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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.005016722408026756\n"
     ]
    }
   ],
   "source": [
    "Gamma = 1.0 # Gamma is here, shouldn't matter as we scale it out.\n",
    "tau = 1/Gamma\n",
    "\n",
    "Nt = 300\n",
    "tlist,dt = np.linspace(-0.5*tau,1*tau,Nt,retstep=True)\n",
    "print(dt)"
   ]
  },
  {
   "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": [
    "omega0 = 2*np.pi*1e-3*Gamma  # as on p38\n",
    "t0 = 0\n",
    "tw = 0.1*tau  # Struggling to get this down to 0.1... seems to break the mesolver\n",
    "def pulse(t, args):\n",
    "    return omega0*np.exp(-4*np.log(2)*((t-t0)/tw)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118ae6240>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WktFBYI2kVZIW0pgkHprWZwjYnLY3Ac9ERKT2wXQV0ipgDXAgzS/cB7wYEV/uxImYmdnF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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11576a240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tlist,pulse(tlist,[]),\".\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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(Gamma)*tdep.sigma(0,1)] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": 10,
     "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": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118c5fb38>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LMmg73cvre+vsjqKUGoYWuxqXC2bHkhkbxgul1XZHUUoNQ4tdjYuIcP3CFD4+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\n1DTz/wFhcNZfCoOrzAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118a979e8>"
      ]
     },
     "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 had to bump up `Nt` (number of time points) up to 300"
   ]
  },
  {
   "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": 12,
   "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": 13,
   "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": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "omega[0,:] = pulse(tlist,[])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "L = 1.0\n",
    "dz = L/Nz\n",
    "Ng = 2*np.pi * 5 * Gamma/L #TODO: I get better agreement with 4-5 here instead of 1\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",
    "    # here we 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": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x119120f28>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Z/Oil9ZyvIcpoS3IBcKeZTQfuDPsQZblND6/5wJWtd9MpC8kf9OQPSbuXcWx1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\njuPkjP8LYVnWTntaWJwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118cf4278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plt.title(\"Re($\\Omega$)\")\n",
    "plt.contourf(np.real(omega),np.linspace(-2*np.pi*10e-4,2*np.pi*10e-4,20), cmap=\"PiYG\", origin=\"lower\")\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Replicate Figure 2.2 (lower):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x119598908>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x118ccbfd0>"
      ]
     },
     "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(-12e-4,12e-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": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11970e4a8>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RRzyIzrfp06croGvWrNGKFSvq6NHer1kVCi+//IUC2qtX0d+r++67TwGdNWtW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119625588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zpt = -2\n",
    "plt.plot(tlist,np.real(omega[zpt,:]),'b:')\n",
    "plt.plot(tlist,np.imag(omega[zpt,:]),'r:')\n",
    "plt.plot(tlist,np.abs(omega[zpt,:]),'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Animate the field $\\Omega$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aO1i6cR/XnjWSnEw9/0Okr/SYXMxsuZltiPO6KcFtxOvU9pOUx277K0Ab8JOg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\n3f8Hd1pkF78F1QgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11966c4a8>"
      ]
     },
     "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": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <video controls src=\"omega.mp4\" loop=1 width=50%/> \n",
       "    "
      ],
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     "execution_count": 21,
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    "    <video controls src=\"{0}\" loop=1 width=50%/> \n",
    "    \"\"\".format('omega.mp4')\n",
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