appendices/B-mb-solve-fixed-frame.ipynb

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    "# Shifting a Solution to the Fixed Frame of Reference\n",
    "\n",
    "We solve the problem in the shifted frame of reference. This means we can keep the time in the system separate from the distance L. If we want to look at how a field actually propagates in time, we need to shift back to a fixed or lab frame of reference. To do that we need to connect the time and space dimensions via the speed of light in the system. Here we'll demonstrate that with a two-level system with no interaction strength, so that the light pulse travels through unimpeded as in a vacuum. In the moving frame of reference, that means the pulse arrives at the same time as it departed, $t = 0$. In the fixed frame it will arrive some finite time later."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Define the Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
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   "outputs": [],
   "source": [
    "mb_solve_json = \"\"\"\n",
    "{\n",
    "  \"ob_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\": 1.0e-3,\n",
    "        \"rabi_freq_t_args\": {\n",
    "          \"ampl_1\": 1.0,\n",
    "          \"centre_1\": 0.0,\n",
    "          \"fwhm_1\": 1.0\n",
    "        },\n",
    "        \"rabi_freq_t_func\": \"gaussian_1\"\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\": 140,\n",
    "  \"z_steps_inner\": 1,\n",
    "  \"num_density_z_func\": \"square_1\",\n",
    "  \"num_density_z_args\": {\n",
    "    \"on_1\": 0.0,\n",
    "    \"off_1\": 1.0,\n",
    "    \"ampl_1\": 1.0\n",
    "  },\n",
    "  \"interaction_strengths\": [\n",
    "    0.0\n",
    "  ],\n",
    "  \"velocity_classes\": {\n",
    "    \"thermal_delta_min\": -0.0,\n",
    "    \"thermal_delta_max\": 0.0,\n",
    "    \"thermal_delta_steps\": 0,\n",
    "    \"thermal_delta_inner_min\": 0.0,\n",
    "    \"thermal_delta_inner_max\": 0.0,\n",
    "    \"thermal_delta_inner_steps\": 0,\n",
    "    \"thermal_width\": 1.0\n",
    "  },\n",
    "  \"method\": \"mesolve\",\n",
    "  \"opts\": {},\n",
    "  \"savefile\": \"mb-solve-fixed-frame\"\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from maxwellbloch import mb_solve\n",
    "mb_solve_00 = mb_solve.MBSolve().from_json_str(mb_solve_json)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Solve the Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded tuple object.\n",
      "CPU times: user 1.91 ms, sys: 2.75 ms, total: 4.66 ms\n",
      "Wall time: 5.3 ms\n"
     ]
    }
   ],
   "source": [
    "%time Omegas_zt, states_zt = mb_solve_00.mbsolve(recalc=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Field Output\n",
    "\n",
    "In the moving frame of reference, we see that the pulse arrives at the back of the medium ($z = 1$) at the same time ($t = 0$) it left the front of the medium ($z = 0$).\n",
    "\n",
    "This of course is non-physical — the information in the pulse must take some finite time to cross the medium."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x11903e2e8>"
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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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FJBADAABQSAIxAAAAhSQQAwAAUEgCMQAAAIXUvbMLAAAA4MOrbO8DOruE980JMQAAAIUk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1150d9278>"
      ]
     },
     "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",
    "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(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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "source": [
    "##  Shifting to the Fixed Frame\n",
    "\n",
    "To return the solution to a physical system, we must introduce a relation between the time and space dimensions in the problem. This is given by the speed of light in the chosen units.\n",
    "\n",
    "For example, if in our lab system the speed of light is such that in vacuum it will cover the length of the medium $1.0 L$ in $2.0 \\tau$, then the speed of light must be $0.5 L/\\tau$.\n",
    "\n",
    "Note that this is just a skewing of the results along the time axis to return it to the 'real' time. Nothing changes in the problem.\n",
    "\n",
    "We use the `fixed` module and get the fixed frame tlist with the call\n",
    "\n",
    "    fixed.t_list(mb_solve_00, speed_of_light)\n",
    "    \n",
    "and the field via\n",
    "\n",
    "    fixed.rabi_freq_abs(mb_solve_00, 0, speed_of_light)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from maxwellbloch import fixed\n",
    "\n",
    "speed_of_light = 0.5 # [L Γ]\n",
    "\n",
    "tlist_fixed_frame = fixed.t_list(mb_solve_00, speed_of_light)\n",
    "field_fixed_frame = fixed.rabi_freq_abs(mb_solve_00, 0, speed_of_light, interp_kind='cubic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1197577b8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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30uFkEvZhWqTDAAAA6YOCGEgyZulwosO0UjEddjpMCwAAAOmDghhpK6ey6zPr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\nAIAhURADAAAAAAyJghgAAAAAYEj/AUfWNjyLsvqkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119533588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(2, figsize=(16, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "cmap_range = np.linspace(0.0, 1.0e-3, 11)\n",
    "cf = ax.contourf(tlist_fixed_frame, mb_solve_00.zlist, \n",
    "                 np.abs(field_fixed_frame/(2*np.pi)), \n",
    "                 cmap_range, cmap=plt.cm.Blues)\n",
    "ax.set_title('Rabi Frequency ($\\Gamma / 2\\pi $)')\n",
    "ax.set_xlabel('Fixed Time $1/\\Gamma$)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "for x in [0.0, 1/speed_of_light]:\n",
    "    ax.axvline(x, c='red', lw=1.0, ls='dashed')\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": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "And we can change the speed of light if we like.\n",
    "\n",
    "If in our lab system the speed of light is such that in vacuum it will cover the length of the medium $1.0 L$ in $5.0 \\tau$, then the speed of light must be $0.2 L/\\tau$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "speed_of_light = 0.2 # [L Γ]\n",
    "\n",
    "tlist_fixed_frame = fixed.t_list(mb_solve_00, speed_of_light)\n",
    "field_fixed_frame = fixed.rabi_freq_abs(mb_solve_00, 0, speed_of_light, interp_kind='cubic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DD6qiokLPPvusnnzySd10003av998FQcA7LDbRCvmdQFtopUI45UAAAACFIjL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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119b6ba58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(2, figsize=(16, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "cmap_range = np.linspace(0.0, 1.0e-3, 11)\n",
    "cf = ax.contourf(tlist_fixed_frame, mb_solve_00.zlist, \n",
    "                 np.abs(field_fixed_frame/(2*np.pi)), \n",
    "                 cmap_range, cmap=plt.cm.Blues)\n",
    "ax.set_title('Rabi Frequency ($\\Gamma / 2\\pi $)')\n",
    "ax.set_xlabel('Fixed Time $1/\\Gamma$)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "for x in [0.0, 1/speed_of_light]:\n",
    "    ax.axvline(x, c='red', lw=1.0, ls='dashed')\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-fixed-frame.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The field must be interpolated to find the value at the shifted time points. We can choose the kind of spline interpolation with `interp_kind` which may be `'linear'`, `'cubic'` or `'quintic'`. It is linear by default."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}