examples/mb-solve-two-sech-6pi.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two-Level: Sech Pulse 6π — Pulse Breakup\n",
    "\n",
    "Time taken to solve this problem on a 2013 MacBook Pro:\n",
    "**1min 25s**"
   ]
  },
  {
   "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 2.5152043096265\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 = 6.0 # 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\": 2.5152043096265,\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-6pi\"\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 5.980281932418772\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": "markdown",
   "metadata": {},
   "source": [
    "## Solve the Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded tuple object.\n",
      "CPU times: user 4.27 ms, sys: 8.22 ms, total: 12.5 ms\n",
      "Wall time: 13.7 ms\n"
     ]
    }
   ],
   "source": [
    "%time Omegas_zt, states_zt = mb_solve_00.mbsolve(step='ab', 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, 4.0, 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-6pi.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, clip_on=False)\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 $6 \\pi$ sech pulse breaks up into three $2 \\pi$ 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-6pi\"\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-6pi.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-6pi.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-6pi.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-6pi.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: 992 kb/s\n",
      "    Stream #0:0(und): Video: h264 (High) (avc1 / 0x31637661), yuv420p, 1200x400, 985 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 @ 0x7fd30b501960] \u001b[0m255(+1) colors generated out of 85002 colors; ratio=0.003000\n",
      "\u001b[1;32m[Parsed_palettegen_2 @ 0x7fd30b501960] \u001b[0m\u001b[0;33mDupped color: FF9DC5AB\n",
      "\u001b[0m\u001b[1;32m[Parsed_palettegen_2 @ 0x7fd30b501960] \u001b[0m\u001b[0;33mDupped color: FFC8CEE1\n",
      "\u001b[0mframe=    1 fps=0.4 q=-0.0 Lsize=N/A time=00:00:00.01 bitrate=N/A speed=0.00745x    \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-6pi.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: 992 kb/s\n",
      "    Stream #0:0(und): Video: h264 (High) (avc1 / 0x31637661), yuv420p, 1200x400, 985 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= 74 q=-0.0 Lsize=    1699kB time=00:00:08.04 bitrate=1730.6kbits/s speed=2.46x    \n",
      "video:1696kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: 0.157613%\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-6pi.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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   "display_name": "Python 3",
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