Reproduce-PRL-68-580-1992-Dalibard.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reproduce: Wave-Function Approach to Dissipative Processes in Quantum Optics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "J. Dalibard and Y. Castin, <a href=\"http://dx.doi.org/10.1103/PhysRevLett.68.580\">Phys. Rev. Lett. <b>68</b>, 580 (1992).</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reproduced by <strong>Eunjong Kim</strong> (ekim7206@gmail.com)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This paper introduces the <strong>Monte-Carlo wave-function (MCWF)</strong> approach and proves its equivalence with the Optical Bloch equation (OBE). In this notebook, I will briefly summarize the main points and reproduce the figures in the paper generated by numerical calculations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup Modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import qutip as qt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# setup for plots\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams\n",
    "%matplotlib inline\n",
    "rcParams.update({\"text.usetex\": True, \"font.size\": 16})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monte-Carlo wave-function (MCWF) approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a two-level atom, with a ground state $|g\\rangle$ and an excited state $|e\\rangle$, coupled to a monochromatic laser field and to the quantized electromagnetic field in its ground state."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Describing the laser field as a classical function $\\mathcal{E} (t) = \\mathcal{E}_0 \\cos{\\omega_L t}$, the atom-laser coupling Hamiltonian under the rotating-wave approximation is written as ($\\hbar = 1$)\n",
    "$$\n",
    "H_0 = -\\delta \\sigma_+ \\sigma_- + \\Omega (\\sigma_+ + \\sigma_-),\n",
    "$$\n",
    "where $\\sigma_+ = |e\\rangle\\langle g|$, $\\sigma_- = (\\sigma_+)^\\dagger$, and $\\delta = \\omega_L - \\omega_A$ is thedetuning between the laser and atomic frequencies; $\\Omega = -d\\mathcal{E}_0$ is the Rabi frequency that characterizes the coupling between the atomic dipole moment $d$ and the laser electric field."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We assume that the total system involving the atom and the quantized field at the time $t$ is represented by the wavefunction\n",
    "$$\n",
    "|\\psi(t)\\rangle = |\\phi(t)\\rangle \\otimes |0\\rangle = (\\alpha_g |g\\rangle + \\alpha_e |e\\rangle) \\otimes |0\\rangle,\n",
    "$$\n",
    "where $|0\\rangle$ denotes the vacuum state of the quantized electromagnetic field."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After a short time step of $dt$, during which at most one photon can be spontaneously emitted ($dt\\ll \\Gamma^{-1}, \\Omega^{-1}, \\delta^{-1}$), the wavefunction can be decomposed into two parts: $|\\psi(t+dt)\\rangle = |\\psi^{(0)}(t+dt)\\rangle + |\\psi^{(1)} (t+dt)\\rangle$, where\n",
    "$$|\\psi^{(0)}(t+dt)\\rangle = (\\alpha'_g |g\\rangle + \\alpha'_e |e\\rangle) \\otimes |0\\rangle$$\n",
    "is the non-decaying part and\n",
    "$$|\\psi^{(1)}(t+dt)\\rangle = |g\\rangle \\otimes \\sum_{\\mathbf{k},\\epsilon}\\beta_{\\mathbf{k},\\epsilon} |\\mathbf{k},\\epsilon\\rangle$$\n",
    "is the decaying part."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that $dp = \\Gamma dt |\\alpha_e|^2= \\Gamma dt \\langle \\phi(t)|\\sigma_+\\sigma_-|\\phi(t)\\rangle$ corresponds to the spontaneously decayed population at time $t+dt$, $$\\langle\\psi^{(1)}(t+dt)|\\psi^{(1)}(t+dt)\\rangle = dp$$\n",
    "and thus $$\\langle\\psi^{(0)}(t+dt)|\\psi^{(0)}(t+dt)\\rangle = 1 - dp$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To obtain the values of $\\alpha'_g$ and $\\alpha'_e$, the evolution of $|\\phi(t)\\rangle$ during $dt$ with the non-Hermitian Hamiltonian is introduced, where\n",
    "$$ H = H_0 - \\frac{i\\Gamma}{2} \\sigma_+ \\sigma_-.$$\n",
    "This amounts to reducing the excited-state amplitude by a factor $1- \\Gamma dt/2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the Monte-Carlo approach, the following scheme is prepared:\n",
    "1. All spontaneous photons are detected with a perfect counter and we measure the number of photons at time $t+dt$.\n",
    "2. Depending on the result $0$ or $1$ of the measurement, we have to project $|\\psi(t + dt)\\rangle$ on $|\\psi^{(0)}(t + dt)\\rangle$ or $|\\psi(t + dt)^{(1)}\\rangle$ and normalize the result. This could be done using a pseudo-random number $0<\\epsilon<1$: <br>\n",
    "(i) $\\epsilon > dp$ corresponds to zero photon detection, which collapses $|\\psi(t+dt)\\rangle$ onto\n",
    "$$\\frac{|\\psi^{(1)}(t+dt)\\rangle}{\\sqrt{\\langle\\psi^{(1)}(t+dt)|\\psi^{(1)}(t+dt)\\rangle}} = \\frac{1}{\\sqrt{1-dp}} (1-i dt\\ H)|\\phi(t)\\rangle \\otimes |0\\rangle$$\n",
    "(ii) $\\epsilon < dp$ corresponds to one photon detection, which collapses $|\\psi(t+dt)\\rangle$ onto $|g\\rangle\\otimes|0\\rangle$. Note that the detected photon has been destroyed after the gedanken measurement process.\n",
    "3. Now, since we returned to a wavefunction in the form of $|\\psi(t+dt)\\rangle = |\\phi(t+dt)\\rangle \\otimes |0\\rangle$, we can go back to the steps 1-2 repeatedly.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the paper, the authors show that this Monte-Carlo wave-function (MCWF) approach is equivalent to the standard master equation approach, also known as the Optical Bloch Equation (OBE). I skip that argument in this notebook and numerically calculate the example to reproduce Figure 1 in the original article."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Rabi transitory regime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sm, sp = qt.sigmam(), qt.sigmap()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Parameters\n",
    "Gamma = 1.0               # decay rate\n",
    "delta = 0.0               # detuning\n",
    "Omega = 3.0 * Gamma       # Rabi frequency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# atom-laser coupling hamiltonian within the rotating-wave approximation\n",
    "H0 = - delta * sp * sm + Omega * (sp + sm)\n",
    "\n",
    "# non-Hermitian Hamiltonian introduced to reduce the excited-state amplitude\n",
    "H = H0 - 1j * Gamma * sp * sm /2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = 2\n",
    "ground = qt.basis(N, 1)   # atom initially in the ground state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dt = 1e-2                 # unit time step for Monte-Carlo approach\n",
    "t = np.arange(0, 4, dt)   # \n",
    "phi0 = ground             # initial state\n",
    "M = 100                   # number of systems to be averaged"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "populations = []\n",
    "\n",
    "for m in range(100):        # repeat for M systems\n",
    "    phi = [phi0]\n",
    "    population = []\n",
    "    for idx in range(len(t)):\n",
    "        dp = Gamma * dt * qt.expect(sp * sm, phi[-1])\n",
    "        mu = 1 / np.sqrt(1 - dp)\n",
    "        # random number generation\n",
    "        epsilon = np.random.random()\n",
    "        if epsilon > dp:  # collapse onto detection of 0 photon\n",
    "            phi_ = mu * (1 - 1j * dt * H) * phi[-1]\n",
    "            phi.append(phi_.unit())  # normalization after evolution\n",
    "        else:             # collapse onto detection of 1 photon\n",
    "            phi.append(ground)\n",
    "        population.append(qt.expect(sp * sm, phi[-1]))\n",
    "    populations.append(np.array(population))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Result obtained from the Optical Bloch Equation (OBE) using qutip mesolver\n",
    "OBE_result = qt.mesolve(H0, phi0, t, [np.sqrt(Gamma) * sm], [sp * sm])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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KJ57iFjyph+dqree5beJvfw760PG/Wuu9rcOVdKRtbXdYiwHqfQyelSJW9jlIKla3jm0R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bsmrbWbrbVPWWtPA56KjPJUhm/nMQEZ034ejTGtqfzcVEXg7+8kCYOuSGq/qi9SI0D6\nIgy6AlRfpITqCyFszkaiB+rHgy+hfQbowVcp1to5HHgxNiLGlGqascADFc5vEfGVQHQNY8xoYHT0\nqFAl+KqM45HRr2syMoIWzdjIqzJ8OY+JyOjTeewGdDPG3BqJQx8GFBpjbokolv0Iyf2dDGHQFQnv\nV/WFK/iuL8KgK0D1RaqovignVM5Gogfqx4MviX36+eCrNEDPGFNkjBkctWhchb/7UfVN7TYxZYyM\nBGyosMoQ0jjaF5HlfWvttMjfXStbz09lHK+M+HBNGmP6ARsrPGhN5LsDEs/8OI+JyogP59Fa+6q1\n9kHnhUzLF1tr/88JHQnY/e0JYdAVSe5X9UX1BF5fhEFXgOqLdMtIhuuLUDkbEao90IA8+OKW0Y8H\nnzGma8SLHQycF/Fqox8kfYmKLbTShKbISOWOW4HF1uOSbInKiJzzW41UFnFqraelbFzkodIImB0Z\nnSgCLoj63vdrMhEZfVLGM4GxFR60/YFXnGUBOI8JyRgAo2ZoZH+tIyNVBZGvfL+/00QYdEXM/fp9\nTam+cFXOwOuKROVUfeGOjJmuL4yVphyhwpR3gSwCNtmo0mLOCbPWnh7P+kGQMfJPHUZ5l8kvMkTZ\nZzxGpkkri/l8xVp7QWQdX6/JZGT045qMGAdOKcLGgLXWjoz63vd7O1EZ9d72lzDoikTl1GsqnIRB\nVyQrp+oLd2TM5Hs7lM6GoiiKoiiKoijBJ4xhVIqiKIqiKIqihAB1NhRFURRFURRF8QR1NhRFURRF\nURRF8QR1NhRFURRFURRF8QR1NhRFURRFURRF8QR1NhRFURRFURRF8QR1NpSMxhjzijGmLI7Xk5H1\nlxhjJvgtt6IoipJeVF8oijfk+S2AonjMv4DFUX93R5rsvII093GYHHnfBGjzGUVRlOxD9YWieIA2\n9VOyCmPMEGAC0rUzVJ05jTFjkO6iG4CxkcWNkW6oQ4DzrLWvRq3fDemSuizdsiqKooQd1ReK4g46\ns6EoIcFaO8IY0xpYYq19MPo7Y0xfoFuFnzwF3Aeo8lAURckiVF8oQUJzNhQliooxuMaY2caYCcaY\nfpHPZcaYWcaY1saYwkiM78bIa3Ql2yuKrLMpss77xpiuqYpZcYG1dipQXGFxV+2e3vAAAAKQSURB\nVGBKivtSFEVRKkH1haLEhzobirI/lv1jcC0yAvQ3YDwwIvL3bGAWUAYMR+J5hxtjBjs/jExLLwa6\nRH4/DugBzE5RgVQV+7gvptgY0w9Yaq3dksJ+FEVRlKpRfaEocaBhVIqyPxVHgQzQGmhjrV0OYIwB\nGAO8bK39XWTZK0iyYA/AiYMdg0xht9u3MWNGIdPUT0XWdQ1r7dTI9Hh/JCZ3U2T0bGZ0bK6iKIri\nCqovFCUO1NlQlNgsdRRHBCem1Um6w1q72RhTDBQCGGMKgb7AiMjnaF4BhnohaGR6fGpkpGpU2JIa\nFUVRQo7qC0WpgDobihKbirGtsZaDVPwAGa0aU8n31hjTwMNp625o/K2iKEq6UX2hKBVQZ0NRvGU4\nMKeyL7xSHBp/qyiKEkpUXygZiTobiuINTvKdsdZOi/4ikgjYOoVtH1BdpAL9kYRERVEUJfiovlAy\nGq1GpSj740qXS2ttMTJCNdIYU+AsN8YUIVVJzk9l8zG+70ekw22k3GKqpRMVRVGUA1F9oShxoM6G\nouxPZaNAsUaGqlpvKJIAuMwYMzrS0XU28vAfkYJ8seQpQBQUwFBr7ZdJ7ktRFEWpGtUXihIHGkal\nZCPVjfRU/K5iHfXqtrHfMmvtl8aY7kjC37DI4i+AqytUK4mLiPLpC3SJlFMca62trNvrGOBCY0xP\noiqgKIqiKAmj+kJRUsRY68osoKIoiqIoiqIoyn5oGJWiKIqiKIqiKJ6gzoaiKIqiKIqiKJ6gzoai\nKIqiKIqiKJ6gzoaiKIqiKIqiKJ6gzoaiKIqiKIqiKJ6gzoaiKIqiKIqiKJ6gzoaiKIqiKIqiKJ6g\nzoaiKIqiKIqiKJ6gzoaiKIqiKIqiKJ7w/wFF7DLOJ9GCsQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f6659b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(13,4))\n",
    "\n",
    "pop0 = np.copy(populations[-1])\n",
    "# mark the points at the discontinuity and connect with dashed lines\n",
    "mask = np.where(np.abs(np.diff(pop0)) >= 1e-1)[0]\n",
    "for mask_ in mask:\n",
    "    axes[0].plot([t[mask_], t[mask_+1]], [pop0[mask_], pop0[mask_+1]], ls='--', color='red', lw=2)\n",
    "\n",
    "pop0[mask] = np.nan\n",
    "axes[0].plot(t, pop0, ls='-', color='red', lw=2)\n",
    "axes[0].set_ylabel(r'Excited-state population $\\ \\pi_e$', fontsize=18)\n",
    "\n",
    "axes[1].plot(t, sum(populations) / len(populations), ls='-', color='blue', lw=2, label='MCWF')\n",
    "axes[1].plot(t, OBE_result.expect[0], ls='--', color='green', lw=2.5, label='OBE')\n",
    "\n",
    "axes[0].set_ylim([-0.01, 1.01]); axes[1].set_ylim([-0.01, 1.01])\n",
    "axes[0].set_title('(a) MCWF approach')\n",
    "axes[1].set_title(r'(b) Average of $\\pi_e(t)$ for $%d$ MCWF' % M)\n",
    "axes[0].set_xlabel(r'Time $\\ \\Gamma t$', fontsize=18)\n",
    "axes[1].set_xlabel(r'Time $\\ \\Gamma t$', fontsize=18)\n",
    "\n",
    "axes[1].legend(loc=0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of averaged MCWF clearly agrees the OBE result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Version Information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.4.3 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.56)]"
        },
        {
         "module": "IPython",
         "version": "3.2.1"
        },
        {
         "module": "OS",
         "version": "Darwin 14.5.0 x86_64 i386 64bit"
        },
        {
         "module": "numpy",
         "version": "1.9.2"
        },
        {
         "module": "qutip",
         "version": "3.2.0.dev-a76dc60"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.4.3 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.56)]</td></tr><tr><td>IPython</td><td>3.2.1</td></tr><tr><td>OS</td><td>Darwin 14.5.0 x86_64 i386 64bit</td></tr><tr><td>numpy</td><td>1.9.2</td></tr><tr><td>qutip</td><td>3.2.0.dev-a76dc60</td></tr><tr><td colspan='2'>Wed Nov 11 16:23:04 2015 KST</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.4.3 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.56)] \\\\ \\hline\n",
       "IPython & 3.2.1 \\\\ \\hline\n",
       "OS & Darwin 14.5.0 x86\\_64 i386 64bit \\\\ \\hline\n",
       "numpy & 1.9.2 \\\\ \\hline\n",
       "qutip & 3.2.0.dev-a76dc60 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Wed Nov 11 16:23:04 2015 KST} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.4.3 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.56)]\n",
       "IPython 3.2.1\n",
       "OS Darwin 14.5.0 x86_64 i386 64bit\n",
       "numpy 1.9.2\n",
       "qutip 3.2.0.dev-a76dc60\n",
       "Wed Nov 11 16:23:04 2015 KST"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%reload_ext version_information\n",
    "\n",
    "%version_information numpy, qutip"
   ]
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}