{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reaction coordinate solver for 2-level bosonic system  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Author: Neill Lambert (nwlambert@gmail.com)\n",
    "        Anubhav Vardhan (anubhavvardhan@gmail.com)\n",
    "\n",
    "For more information about QuTiP see http://qutip.org"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reference: link.aps.org/doi/10.1103/PhysRevA.90.032114 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this model, we take a quantum system coupled to a bosonic environment and map to a model\n",
    "in which a collective mode of the environment, known as the reaction coordinate \n",
    "(RC), is incorporated within an effective system Hamiltonian. We then treat the \n",
    "residual environment within a full second-order Born-Markov master equation\n",
    "formalism. Thus, all important system-bath, and indeed intrabath, correlations \n",
    "are incorporated into the system-RC Hamiltonian in the regimes we study.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from qutip import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qutip import rcsolve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining the 2-level system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Del = 1.0    # The number of qubits in the system.\n",
    "wq = 0.5     # Energy of the 2-level system.\n",
    "Hsys = 0.5 * wq * sigmaz() + 0.5 * Del * sigmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = sigmaz()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Defining the coupling Q such that:\n",
    "\n",
    "Decoupled Hamiltonian-\n",
    "#### $H_0 = \\omega a^\\dagger a + \\frac{1}{2}\\omega_q\\sigma_z + \\frac{1}{2}\\delta\\sigma_x$ \n",
    "\n",
    "Interaction-\n",
    "#### $H_1 = g(a^\\dagger + a)\\sigma_z$\n",
    "\n",
    "Total Hamiltonian-\n",
    "#### $H = H_0 + H_1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving the RC master equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "wc = 0.05                # Cutoff frequency.\n",
    "alpha = 2.5/pi           # Coupling strength.\n",
    "N = 10                   # Number of cavity fock states.\n",
    "Temperature = 1/0.95     # Tempertaure.\n",
    "tlist = np.linspace(0, 40, 600)\n",
    "initial_state = basis(2,1) * basis(2,1).dag()                # Initial state of the system.\n",
    "return_vals = [Q]            # List for which to calculate expectation value                                          \n",
    "options = Options(nsteps=15000, store_states=True)        # Options for the solver.\n",
    "\n",
    "output = rcsolve(Hsys, initial_state, tlist, return_vals, Q, wc, alpha, N, \n",
    "                Temperature, options=options)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the TLS state occupation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x119460cc0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eb2aVwCPuflQ737kOaHT3G9v7/ZqaGl+2rPCvb9uzBz78YViypOXyf/zHcIX38JyX8XWP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\nRFJG4S0iIpIy/x/wS4wSJkqdaAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118f7a668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = subplots(1, 1, sharex=True, figsize=(8,4))\n",
    "axes.plot(tlist, real(output.expect[0]), 'b', linewidth=2, label=\"P12\")\n",
    "\n",
    "axes.legend(loc=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the photon distributions at arbitrary times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[10, 2], [10, 2]], shape = (20, 20), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.654 & 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 & 0.226 & 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\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 3.862\\times10^{-04} & 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 & 1.335\\times10^{-04} & 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 & 4.616\\times10^{-05}\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[10, 2], [10, 2]], shape = (20, 20), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   6.54298105e-01   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   2.26202536e-01\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   7.82022553e-02   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   2.70359158e-02\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   9.34679878e-03   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   3.23135521e-03\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   1.11713719e-03   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   3.86214270e-04\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   1.33521168e-04   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00]\n",
       " [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
       "    0.00000000e+00   0.00000000e+00   0.00000000e+00   4.61606517e-05]]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output.states[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ck2RvkgtJFpIcucbx9yZ5LMm3k3wtya3jjypJktTNmgUnyRRwP7AP2APclWTPsmHfB95W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\nwZEkSc35/wG1OQrHuiUtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1194abf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_idx_vec = range(0,len(tlist),200) \n",
    "\n",
    "fig, axes = subplots(len(t_idx_vec), 1, sharey=True, figsize=(8,2*len(t_idx_vec)))\n",
    "\n",
    "for idx, t_idx in enumerate(t_idx_vec):\n",
    "\n",
    "    psi_a = ptrace(output.states[t_idx], 0)\n",
    "    \n",
    "    cont1 = axes[idx].bar(range(0, N), real(psi_a.diag()))\n",
    "    \n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the wigner function at arbitrary times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1YimfPp+RlHOXsJmW7waKmYgsKWlP5LympG1NzyFnwAjYPFfW5cC67+AVKm27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\nq7ckAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1198170b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xvec = linspace(-5,5,200)\n",
    "t_idx_vec = range(0,len(tlist),200) \n",
    "\n",
    "fig, axes = subplots(len(t_idx_vec), 1, sharex=True, sharey=True, figsize=(8,4*len(t_idx_vec)))\n",
    "\n",
    "for idx, t_idx in enumerate(t_idx_vec):\n",
    "    psi_a = ptrace(output.states[t_idx], 0)\n",
    "    \n",
    "    W_a = wigner(psi_a, xvec, xvec)\n",
    "    \n",
    "    \n",
    "    cont1 = axes[idx].contourf(xvec, xvec, W_a, 100)\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Software versions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>QuTiP</td><td>4.3.0.dev0+6e5b1d43</td></tr><tr><td>Numpy</td><td>1.13.1</td></tr><tr><td>SciPy</td><td>0.19.1</td></tr><tr><td>matplotlib</td><td>2.0.2</td></tr><tr><td>Cython</td><td>0.25.2</td></tr><tr><td>Number of CPUs</td><td>2</td></tr><tr><td>BLAS Info</td><td>INTEL MKL</td></tr><tr><td>IPython</td><td>6.1.0</td></tr><tr><td>Python</td><td>3.6.2 |Anaconda custom (x86_64)| (default, Jul 20 2017, 13:14:59) \n",
       "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td colspan='2'>Thu Jul 20 22:41:41 2017 MDT</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qutip.ipynbtools import version_table\n",
    "\n",
    "version_table()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": 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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}