Notebooks-python/JC Results and Benchmarks.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "os.chdir(\"/home/amit/Documents/qutip/\")\n",
      "from qutip import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def jc_integrate(N, wc, wa, g, kappa, gamma, psi0, use_rwa, tlist):\n",
      "    # Hamiltonian\n",
      "    idc = qeye(N)\n",
      "    ida = qeye(2)\n",
      "    a  = tensor(destroy(N), ida)\n",
      "    sm = tensor(idc, destroy(2))\n",
      "    if use_rwa:\n",
      "        # use the rotating wave approxiation\n",
      "        H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())\n",
      "    else:\n",
      "        H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * (sm + sm.dag())\n",
      "    # collapse operators\n",
      "    c_op_list = []\n",
      "\n",
      "    n_th_a = 0.0 # zero temperature\n",
      "\n",
      "    rate = kappa * (1 + n_th_a)\n",
      "    if rate > 0.0:\n",
      "        c_op_list.append(np.sqrt(rate) * a)\n",
      "\n",
      "    rate = kappa * n_th_a\n",
      "    if rate > 0.0:\n",
      "        c_op_list.append(np.sqrt(rate) * a.dag())\n",
      "\n",
      "    rate = gamma\n",
      "    if rate > 0.0:\n",
      "        c_op_list.append(np.sqrt(rate) * sm)\n",
      "    # print H, c_op_list\n",
      "    # evolve and calculate return state vector\n",
      "    result = mesolve(H, psi0, tlist, c_op_list, [])\n",
      "    return result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# parameters\n",
      "wc = 1.0 * 2 * np.pi   # cavity frequency\n",
      "wa = 1.0 * 2 * np.pi   # atom frequency\n",
      "g  = 0.05 * 2 * np.pi  # coupling strength\n",
      "kappa = 0.05        # cavity dissipation rate\n",
      "gamma = 0.15        # atom dissipation rate\n",
      "N = 2              # number of cavity fock states\n",
      "\n",
      "use_rwa = True\n",
      "\n",
      "# initial state\n",
      "psi0 = tensor(basis(N,0), basis(2,1))\n",
      "# print psi0  # start with an excited atom\n",
      "#psi0 = tensor(coherent(N,1.5), basis(2,0))  # or a coherent state the in cavity\n",
      "#psi0 = tensor((coherent(N,2.0)+coherent(N,-2.0)).unit(), basis(2,0))  # or a superposition of coherent states\n",
      "\n",
      "tlist = np.linspace(0, 30, 150)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = jc_integrate(N, wc, wa, g, kappa, gamma, psi0, use_rwa, tlist)\n",
      "q = []\n",
      "for i in result.states:\n",
      "    q.append(i.full())\n",
      "x=[1]*4\n",
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "[1, 1, 1, 1]"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(len(q)):\n",
      "    for j in range(len(q[i])):\n",
      "        x = [tlist[i]]*len(q[i])\n",
      "        print x, list(q[i][j].real)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
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        "[29.19463087248322, 29.19463087248322, 29.19463087248322, 29.19463087248322] [0.0, 0.0, 0.0, 0.0]\n",
        "[29.395973154362416, 29.395973154362416, 29.395973154362416, 29.395973154362416] [0.9452900564959914, 0.0, 0.0, 0.0]\n",
        "[29.395973154362416, 29.395973154362416, 29.395973154362416, 29.395973154362416] [0.0, 0.05219674647305933, 0.0, 0.0]\n",
        "[29.395973154362416, 29.395973154362416, 29.395973154362416, 29.395973154362416] [0.0, 0.0, 0.0025131970309496534, 0.0]\n",
        "[29.395973154362416, 29.395973154362416, 29.395973154362416, 29.395973154362416] [0.0, 0.0, 0.0, 0.0]\n",
        "[29.597315436241608, 29.597315436241608, 29.597315436241608, 29.597315436241608] [0.94688104753618452, 0.0, 0.0, 0.0]\n",
        "[29.597315436241608, 29.597315436241608, 29.597315436241608, 29.597315436241608] [0.0, 0.051859918842526963, 0.0, 0.0]\n",
        "[29.597315436241608, 29.597315436241608, 29.597315436241608, 29.597315436241608] [0.0, 0.0, 0.0012590336212889716, 0.0]\n",
        "[29.597315436241608, 29.597315436241608, 29.597315436241608, 29.597315436241608] [0.0, 0.0, 0.0, 0.0]\n",
        "[29.798657718120804, 29.798657718120804, 29.798657718120804, 29.798657718120804] [0.94844523155424254, 0.0, 0.0, 0.0]\n",
        "[29.798657718120804, 29.798657718120804, 29.798657718120804, 29.798657718120804] [0.0, 0.051114546837130959, 0.0, 0.0]\n",
        "[29.798657718120804, 29.798657718120804, 29.798657718120804, 29.798657718120804] [0.0, 0.0, 0.00044022160862697767, 0.0]\n",
        "[29.798657718120804, 29.798657718120804, 29.798657718120804, 29.798657718120804] [0.0, 0.0, 0.0, 0.0]\n",
        "[30.0, 30.0, 30.0, 30.0] [0.94997487505303491, 0.0, 0.0, 0.0]\n",
        "[30.0, 30.0, 30.0, 30.0] [0.0, 0.049980530422525662, 0.0, 0.0]\n",
        "[30.0, 30.0, 30.0, 30.0] [0.0, 0.0, 4.4594524439867354e-05, 0.0]\n",
        "[30.0, 30.0, 30.0, 30.0] [0.0, 0.0, 0.0, 0.0]\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(len(q)):\n",
      "    for j in range(len(q[i])):\n",
      "        x = [tlist[i] for k in len(q[i])] \n",
      "        plt.plot(x, q[i][j].real, 'ro')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "TypeError",
       "evalue": "'int' object is not iterable",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-18-f4a93207f4cc>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m         \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mtlist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m         \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'ro'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mTypeError\u001b[0m: 'int' object is not iterable"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(len(q)):\n",
      "    for j in range(len(q[i])):\n",
      "        plt.plot(tlist[i], q[i][j].imag, 'ro')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "ValueError",
       "evalue": "x and y must have same first dimension",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-17-28459f64958d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m         \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtlist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimag\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'ro'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[0;32m/usr/local/lib/python2.7/dist-packages/matplotlib/pyplot.pyc\u001b[0m in \u001b[0;36mplot\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m   3097\u001b[0m         \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhold\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhold\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3098\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3099\u001b[0;31m         \u001b[0mret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3100\u001b[0m         \u001b[0mdraw_if_interactive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3101\u001b[0m     \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/usr/local/lib/python2.7/dist-packages/matplotlib/axes/_axes.pyc\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1371\u001b[0m         \u001b[0mlines\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1372\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1373\u001b[0;31m         \u001b[0;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1374\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1375\u001b[0m             \u001b[0mlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/usr/local/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_grab_next_args\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    302\u001b[0m                 \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    303\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mremaining\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 304\u001b[0;31m                 \u001b[0;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mremaining\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    305\u001b[0m                     \u001b[0;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    306\u001b[0m                 \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/usr/local/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_plot_args\u001b[0;34m(self, tup, kwargs)\u001b[0m\n\u001b[1;32m    280\u001b[0m             \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfloat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    281\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 282\u001b[0;31m         \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    283\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    284\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'plot'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/usr/local/lib/python2.7/dist-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[0;34m(self, x, y)\u001b[0m\n\u001b[1;32m    221\u001b[0m         \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0matleast_1d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    222\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 223\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"x and y must have same first dimension\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    224\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    225\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"x and y can be no greater than 2-D\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mValueError\u001b[0m: x and y must have same first dimension"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bhO+ttWvXav78+W89P5VupjTufOlpRDJ78W/Hjh3Txo0bMzFaxiX7+6KtrW34r6+w+LHZ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\ng/4PREe1gDvOnI4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1bdf44cf50>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def jc_integrate(N, wc, wa, g, kappa, gamma, psi0, use_rwa, tlist):\n",
      "    # Hamiltonian\n",
      "    idc = qeye(N)\n",
      "    ida = qeye(2)\n",
      "    a  = tensor(destroy(N), ida)\n",
      "    sm = tensor(idc, destroy(2))\n",
      "    if use_rwa:\n",
      "        # use the rotating wave approxiation\n",
      "        H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())\n",
      "    else:\n",
      "        H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * (sm + sm.dag())\n",
      "    # collapse operators\n",
      "    c_op_list = []\n",
      "\n",
      "    n_th_a = 0.0 # zero temperature\n",
      "\n",
      "    rate = kappa * (1 + n_th_a)\n",
      "    if rate > 0.0:\n",
      "        c_op_list.append(np.sqrt(rate) * a)\n",
      "\n",
      "    rate = kappa * n_th_a\n",
      "    if rate > 0.0:\n",
      "        c_op_list.append(np.sqrt(rate) * a.dag())\n",
      "\n",
      "    rate = gamma\n",
      "    if rate > 0.0:\n",
      "        c_op_list.append(np.sqrt(rate) * sm)\n",
      "    # print H, c_op_list\n",
      "    # evolve and calculate return state vector\n",
      "    result = mesolve(H, psi0, tlist, c_op_list, [a*a.dag()])\n",
      "    return result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 114
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = jc_integrate(N, wc, wa, g, kappa, gamma, psi0, use_rwa, tlist)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 115
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "q = []\n",
      "for i in result.expect[0]:\n",
      "    q.append(i)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 122
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i,j in enumerate(q):\n",
      "    plt.plot(tlist[i], j, \"ro\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LnDlzBlOnToVOp4PdbocQYlRAJ3mcLRCR+vkN6gkJCaiurobZbIbD4UBJSQmM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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ffe0a26dd50>"
       ]
      }
     ],
     "prompt_number": 127
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def jc_integrate(N, wc, wa, g, kappa, gamma, psi0, use_rwa, tlist):\n",
      "    # Hamiltonian\n",
      "    idc = qeye(N)\n",
      "    ida = qeye(2)\n",
      "    a  = tensor(destroy(N), ida)\n",
      "    sm = tensor(idc, destroy(2))\n",
      "    if use_rwa:\n",
      "        # use the rotating wave approxiation\n",
      "        H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())\n",
      "    else:\n",
      "        H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * (sm + sm.dag())\n",
      "    # collapse operators\n",
      "    c_op_list = []\n",
      "\n",
      "    n_th_a = 0.0 # zero temperature\n",
      "\n",
      "    rate = kappa * (1 + n_th_a)\n",
      "    if rate > 0.0:\n",
      "        c_op_list.append(np.sqrt(rate) * a)\n",
      "\n",
      "    rate = kappa * n_th_a\n",
      "    if rate > 0.0:\n",
      "        c_op_list.append(np.sqrt(rate) * a.dag())\n",
      "\n",
      "    rate = gamma\n",
      "    if rate > 0.0:\n",
      "        c_op_list.append(np.sqrt(rate) * sm)\n",
      "    # print H, c_op_list\n",
      "    # evolve and calculate return state vector\n",
      "    result = mesolve(H, psi0, tlist, c_op_list, [tensor(idc, sigmaz())])\n",
      "    return result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 137
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = jc_integrate(N, wc, wa, g, kappa, gamma, psi0, use_rwa, tlist)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 138
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "q = []\n",
      "for i in result.expect[0]:\n",
      "    q.append(i)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 141
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i,j in enumerate(q):\n",
      "    plt.plot(tlist[i], j, \"ro\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7ffe0b598b50>"
       ]
      }
     ],
     "prompt_number": 140
    }
   ],
   "metadata": {}
  }
 ]
}