{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Open Dicke Model: Superradiance of $N$ qubits in an open cavity\n",
    "\n",
    "Notebook author: Nathan Shammah (nathan.shammah at gmail.com)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider a system of $N$ two-level systems (TLSs) coupled to a cavity mode. This is known as the Dicke model \n",
    "\n",
    "\\begin{eqnarray}\n",
    "H&=&\\omega_{0}J_z +  \\omega_{c}a^\\dagger a + g\\left(a^\\dagger + a\\right)\\left(J_{+} + J_{-}\\right)\n",
    "\\end{eqnarray}\n",
    "\n",
    "where each TLS has identical frequency $\\omega_{0}$. The light matter coupling can be in the ultrastrong coupling (USC) regime, $g/\\omega_{0}>0.1$.\n",
    "\n",
    "If we study this model as an open quantum system, the cavity can leak photons at a rate $\\kappa$. Moreover, we can introduce the effect of incoherent local and collective processes also on the TLSs. For example the system can be incoherently pumped at a rate $\\gamma_\\text{P}$, the TLSs are subject to dephasing at a rate $\\gamma_\\text{D}$, and local incoherent emission occurs at a rate $\\gamma_\\text{E}$. The dynamics of the coupled light-matter system is governed by\n",
    "\n",
    "\\begin{eqnarray}\\dot{\\rho} &=& \n",
    "-i\\lbrack \\omega_{0}J_z +  \\omega_{a}a^\\dagger a + g\\left(a^\\dagger + a\\right)\\left(J_{+} + J_{-}\\right),\\rho \\rbrack\n",
    "+\\frac{\\kappa}{2}\\mathcal{L}_{a}[\\rho]\n",
    "+\\sum_{n=1}^{N}\\left(\\frac{\\gamma_\\text{P}}{2}\\mathcal{L}_{J_{+,n}}[\\rho] \n",
    "+\\frac{\\gamma_\\text{E}}{2}\\mathcal{L}_{J_{+,n}}[\\rho]\n",
    "+\\frac{\\gamma_\\text{D}}{2}\\mathcal{L}_{J_{+,n}}[\\rho]\\right)\n",
    "\\end{eqnarray}\n",
    "\n",
    "When only the dissipation of the cavity is present, beyond a critical value of the coupling $g$, the steady state of the system becomes superradiant. This is visible by looking at the Wigner function of the photonic part of the density matrix, which displays two displaced lobes in the $x$ and $p$ plane.   \n",
    "\n",
    "As it has been shown in Ref. [1], the presence of dephasing suppresses the superradiant phase transition, while the presence of local emission restores it [2].\n",
    "\n",
    "In order to study this system using QuTiP and $\\texttt{qutip.piqs}$, we will first build the TLS Liouvillian, then we will build the photonic Liouvillian and finally we will build the light-matter interaction. The total dynamics of the system is thus defined in a Liouvillian space that has both TLS and photonic degrees of freedom. \n",
    "\n",
    "Ref. [6] contains a review of the open Dicke model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "from matplotlib import cm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from qutip import *\n",
    "from qutip.piqs import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 6\n",
      "Hilbert space dim = (16, 16)\n",
      "Number of Dicke states = 16\n",
      "Liouvillian space dim = (256, 256)\n",
      "dephasing = 0.01\n",
      "pumping = 0.1\n"
     ]
    }
   ],
   "source": [
    "#TLS parameters\n",
    "N = 6\n",
    "ntls = N\n",
    "nds = num_dicke_states(ntls)\n",
    "[jx, jy, jz] = jspin(N)\n",
    "jp = jspin(N, \"+\")\n",
    "jm = jp.dag()\n",
    "w0 = 1\n",
    "gE = 0.1\n",
    "gD = 0.01\n",
    "gP = 0.1\n",
    "gCP = 0.1\n",
    "gCE = 0.1\n",
    "gCD = 0.1\n",
    "h = w0 * jz\n",
    "#photonic parameters\n",
    "nphot = 16\n",
    "wc = 1\n",
    "kappa = 1\n",
    "ratio_g = 2\n",
    "g = ratio_g/np.sqrt(N)\n",
    "a = destroy(nphot)\n",
    "\n",
    "#TLS liouvillian\n",
    "system = Dicke(N = N)\n",
    "system.hamiltonian = h \n",
    "system.emission = 0 \n",
    "system.dephasing = gD\n",
    "system.pumping = gP\n",
    "system.collective_pumping = 0\n",
    "system.collective_emission = 0\n",
    "system.collective_dephasing = 0\n",
    "liouv = system.liouvillian() \n",
    "system\n",
    "\n",
    "#TLS liouvillian 2\n",
    "system2 = Dicke(N = N)\n",
    "system2.hamiltonian = h \n",
    "system2.emission = gE \n",
    "system2.dephasing = gD\n",
    "system2.pumping = 0\n",
    "system2.collective_pumping = 0\n",
    "system2.collective_emission = 0\n",
    "system2.collective_dephasing = 0\n",
    "liouv2 = system2.liouvillian() \n",
    "\n",
    "#TLS liouvillian 3\n",
    "system3 = Dicke(N = N)\n",
    "system3.hamiltonian = h \n",
    "system3.emission = gE \n",
    "system3.dephasing = gD\n",
    "system3.pumping = 0#gP\n",
    "system3.collective_pumping = gCP\n",
    "system3.collective_emission = 0\n",
    "system3.collective_dephasing = 0\n",
    "liouv3 = system3.liouvillian() \n",
    "\n",
    "#TLS liouvillian 4\n",
    "system4 = Dicke(N = N)\n",
    "system4.hamiltonian = h \n",
    "system4.emission = gE \n",
    "system4.dephasing = gD\n",
    "system4.pumping = 0\n",
    "system4.collective_pumping = 0\n",
    "system4.collective_emission = gCE\n",
    "system4.collective_dephasing = 0\n",
    "liouv4 = system4.liouvillian() \n",
    "print(system)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#photonic liouvilian\n",
    "h_phot = wc * a.dag() * a\n",
    "c_ops_phot = [np.sqrt(kappa) * a]\n",
    "liouv_phot = liouvillian(h_phot, c_ops_phot)\n",
    "\n",
    "#identity operators\n",
    "id_tls = to_super(qeye(nds))\n",
    "id_phot = to_super(qeye(nphot))\n",
    "\n",
    "# light-matter superoperator \n",
    "h_int = g * tensor(a + a.dag(), jx)\n",
    "liouv_int = -1j* spre(h_int) + 1j* spost(h_int)\n",
    "\n",
    "# 1 total liouvillian\n",
    "liouv_sum = super_tensor(liouv_phot, id_tls) + super_tensor(id_phot, liouv)\n",
    "liouv_tot = liouv_sum + liouv_int\n",
    "\n",
    "#2 total liouvillian\n",
    "liouv_sum2 = super_tensor(liouv_phot, id_tls) + super_tensor(id_phot, liouv2)\n",
    "liouv_tot2 = liouv_sum2 + liouv_int\n",
    "\n",
    "#3 total liouvillian\n",
    "liouv_sum3 = super_tensor(liouv_phot, id_tls) + super_tensor(id_phot, liouv3)\n",
    "liouv_tot3 = liouv_sum3 + liouv_int\n",
    "\n",
    "#4 total liouvillian\n",
    "liouv_sum4 = super_tensor(liouv_phot, id_tls) + super_tensor(id_phot, liouv4)\n",
    "liouv_tot4 = liouv_sum4 + liouv_int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#total operators\n",
    "jz_tot = tensor(qeye(nphot), jz)\n",
    "jp_tot = tensor(qeye(nphot), jp)\n",
    "jm_tot = tensor(qeye(nphot), jm)\n",
    "jpjm_tot = tensor(qeye(nphot), jp*jm)\n",
    "nphot_tot = tensor(a.dag()*a, qeye(nds))\n",
    "adag_tot = tensor(a.dag(), qeye(nds))\n",
    "a_tot = tensor(a, qeye(nds))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ensemble 4 is ok\n"
     ]
    }
   ],
   "source": [
    "# 4 calculate steady state\n",
    "rho_ss4 = steadystate(liouv_tot4, method=\"direct\")\n",
    "nphot_ss4 = expect(nphot_tot, rho_ss4)\n",
    "psi4 = rho_ss4.ptrace(0)\n",
    "print(\"Ensemble 4 is ok\")\n",
    "# takes a couple of minutes "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1 calculate steady state\n",
    "rho_ss = steadystate(liouv_tot, method=\"direct\")\n",
    "nphot_ss = expect(nphot_tot, rho_ss)\n",
    "psi = rho_ss.ptrace(0)\n",
    "\n",
    "# 2 calculate steady state\n",
    "rho_ss2 = steadystate(liouv_tot2, method=\"direct\")\n",
    "nphot_ss2 = expect(nphot_tot, rho_ss2)\n",
    "psi2 = rho_ss2.ptrace(0)\n",
    "\n",
    "# 3 calculate steady state\n",
    "rho_ss3 = steadystate(liouv_tot3, method=\"direct\")\n",
    "nphot_ss3 = expect(nphot_tot, rho_ss3)\n",
    "psi3 = rho_ss3.ptrace(0)\n",
    "\n",
    "# 4 calculate steady state\n",
    "rho_ss4 = steadystate(liouv_tot4, method=\"direct\")\n",
    "nphot_ss4 = expect(nphot_tot, rho_ss4)\n",
    "psi4 = rho_ss4.ptrace(0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 ok\n",
      "2 ok\n",
      "3 ok\n",
      "4 ok\n"
     ]
    }
   ],
   "source": [
    "# calculate Wigner function for photonic states\n",
    "nx = 1000\n",
    "xvec = np.linspace(-6, 6, nx)\n",
    "W = wigner(psi, xvec, xvec)\n",
    "print(\"1 ok\")\n",
    "W2 = wigner(psi2, xvec, xvec)\n",
    "print(\"2 ok\")\n",
    "W3 = wigner(psi3, xvec, xvec)\n",
    "print(\"3 ok\")\n",
    "W4 = wigner(psi4, xvec, xvec)\n",
    "print(\"4 ok\")\n",
    "# strings for the plot title\n",
    "g_string = np.round(g,4)\n",
    "gE_string = np.round(gE,4)\n",
    "gD_string = np.round(gD,4)\n",
    "gP_string = np.round(gP,4)\n",
    "gCE_string = np.round(gCE,4)\n",
    "gCP_string = np.round(gCP,4)\n",
    "gCD_string = np.round(gCD,4)\n",
    "k_string = np.round(kappa,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wigner function Visualization "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rc('text', usetex = True)\n",
    "label_size = 25\n",
    "plt.rc('xtick', labelsize=label_size) \n",
    "plt.rc('ytick', labelsize=label_size)\n",
    "\n",
    "# 1\n",
    "Wp = np.round(W,3)\n",
    "wmap = wigner_cmap(Wp)  # Generate Wigner colormap\n",
    "nrm = mpl.colors.Normalize(0, Wp.max())\n",
    "# 2\n",
    "Wp2 = np.round(W2,3)\n",
    "wmap2 = wigner_cmap(Wp2)  # Generate Wigner colormap\n",
    "nrm2 = mpl.colors.Normalize(0, Wp2.max())\n",
    "# 3\n",
    "Wp3 = np.round(W3,3)\n",
    "wmap3 = wigner_cmap(Wp3)  # Generate Wigner colormap\n",
    "nrm3 = mpl.colors.Normalize(0, Wp3.max())\n",
    "# 4\n",
    "Wp4 = np.round(W4,3)\n",
    "wmap4 = wigner_cmap(Wp4)  # Generate Wigner colormap\n",
    "nrm4 = mpl.colors.Normalize(0, Wp4.max())\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10, 10))\n",
    "\n",
    "axes[0,0].contourf(xvec, xvec, Wp, 100, cmap=wmap, norm=nrm)\n",
    "axes[0,1].contourf(xvec, xvec, Wp2, 100, cmap=wmap2, norm=nrm2)\n",
    "axes[1,0].contourf(xvec, xvec, Wp3, 100, cmap=wmap3, norm=nrm3)\n",
    "axes[1,1].contourf(xvec, xvec, Wp4, 100, cmap=wmap4, norm=nrm4)\n",
    "axes[1,0].set_xlabel(r'$x$', fontsize = label_size)\n",
    "axes[1,1].set_xlabel(r'$x$', fontsize = label_size)\n",
    "\n",
    "#axes[0,0].set_ylabel(r'$p$', fontsize = label_size)\n",
    "axes[0, 0].set_title(r\"$\\kappa$, $\\gamma_\\phi$, $\\gamma_\\uparrow$\", \n",
    "                     fontsize = label_size, position=(0.2, 0.85))\n",
    "axes[0, 1].set_title(r\"$\\kappa$, $\\gamma_\\phi$, $\\gamma_\\downarrow$\", \n",
    "                     fontsize = label_size, position=(0.8, 0.85))\n",
    "axes[1, 0].set_title(r\"$\\kappa$, $\\gamma_\\phi$, $\\gamma_\\downarrow$, $\\gamma_\\Uparrow$\", \n",
    "                     fontsize = label_size, position=(0.3, 0.85))\n",
    "axes[1, 1].set_title(r\"$\\kappa$, $\\gamma_\\phi$, $\\gamma_\\downarrow$, $\\gamma_\\Downarrow$\", \n",
    "                     fontsize = label_size, position=(0.7, 0.85))\n",
    "\n",
    "axes[0,0].set_xticks([-5,0,5])\n",
    "axes[0,0].set_yticks([-5,0,5])\n",
    "axes[0,0].set_ylabel(r'$p$', fontsize = label_size)\n",
    "\n",
    "axes[0,1].set_xticks([-5,0,5])\n",
    "axes[0,1].set_yticks([-5,0,5])\n",
    "\n",
    "axes[1,0].set_ylabel(r'$p$', fontsize = label_size)\n",
    "axes[1,0].set_xticks([-5,0,5])\n",
    "axes[1,0].set_yticks([-5,0,5])\n",
    "\n",
    "axes[1,1].set_xticks([-5,0,5])\n",
    "axes[1,1].set_yticks([-5,0,5])\n",
    "\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Wigner function of the photonic part of the system displays the two displaced squeezed blobs typical of superradiance depending on the local and collective incoherent terms affecting the dynamics [2,3]. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "rhoss_list = []\n",
    "rhoss_list.append(rho_ss)\n",
    "rhoss_list.append(rho_ss2)\n",
    "rhoss_list.append(rho_ss3)\n",
    "rhoss_list.append(rho_ss4)\n",
    "wigner_list = []\n",
    "wigner_list.append(W)\n",
    "wigner_list.append(W2)\n",
    "wigner_list.append(W3)\n",
    "wigner_list.append(W4)\n",
    "\n",
    "# save data \n",
    "save_file = False\n",
    "if save_file == True:\n",
    "    file_name = str(\"superradiance_rhoss_Nmax{}.npz\".format(N))\n",
    "    np.savez('{}'.format(file_name), rhoss_list)\n",
    "    file_name = str(\"superradiance_wigner_list_Nmax{}.npz\".format(N))\n",
    "    np.savez('{}'.format(file_name), wigner_list)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] E.G. Dalla Torre *et al.*, *Phys Rev. A* **94**, 061802(R) (2016)\n",
    "\n",
    "[2] P. Kirton and J. Keeling, *Phys. Rev. Lett.* **118**, 123602 (2017)\n",
    "\n",
    "[3] N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, https://arxiv.org/abs/1805.05129\n",
    "\n",
    "[4] N. Shammah, N. Lambert, F. Nori, and S. De Liberato, *Phys Rev. A* **96**, 023863 (2017)\n",
    "\n",
    "[5] J. R. Johansson, P. D. Nation, and F. Nori, *Comp. Phys. Comm.* **183**, 1760 (2012) http://qutip.org\n",
    "\n",
    "[6] P. Kirton, M. M. Roses, J. Keeling, and E. G. Dalla Torre, arXiv:1805.09828 (2018)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "QuTiP: Quantum Toolbox in Python\n",
      "Copyright (c) 2011 and later.\n",
      "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n",
      "\n",
      "QuTiP Version:      4.3.1\n",
      "Numpy Version:      1.14.2\n",
      "Scipy Version:      1.1.0\n",
      "Cython Version:     0.28.5\n",
      "Matplotlib Version: 2.2.3\n",
      "Python Version:     3.6.7\n",
      "Number of CPUs:     2\n",
      "BLAS Info:          INTEL MKL\n",
      "OPENMP Installed:   False\n",
      "INTEL MKL Ext:      True\n",
      "Platform Info:      Darwin (x86_64)\n",
      "Installation path:  /Users/nathanshammah/miniconda3/lib/python3.6/site-packages/qutip\n",
      "==============================================================================\n",
      "Please cite QuTiP in your publication.\n",
      "==============================================================================\n",
      "For your convenience a bibtex file can be easily generated using `qutip.cite()`\n"
     ]
    }
   ],
   "source": [
    "qutip.about()"
   ]
  }
 ],
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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