OpticalBloch Two-level.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from opticalbloch import ob\n",
    "import numpy as np\n",
    "import qutip as qu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from scipy.interpolate import interp1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from IPython.core.display import HTML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### A time-dependent example to get used to how the OB works"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Nt = 400\n",
    "tlist = np.linspace(-0.5,1,Nt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "tdep = ob.OB()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def pulse(t, args):\n",
    "    return 2*np.pi*1e-3*np.exp(-(t/0.1)**2) # TODO: check the math if this is 0.1τ, seems too big"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "omega0 = 2*np.pi*1e-3  # as on p38 (if Γ=1)\n",
    "t0 = 0\n",
    "tw = 0.1\n",
    "def pulse(t, args):\n",
    "    return omega0*np.exp(-4*np.log(2)*((t-t0)/tw)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118b40d30>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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IEqnBiRx1NVXUZ6sj2V8xWHTqqUj8FAgSqYHxHC0RXJRWVDz0VBysFpH4KBAkUoPj0Vyl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\niAAKBBERCSgQREQEgP8ParaoyUdaf6oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1157c4978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tlist,pulse(tlist,[]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "tdep.num_states = 2\n",
    "\n",
    "tdep.set_H_0([0,0]) # zeros because we don't care about absolute energies.\n",
    "\n",
    "# Trying this because I know QuTip can take this kind of Hamiltonian\n",
    "tdep.H_Omega_list = [[qu.Qobj([[0,1],[1,0]]),pulse]]\n",
    "\n",
    "Delta = 0\n",
    "tdep.H_Delta = qu.Qobj([[0,0],[0,Delta]])\n",
    "\n",
    "tdep.c_ops = [np.sqrt(6)*tdep.sigma(0,1)] # Gamma is 1 here, increase if needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Result object with mesolve data.\n",
       "--------------------------------\n",
       "states = True\n",
       "num_collapse = 0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# added e_ops just to verify results, but not a likely use case.\n",
    "tdep.mesolve(tlist,td=True,e_ops=[tdep.sigma(0,0),tdep.sigma(1,1)],opts=qu.Options(store_states=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118ccd908>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HDrd13d7VTbvbWtfV3XMxuD32tb3c2e2xlrs9dHns625DV8/99vYeYz2m2xi6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\nnBCY1FKbexIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118af1550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the expectation of the two levels as a function of time.\n",
    "# We'd expect very small changes given how weak the driving field is.\n",
    "plt.subplot(211)\n",
    "plt.plot(tlist,tdep.result.expect[1])\n",
    "plt.subplot(212)\n",
    "plt.plot(tlist,tdep.result.expect[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Seems to work (but have to bump up to `Nt=400` time points to get smaller than `tw=0.2`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Next, to explore the `(z,t)` integration of these equations\n",
    "First, neglecting doppler broadening (i.e. stationary atoms). The following is from Ogden, Eq. 2.52 (p36).\n",
    "$$\\frac{d}{dz}\\Omega(z,t') = \\mathrm{i}N(z)g \\rho_{01}(z,t')$$\n",
    "where $$g=\\frac{d_{01}^2 k}{2\\epsilon_0\\hbar}$$\n",
    "\n",
    "Approach is:\n",
    " - evaluate $\\rho_{01}$ for all time at $z=0$ (no loop necessary since only one velocity class in this prototype).\n",
    " - Calculate field $\\Omega$ one space step forward via Adams-Bashforth\n",
    " - evaluate $\\Omega$ one step forward based on $\\rho$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Euler step in space is $d\\Omega = \\mathrm{i}N(z)g\\rho_{01}dz$ and the initial condition is the drive pulse at the front of the medium."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Nz = 200\n",
    "rho01 = np.zeros([Nz+1,Nt],dtype=np.complex_) # index: z, t\n",
    "omega = np.zeros([Nz+1,Nt],dtype=np.complex_) #TODO: is this complex type ok?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Set up initial conditions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "rho01[0,:] = np.array([tdep.result.states[i][0,1] for i in range(Nt)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "omega[0,:] = pulse(tlist,[])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def i_to_f(interp_in):\n",
    "    \"\"\"A function to convert an interp1d object to a function\n",
    "    TODO: find a more elegant way to do this\"\"\"\n",
    "    def interp_func(x,args=[]):\n",
    "        return np.complex128(interp_in(x))\n",
    "    return interp_func"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dz = 1.0/Nz  #TODO: automatic from linspace\n",
    "Ng = 2*np.pi * 10 # trying to match figures in paper, maybe a typo (1 vs 10) on pg39?\n",
    "for z in range(Nz-1):\n",
    "    #TODO: replace Euler with AB method:\n",
    "    omega[z+1,:] = omega[z,:] + 1j*Ng*rho01[z,:]*dz\n",
    "    \n",
    "    # convert omega into a function (interpolate) run linblad solver.\n",
    "    # AMCD: I had to use linear so I could let it extrapolate past the end\n",
    "    # TODO: find out why mesolve runs past t > t_max\n",
    "    omega_f = interp1d(tlist, omega[z+1,:], kind='linear',fill_value=\"extrapolate\")\n",
    "    tdep.H_Omega_list = [[qu.Qobj([[0,1],[1,0]]),i_to_f(omega_f)]]\n",
    "    \n",
    "    tdep.mesolve(tlist,td=True,e_ops=[tdep.sigma(0,0),tdep.sigma(1,1)],opts=qu.Options(store_states=True))\n",
    "    rho01[z+1,:] = np.array([tdep.result.states[i][0,1] for i in range(Nt)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Replicate Figure 2.1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x119308d68>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6XZTSAD4MfAsYAB4Ebkj3nyZpPfBHwI8lLU35zwUOBP5B0sr0KvVzfwL4tKS7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\n4+BsZmZWMP8HOuhXWkXZTV4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118d3cd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plt.title(\"Re($\\Omega$)\")\n",
    "plt.contourf(np.real(omega),np.linspace(-8e-3,8e-3,20), cmap=\"PiYG\", origin=\"lower\", aspect=2)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Replicate Figure 2.2 (lower):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1198cd470>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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s9OFc4DpJJxFc/D8BwaoL+JyZnWxmyyUlVl3Q16prOmG48TY2turq06+ZLZD0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\nX6mTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118f97198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,2))\n",
    "plt.title(\"Im($\\\\rho_{01}$)\")\n",
    "plt.contourf(np.imag(rho01),np.linspace(-8e-4,8e-4,20), cmap=\"PuOr\", origin=\"lower\")\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Plot of $\\Omega(L,t)$ (exiting pulse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11948b668>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JyMhp0pgqKirk+PHjkp+fL3l5eZKbmyuHDh2SQ4cOybFjxxz5s1AbbM7DMFbZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11991f940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tlist,np.real(omega[-2,:]),'b:')\n",
    "plt.plot(tlist,np.imag(omega[-2,:]),'r:')\n",
    "plt.plot(tlist,np.abs(omega[-2,:]),'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Animate the field $\\Omega$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IcmBhsn4ASYOBa4FpwFTg2qwkdAtwJVCevKZnNb0xIiYnrweSviYBM4FTkro/\nlFRc4DGYmVnKCk0uM4C5yfJc4NIcdS4CFkTE1ojYBiwApksaBfSPiEUREcAdLbRvvr+7I2JfRKwF\nqsgkLDMz60IKTS4jIqIGIHkfnqPOaGB91np1UjY6WW5evt9VkpZJuj3rTKelvg4i6UpJlZIqt2zZ\ncjjHZGZmBWo1uUh6UNLyHK8Zee5DOcriEOWQGS47HpgM1AA3tNLXwYURcyKiIiIqhg0blmeoZmaW\nhpLWKkTE+S1tk7RJ0qiIqEmGuTbnqFYNnJu1PgZ4JCkf06x8Y7LPTVn7+DHw26y+xuZqY2ZmXUeh\nw2LzgP13f80C7s9RZz5woaRByfDWhcD8ZBhtp6SzkrvEPra/fZKo9nsfsDxrfzMllUmaQOYmgCcK\nPAYzM0tZq2curfg2cK+k2cBLwAcAJFUAn4mIT0bEVknfBBYnba6PiK3J8meBnwC9gN8nL4DvSppM\nZsjrReDTABGxQtK9wEqgAfh8RDQWeAxmZpYyZW7UOrJVVFREZWVlZ4dhZtatSFoSERVtaesn9M3M\nLHVOLmZmljonFzMzS52Ti5mZpc7JxczMUufkYmZmqXNyMTOz1Dm5mJlZ6pxczMwsdU4uZmaWOicX\nMzNLnZOLmZmlzsnFzMxS5+RiZmapc3IxM7PUObmYmVnqnFzMzCx1Ti5mZpa6gpKLpMGSFkhanbwP\naqHerKTOakmzssqnSHpGUpWkH0hSUn6PpKXJ60VJS5Py8ZL2ZG37USHxm5lZ+yj0zOVqYGFElAML\nk/UDSBoMXAtMA6YC12YloVuAK4Hy5DUdICIuj4jJETEZ+AXwy6wu1+zfFhGfKTB+MzNrB4UmlxnA\n3GR5LnBpjjoXAQsiYmtEbAMWANMljQL6R8SiiAjgjubtkzOZDwI/KzBOMzPrQIUmlxERUQOQvA/P\nUWc0sD5rvTopG50sNy/PdjawKSJWZ5VNkPSUpD9JOrvA+M3MrB2UtFZB0oPAyBybvpHnPpSjLA5R\nnu0KDjxrqQHGRcSrkqYAv5Z0SkTsOGin0pVkhtwYN25cnqGamVkaWk0uEXF+S9skbZI0KiJqkmGu\nzTmqVQPnZq2PAR5Jysc0K9+Y1XcJ8PfAlKxY9gH7kuUlktYAE4HKHHHPAeYAVFRUNE9aZmbWjgod\nFpsH7L/7axZwf44684ELJQ1KLuRfCMxPhtF2SjorubbysWbtzweei4jXh84kDZNUnCwfR+YmgBcK\nPAYzM0sRYqPyAAAHJUlEQVRZocnl28AFklYDFyTrSKqQdCtARGwFvgksTl7XJ2UAnwVuBaqANcDv\ns/qeycEX8s8Blkl6GrgP+ExWX2Zm1kUoc6PWka2ioiIqKw8aOTMzs0OQtCQiKtrS1k/om5lZ6pxc\nzMwsdU4uZmaWOicXMzNLnZOLmZmlzsnFzMxS5+RiZmapc3IxM7PUObmYmVnqnFzMzCx1Ti5mZpY6\nJxczM0udk4uZmaXOycXMzFLn5GJmZqlzcjEzs9Q5uZiZWeqcXMzMLHVOLmZmlrqCkoukwZIWSFqd\nvA9qod6spM5qSbOyyr8lab2kXc3ql0m6R1KVpMcljc/adk1SvkrSRYXEb2Zm7aPQM5ergYURUQ4s\nTNYPIGkwcC0wDZgKXJuVhH6TlDU3G9gWEScANwLfSfqaBMwETgGmAz+UVFzgMZiZWcoKTS4zgLnJ\n8lzg0hx1LgIWRMTWiNgGLCCTGIiIxyKippV+7wPOk6Sk/O6I2BcRa4EqcicnMzPrRCUFth+xPzlE\nRI2k4TnqjAbWZ61XJ2WH8nqbiGiQtB0YkpQ/lk9fkq4ErkxWd0la1co+22oo8Eo79d0eulu84Jg7\nQneLF7pfzN0tXoAT29qw1eQi6UFgZI5N38hzH8pRFm1sk3dfETEHmNPKfgomqTIiKtp7P2npbvGC\nY+4I3S1e6H4xd7d4IRNzW9u2mlwi4vxD7HiTpFHJWcsoYHOOatXAuVnrY4BHWtltNTAWqJZUAgwA\ntmaVZ/e1sbVjMDOzjlXoNZd5wP67v2YB9+eoMx+4UNKg5EL+hUlZvv1eBjwUEZGUz0zuJpsAlANP\nFHgMZmaWskKTy7eBCyStBi5I1pFUIelWgIjYCnwTWJy8rk/KkPRdSdVAb0nVkq5L+r0NGCKpCvgy\nyV1oEbECuBdYCfwB+HxENBZ4DIVq96G3lHW3eMExd4TuFi90v5i7W7xQQMzKnBCYmZmlx0/om5lZ\n6pxczMwsdU4uhynfKW+Suv0lbZB0U0fG2CyGVuOVNFnSIkkrJC2TdHknxTo9mdanSlKu2R5anBao\nM+QR75clrUw+04WSju2MOJvFdMiYs+pdJikkdfqts/nELOmDyWe9QtJPOzrGZrG09nMxTtLDkp5K\nfjYu7ow4s+K5XdJmSctb2C5JP0iOZ5mkM/PqOCL8OowX8F3g6mT5auA7h6j7feCnwE1dOV5gIlCe\nLB8D1AADOzjOYmANcBzQA3gamNSszueAHyXLM4F7OvFzzSfedwK9k+XPdma8+cac1OsH/JnMA8sV\nXT1mMneNPgUMStaHd/F45wCfTZYnAS928md8DnAmsLyF7RcDvyfznOFZwOP59Oszl8OXz5Q3SJoC\njAD+2EFxtaTVeCPi+YhYnSxvJPO80rAOizBjKlAVES9ERB1wN5nYs7U0LVBnaDXeiHg4InYnq4+R\neS6rM+XzGUPm7s7vAns7MrgW5BPzp4CbIzO9FBGR63m7jpJPvAH0T5YH0MnP6kXEn8k8R9iSGcAd\nkfEYMDB5rvGQnFwO3wFT3gAHTXkjqQi4AfhqB8eWS6vxZpM0lcxfXGs6ILZs+UwTdMC0QMD+aYE6\nw+FOazSbzF9/nanVmCWdAYyNiN92ZGCHkM/nPBGYKOlvkh6TNL3DojtYPvFeB3wkeQzjAeAfOya0\nNmvLFF4Fzy12REphypvPAQ9ExPqO+MM6hXj39zMKuBOYFRFNacR2OLvPUdb8Pvm2TCXUXvKORdJH\ngArgHe0aUesOGXPyR9GNwMc7KqA85PM5l5AZGjuXzNnhXySdGhG17RxbLvnEewXwk4i4QdJbgDuT\neDv6dy5fbfq9c3LJIQqf8uYtwNmSPgf0BXpI2hURLV5A7eR4kdQf+B3wv5NT346Wz9Q+LU0L1Bny\nmopI0vlkkvw7ImJfB8XWktZi7gecCjyS/FE0Epgn6b0R0eY5pgqU78/FYxFRD6xVZpLacjIPbXe0\nfOKdzRszwy+S1JPMpJadOZx3KG2adsvDYoev1SlvIuLDETEuIsYDXyEzXtkuiSUPrcYrqQfwKzJx\n/rwDY8u2GCiXNCGJZyaZ2LO1NC1QZ2g13mSI6b+A93bydYD9DhlzRGyPiKERMT752X2MTOydlVgg\nv5+LX5O5eQJJQ8kMk73QoVG+IZ94XwLOA5B0MtAT2NKhUR6eecDHkrvGzgK2R+6vSjlQZ96l0B1f\nZMb4FwKrk/fBSXkFcGuO+h+nc+8WazVe4CNAPbA06zW5E2K9GHiezPWebyRl15P5Bw4yv4Q/J/M9\nPk8Ax3Xyz0Jr8T4IbMr6TOd1Zrz5xNys7iN08t1ieX7OAr5HZlqoZ4CZXTzeScDfyNxJthS4sJPj\n/RmZO0TryZylzAY+A3wm6/O9OTmeZ/L9mfD0L2ZmljoPi5mZWeqcXMzMLHVOLmZmljonFzMzS52T\ni5mZpc7JxczMUufkYmZmqfv/Dl4wscEEbDYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119a04748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.animation import FuncAnimation\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "xdata, ydata = [], []\n",
    "ln, = plt.plot([], [], animated=True)\n",
    "ln2, = plt.plot([], [], animated=True)\n",
    "\n",
    "def init():\n",
    "    ax.set_xlim(-0.5, 1)\n",
    "    ax.set_ylim(-0.01,0.01)\n",
    "    return ln,\n",
    "\n",
    "def update(frame):\n",
    "    ln.set_data(tlist, np.real(omega[frame,:]))\n",
    "    ln2.set_data(tlist, np.imag(omega[frame,:]))\n",
    "    return ln,\n",
    "\n",
    "ani = FuncAnimation(fig, update, frames=range(200),\n",
    "                    init_func=init, blit=True, interval=30)\n",
    "\n",
    "ani.save('omega.mp4', writer=\"ffmpeg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <video controls src=\"omega.mp4\" loop=1 width=50%/> \n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(\"\"\"\n",
    "    <video controls src=\"{0}\" loop=1 width=50%/> \n",
    "    \"\"\".format('omega.mp4')\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}