
      "Output #0, gif, to '.gif':\n",
      "  Metadata:\n",
      "    major_brand     : isom\n",
      "    minor_version   : 512\n",
      "    compatible_brands: isomiso2avc1mp41\n",
      "    artist          : Me\n",
      "    encoder         : Lavf57.56.101\n",
      "    Stream #0:0: Video: gif, pal8, 900x300, q=2-31, 200 kb/s, 30 fps, 100 tbn, 30 tbc (default)\n",
      "    Metadata:\n",
      "      encoder         : Lavc57.64.101 gif\n",
      "Stream mapping:\n",
      "  Stream #0:0 (h264) -> fps\n",
      "  Stream #1:0 (png) -> paletteuse:palette\n",
      "  paletteuse -> Stream #0:0 (gif)\n",
      "Press [q] to stop, [?] for help\n",
      "frame=  242 fps= 79 q=-0.0 Lsize=    1372kB time=00:00:08.04 bitrate=1398.3kbits/s speed=2.62x    \n",
      "video:1370kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: 0.195143%\n"
     ]
    }
   ],
   "source": [
    "FNAME_MP4 = FNAME + '.mp4'\n",
    "!make-gif-ffmpeg.sh -f $FNAME_MP4 --in-fps $FPS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"images/mb-solve-two-sech-4pi.mp4.gif\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(url=FNAME_MP4 +'.gif', format='gif')"
   ]
  }
 ],
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