Chapter 12 - SHO.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 12 - Simple Harmonic Oscillator\n",
    "Several examples that make use of the built-in Simple Harmonic Oscillator tools:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import sqrt,linspace,exp\n",
    "from qutip import *\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 40 # size of the Hilbert space.\n",
    "       # N needs to be large enough that matrix is not truncated\n",
    "a = destroy(N)\n",
    "n = a.dag()*a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a coherent state with $\\alpha = 2:$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi = coherent(N,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[40], [1]], shape = (40, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.607\\\\0.607\\\\0.429\\\\0.248\\\\0.124\\\\\\vdots\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[40], [1]], shape = (40, 1), type = ket\n",
       "Qobj data =\n",
       "[[  6.06530660e-01]\n",
       " [  6.06530660e-01]\n",
       " [  4.28881942e-01]\n",
       " [  2.47615105e-01]\n",
       " [  1.23807552e-01]\n",
       " [  5.53684207e-02]\n",
       " [  2.26040631e-02]\n",
       " [  8.54353279e-03]\n",
       " [  3.02059499e-03]\n",
       " [  1.00686500e-03]\n",
       " [  3.18398668e-04]\n",
       " [  9.60008106e-05]\n",
       " [  2.77130469e-05]\n",
       " [  7.68621628e-06]\n",
       " [  2.05422771e-06]\n",
       " [  5.30399314e-07]\n",
       " [  1.32599828e-07]\n",
       " [  3.21601823e-08]\n",
       " [  7.58022766e-09]\n",
       " [  1.73902349e-09]\n",
       " [  3.88857474e-10]\n",
       " [  8.48556576e-11]\n",
       " [  1.80912870e-11]\n",
       " [  3.77229410e-12]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]\n",
       " [  0.00000000e+00]]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Expectation value $\\langle n\\rangle$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[1], [1]], shape = (1, 1), type = bra\\begin{equation*}\\left(\\begin{array}{*{11}c}1.000\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[1], [1]], shape = (1, 1), type = bra\n",
       "Qobj data =\n",
       "[[ 1.]]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psi.dag()*n*psi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert to a density matrix:\n",
    "psi_dm = ket2dm(psi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[40], [40]], shape = (40, 40), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.368 & 0.368 & 0.260 & 0.150 & 0.075 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.368 & 0.368 & 0.260 & 0.150 & 0.075 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.260 & 0.260 & 0.184 & 0.106 & 0.053 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.150 & 0.150 & 0.106 & 0.061 & 0.031 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.075 & 0.075 & 0.053 & 0.031 & 0.015 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[40], [40]], shape = (40, 40), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 0.36787944  0.36787944  0.26013005 ...,  0.          0.          0.        ]\n",
       " [ 0.36787944  0.36787944  0.26013005 ...,  0.          0.          0.        ]\n",
       " [ 0.26013005  0.26013005  0.18393972 ...,  0.          0.          0.        ]\n",
       " ..., \n",
       " [ 0.          0.          0.         ...,  0.          0.          0.        ]\n",
       " [ 0.          0.          0.         ...,  0.          0.          0.        ]\n",
       " [ 0.          0.          0.         ...,  0.          0.          0.        ]]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psi*psi.dag()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<matplotlib.figure.Figure at 0x11a2f3358>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x11a3396d8>)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a2f3358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fock state distribution of the coherent state:\n",
    "plot_fock_distribution(psi_dm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also look at other coherent states:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<matplotlib.figure.Figure at 0x11a549ef0>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x11a8247b8>)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a549ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# With larger N and α:\n",
    "plot_fock_distribution(coherent_dm(100,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And some other density matrices, like a fock-state (or n eigenstate):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<matplotlib.figure.Figure at 0x1022aa5c0>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x1022f9940>)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1022aa5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# With a Fock state (number state):\n",
    "plot_fock_distribution(fock_dm(20,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[20], [1]], shape = (20, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\1.0\\\\0.0\\\\0.0\\\\\\vdots\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[20], [1]], shape = (20, 1), type = ket\n",
       "Qobj data =\n",
       "[[ 0.]\n",
       " [ 0.]\n",
       " [ 1.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]\n",
       " [ 0.]]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fock(20,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a thermal state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<matplotlib.figure.Figure at 0x124a1c2b0>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x124e6beb8>)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x124a1c2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A thermal state has decaying amplitudes\n",
    "plot_fock_distribution(thermal_dm(20,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finally, can visualize the phasor using what is called the Wigner function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11c80bc50>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c5d2470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xvec = linspace(-10,10,200) # Create an array for the phase space coordinates.\n",
    "plt.imshow(wigner(coherent(40,5j)+coherent(40,-5j),xvec,xvec), extent=[-10,10,-10,10]) # contour plot of Wigner function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "inputHidden": false,
    "outputHidden": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernel_info": {
   "name": "python3"
  },
  "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": "3.6.3"
  },
  "nteract": {
   "version": "0.8.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}