{
 "metadata": {
  "name": "Pure dephasing monte carlo"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Monte carlo simulation of cross dephasing events."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def calculate_phase(t, FSS, phase = None):\n",
      "    \"\"\" \n",
      "        Calculated the exciton - biexciton phase\n",
      "    \"\"\"\n",
      "    \n",
      "    if phase == None:\n",
      "        phase = 0\n",
      "    \n",
      "    hbar = 6.56e-16 \n",
      "    return np.exp((1.0j*(FSS*1e-6*t*1e-9 + phase))/hbar)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 364
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def phase_with_dephasing(xlifetime, crosstau, FSS):\n",
      "    \"\"\"\n",
      "        Calculated the phase including dephasing.\n",
      "    \"\"\"\n",
      "    \n",
      "    t = np.linspace(0, xlifetime, 100)\n",
      "    sin = []\n",
      "    phase = 0\n",
      "    dephasing_event = np.random.exponential(crosstau, 1)[0]    \n",
      "\n",
      "    for i in xrange(t.size):\n",
      "    \n",
      "        p = calculate_phase(t[i], FSS, phase)\n",
      "        sin.append(p)\n",
      "        \n",
      "        if t[i] > dephasing_event:\n",
      "\n",
      "            if dephasing_event < xlifetime:   \n",
      "                phase = np.random.random_sample()*1e-9\n",
      "                dephasing_event += np.random.exponential(crosstau, 1)[0]        \n",
      "                \n",
      "    sin = np.array(sin)\n",
      "    return sin[-1], sin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 490
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xtau = 1.\n",
      "crosstau = 1.\n",
      "FSS = 2."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 519
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xlifetime = np.random.exponential(1, 1)[0]\n",
      "plt.figure(figsize = (16./1.5, 9./1.5))\n",
      "\n",
      "t = np.linspace(0, xlifetime, 100)\n",
      "plt.plot(t, phase_with_dephasing(xlifetime, crosstau, FSS)[1],'bo', markersize = 2)\n",
      "plt.plot(t, phase_with_dephasing(xlifetime, 1e20, FSS)[1],'r--', markersize = 2)\n",
      "\n",
      "plt.xlabel('$\\\\tau_x (ns)$', fontsize = 16) ; plt.ylabel('$Re(\\\\phi)$', fontsize = 16)\n",
      "plt.xlim([0, xlifetime]) ; plt.ylim([-1.1, 1.1])\n",
      "plt.legend(['No decoherence', 'With decoherence'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 525,
       "text": [
        "<matplotlib.legend.Legend at 0x1314ae210>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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UqampbNiwgZtuuonQ0FAaN27MmjVrnMfHxMTwyiuvcPPNN1O6dGnuvPNOTp065bz/u+++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\nREREROQ0DpVERERE5LR/AUv4wTLH0F80AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 525
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_phases = np.array([phase_with_dephasing(xl, crosstau, 0)[0] for xl in np.random.exponential(xtau, 500)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 512
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "real_t_p = np.real(test_phases)\n",
      "1.0 - float(real_t_p[real_t_p != 1.].size) / real_t_p.size"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 513,
       "text": [
        "0.518"
       ]
      }
     ],
     "prompt_number": 513
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ghv = 1./(1 + xtau / crosstau)\n",
      "ghv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 514,
       "text": [
        "0.5"
       ]
      }
     ],
     "prompt_number": 514
    }
   ],
   "metadata": {}
  }
 ]
}