examples/piqs-superradiant-light-emission.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Superradiant light emission (Dicke superradiance)\n",
    "\n",
    "Notebook author: Nathan Shammah (nathan.shammah at gmail.com)\n",
    "\n",
    "We consider a system of $N$ two-level systems (TLSs) with identical frequency $\\omega_{0}$, which can emit collectively at a rate $\\gamma_\\text{CE}$ [1], and suffer from dephasing and local losses at rates $\\gamma_\\text{D}$ and $\\gamma_\\text{E}$, respectively. The dynamics can be written as\n",
    "\\begin{eqnarray}\n",
    "\\dot{\\rho} &=&-i\\lbrack \\omega_{0}J_z,\\rho \\rbrack\n",
    "+\\frac{\\gamma_\\text {CE}}{2}\\mathcal{L}_{J_{-}}[\\rho]\n",
    "+\\sum_{n=1}^{N}\\frac{\\gamma_\\text{D}}{2}\\mathcal{L}_{J_{z,n}}[\\rho]\n",
    "+\\frac{\\gamma_\\text{E}}{2}\\mathcal{L}_{J_{-,n}}[\\rho]\n",
    "\\end{eqnarray}\n",
    "\n",
    "When $\\gamma_\\text{E}=\\gamma_\\text{D}=0$ this dynamics is the classical superradiant master equation.\n",
    "In this limit, a system initially prepared in the fully-excited state undergoes superradiant light emission whose peak intensity scales proportionally to $N^2$.\n",
    "\n",
    "This dynamics has been studied in Refs. [2-4] and implemented in various quantum optical platforms, including in the solid state [5-10]. A discussion of the difference between superradiant phase transition (typical of the Dicke model) and Dicke superradiance is present in Refs. [3] and [11].\n",
    "\n",
    "Below, using PIQS [4] and QuTiP [12], we investigate the time evolution of the collective dynamics for an ensemble initialized in different initial quantum states.\n",
    "\n",
    "Note that in the table above and in $\\texttt{qutip.piqs}$ functions, the Lindbladian $\\mathcal{L}[\\rho]$ is written with a factor 1/2 with respect to $\\mathcal{L}_{A}[\\rho]$ reported in the LaTeX math equations, in order to have the Lindbladian and full Liouvillian matrix consistently defined by the rates $\\gamma_\\alpha$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from time import clock\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "\n",
    "from qutip import *\n",
    "from qutip.piqs import *\n",
    "\n",
    "from scipy.sparse import load_npz, save_npz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of Dicke states is 121\n"
     ]
    }
   ],
   "source": [
    "N = 20\n",
    "ntls = N\n",
    "nds = num_dicke_states(N)\n",
    "print(\"The number of Dicke states is\", nds)\n",
    "[jx, jy, jz] = jspin(N)\n",
    "jp = jspin(N, \"+\")\n",
    "jm = jspin(N, \"-\")\n",
    "system = Dicke(N = N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 1/np.sqrt(2)\n",
    "b = 1/np.sqrt(2)\n",
    "css_symmetric = css(N, a, b)\n",
    "css_antisymmetric = css(N, a,-b)\n",
    "excited_ = dicke(N, N/2,N/2)\n",
    "superradiant = dicke(N,N/2,0)\n",
    "subradiant = dicke(N,j_min(N),-j_min(N))\n",
    "ground_ = dicke(N,N/2,-N/2)\n",
    "ghz_ = ghz(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time (in seconds) to generate the Liouvillian for N = 20 TLSs: 0.05499199999999993\n"
     ]
    }
   ],
   "source": [
    "# here we set the initial coefficients\n",
    "gE = 0 # local emission\n",
    "gD = 0 # local dephasing\n",
    "gP = 0 # local pumping\n",
    "gCE = 1 # collective emission\n",
    "gCD = 0 # collective dephasing\n",
    "gCP = 0 # collective pumping\n",
    "w0 = 1  # bare frequency\n",
    "wi = 0  # coherent drive frequency\n",
    "\n",
    "# spin hamiltonian\n",
    "h0 = w0 * jz\n",
    "hint = wi * jx\n",
    "h = h0 #+ hint\n",
    "\n",
    "#set initial conditions for spins by initializing the system and building the Liouvillian matrix\n",
    "system = Dicke(hamiltonian = h, \n",
    "               N = N, \n",
    "               emission = gE, \n",
    "               pumping = gP, \n",
    "               dephasing = gD, \n",
    "               collective_emission = gCE, \n",
    "               collective_pumping = gCP, \n",
    "               collective_dephasing = gCD)\n",
    "clock_t0 = clock()\n",
    "lind = system.lindbladian()\n",
    "liouv = system.liouvillian()\n",
    "clock_tf = clock()\n",
    "dt_clock = clock_tf - clock_t0\n",
    "print(\"Time (in seconds) to generate the Liouvillian for N = 20 TLSs:\", dt_clock)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time (in seconds) for this run:  1.4128720000000001\n",
      "Elapsed time (in seconds) for this run:  1.3064499999999994\n",
      "Elapsed time (in seconds) for this run:  1.2567909999999998\n",
      "Elapsed time (in seconds) for this run:  1.333939\n",
      "Elapsed time (in seconds) for this run:  0.5167439999999992\n",
      "Elapsed time (in seconds) for this run:  1.3920459999999997\n"
     ]
    }
   ],
   "source": [
    "## Solution of the dynamics for different initial conditions\n",
    "\n",
    "# parameters for the time integration of the dynamics\n",
    "nt = 1001\n",
    "td0 = np.log(N)/(N*gCE) # delay time is used as a reference\n",
    "tmax = 10 * td0\n",
    "t = np.linspace(0, tmax, nt)\n",
    "\n",
    "# initial states \n",
    "rho01 = excited_\n",
    "rho02 = superradiant\n",
    "rho03 = css_symmetric\n",
    "rho04 = css_antisymmetric\n",
    "rho05 = subradiant\n",
    "rho06 = ghz_\n",
    "\n",
    "#Excited\n",
    "clock_t0 = clock()\n",
    "result1 = mesolve(liouv, rho01, t, [], e_ops = [jz, jp*jm, jz**2], \n",
    "                  options = Options(store_states=True))\n",
    "rhot1 = result1.states\n",
    "jz_t1 = result1.expect[0]\n",
    "jpjm_t1 = result1.expect[1]\n",
    "jz2_t1 = result1.expect[2]\n",
    "clock_tf = clock()\n",
    "dt_clock = clock_tf - clock_t0\n",
    "print(\"Elapsed time (in seconds) for this run: \", dt_clock)\n",
    "\n",
    "#Superradiant\n",
    "clock_t0 = clock()\n",
    "result2 = mesolve(liouv, rho02, t, [], e_ops = [jz, jp*jm, jz**2], \n",
    "                  options = Options(store_states=True))\n",
    "rhot2 = result2.states\n",
    "jz_t2 = result2.expect[0]\n",
    "jpjm_t2 = result2.expect[1]\n",
    "jz2_t2 = result2.expect[2]\n",
    "clock_tf = clock()\n",
    "dt_clock = clock_tf - clock_t0\n",
    "print(\"Elapsed time (in seconds) for this run: \", dt_clock)\n",
    "\n",
    "#CSS Symmetric\n",
    "clock_t0 = clock()\n",
    "result3 = mesolve(liouv, rho03, t, [], e_ops = [jz, jp*jm, jz**2], \n",
    "                  options = Options(store_states=True))\n",
    "rhot3 = result3.states\n",
    "jz_t3 = result3.expect[0]\n",
    "jpjm_t3 = result3.expect[1]\n",
    "jz2_t3 = result3.expect[2]\n",
    "clock_tf = clock()\n",
    "dt_clock = clock_tf - clock_t0\n",
    "print(\"Elapsed time (in seconds) for this run: \", dt_clock)\n",
    "\n",
    "#CSS Antisymmetric\n",
    "clock_t0 = clock()\n",
    "result4 = mesolve(liouv, rho04, t, [], e_ops = [jz, jp*jm, jz**2], \n",
    "                  options = Options(store_states=True))\n",
    "rhot4 = result4.states\n",
    "jz_t4 = result4.expect[0]\n",
    "jpjm_t4 = result4.expect[1]\n",
    "jz2_t4 = result4.expect[2]\n",
    "clock_tf = clock()\n",
    "dt_clock = clock_tf - clock_t0\n",
    "print(\"Elapsed time (in seconds) for this run: \", dt_clock)\n",
    "\n",
    "#Subradiant\n",
    "clock_t0 = clock()\n",
    "result5 = mesolve(liouv, rho05, t, [], e_ops = [jz, jp*jm, jz**2], \n",
    "                  options = Options(store_states=True))\n",
    "rhot5 = result5.states\n",
    "jz_t5 = result5.expect[0]\n",
    "jpjm_t5 = result5.expect[1]\n",
    "jz2_t5 = result5.expect[2]\n",
    "clock_tf = clock()\n",
    "dt_clock = clock_tf - clock_t0\n",
    "print(\"Elapsed time (in seconds) for this run: \", dt_clock)\n",
    "\n",
    "#GHZ\n",
    "clock_t0 = clock()\n",
    "result6 = mesolve(liouv, rho06, t, [], e_ops = [jz, jp*jm, jz**2], \n",
    "                  options = Options(store_states=True))\n",
    "rhot6 = result6.states\n",
    "jz_t6 = result6.expect[0]\n",
    "jpjm_t6 = result6.expect[1]\n",
    "jz2_t6 = result6.expect[2]\n",
    "clock_tf = clock()\n",
    "dt_clock = clock_tf - clock_t0\n",
    "print(\"Elapsed time (in seconds) for this run: \", dt_clock)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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91OtGcoCXGoYfM80zuZClMDcqOmURQhFCWuuer9LSUkpLS9myZUuf44MFC3C1efd/a7XZbAP6QkZisBjNAg3UQ73OE+BHGqlh+BFnjKM5J4VFB1qwXTnC/GgXSPT1wuNw+XB07j1pEXzwO8POxmq1UlhYiMVioaSkhJKSEq99DZ6x+t72BS8sLKS6urrnnM1m67OXt9VqDbozXfjnK1AXFRWF5LqRGuClhjEIx4wckjvgTM3paBdFjEE2m61nGKXFYuH0ae+/Z7t27fI5zn/nzp3s2rWL3bt3U1xczM6dO/ucLy8vHxPbg440nkDt0TtQV1dX+5zI5+86GNkBXmoYg0jMmw0co/HS1WgXRfQXgjf8aOs9KmrPnj0+HxQ7duzwOcbfbDb3LFbYPzCM1DfVsWDnzp1s374dm81GRUVFn0C9a9cuqqurvQ6R9XcduAK8ZzHKkUYCxiDS5y0Cfk9HQxfYuyAmNtpFEmOQZ96Ev5rAUNq0y8rK2LRp05DLJXzzF6jHaoCXJqlBTJu5hLZYMLQYofl8tIsjxihPx7cvvfsoglFRUTGk68TwjcUALwFjEDNTLdSmQ3KzwtEo/Rhi6LwNqQTXJkrbtm0D8PlWmp+fP+gInP6am5tH9MNnLBurAV4CxiASTYk0ToxnciPU1h2MdnHEKJWfn++1uclqtbJ582YKCgr67LwXCmazWTq7Q8xX0O9vrAZ46cMIQFduNpkHz3Pm0lGmRrswYkwpLCykqakp2sUQAcjPzw/r2/9oCPASMAIQM2M6cJ66c2dCluf1Tjulr57mtZNXSU0w8dg9c1icO3I7u4QQQpqkApAy2zVl79ql0LwJ1ja386Ef7OXHfzlFnNFAl93BzExZ2FAIMbJJDSMAk+fl41TgbOgGpwMMxiHn1d7l4DP/9Q4N17t4cssqVs58v030RqedF49c5uGC3FAUWwghQkpqGAGwZM2lPhViWxS01g4rr5I/vcfJ+uv8xyfz+wQLgF/sO8tjuw9yrLZ1WPcQQohwkBpGALITs/lLhoGsRictdUdINQ+t6/tU/XV+8eZZPnHzNFbPzhpw/pHbLdwxJ4ubpqQMt8hCCBFyUsMIgEEZaJucyuRGOHt56MMev289QbzJyFfXeV/SOTbGwIIpqQA0XO8c8n2EECIcJGAESE/PJc4OF84cGdL17V0OLjS28fnbZpKZHOc37S/3neXu773KtY7uId1LCCHCQQJGgBJnuWoFTeeHtjxIQqyR33/xNr5SOHvQtMumptHS3s1v3palSIQYKaqrq3tWFu7NarVSVFTUszy9Z7c8z+rCNpuN4uJilFKsW7euZzb/7t27WbduHUopiouLe9YTy8vLIy0trU+ennTgmuDna+XicJM+jABlzl0CPE3n5WtBX9vR7aDT7iQ1wUSMcfCd1hblprJ6dib/+foZPn/bTGJjJK6PdtXV1dhstqAnZjU3N7N9+/aexepEdPXfy6KkpISKigrKy8v7HN+wYUPPWlIWi4UdO3ZQUlLCjh07eib/rV+/HrPZTGVlZZ9/X7PZTFVVVZ9FCEtLS3vS+NqEKRLkSRSgqdMXcj0eDA3dEMBOaL398WAtN3/byrmGGwFf87nbZnDlWicvvVsXbFHFCDWUfaCj+XAQ/lmtVkpLSwcEC2BYAX7Tpk19gkVJSQlAn421NmzY4LW2E24SMAI0PWU6tekwoRns1+uDunZhTiqP3G5hWnpiwNfcMSebyanx/E/FhWCLKkYhf//5o/VwEP4VFxf73GHPYrEMeRmR3pspeZqf+q9kXFhY6HWvjXCTgBGgRFMizZmxrkUIL1UGde38ySk89oG5PW2QgTAaFBuWT2XvyStcaGwLtrhilKmoqPB5LloPB+HfYCvSDrWW0TvPzZs3U1hY2CeIeESj9il9GEHompJBxqFLnD1XwbQ59wd0TeXZRjSwfHpaUAEDYNOKqfzw5ZPsrrrocyiuGB88D4eRvLnOUO3658cHHJt7y2qWfuB+ujs7eOY73xhwfsEdhSy8s5C21hb++P3tA84vWXcf825dQ+vVK7zw4+8NOL/8Qw+SV3DzkMvs6aAOdPVaj9LSUvLy8no++9qSF97vZPeVpqioiLKyMq97wIeLBIwgxMycCVyi/tQxCHDL3e9bT1Db3MHLX7sj6PvlmBNYOSOd5w7V8pXC2UEHHDF2+Ho4eEbkeB5cFRUVPW+2JSUlPUtsB3JcBM7z8+vfL+XZo72iooLm5maKior6DHQoKirqU4OwWq089dRTXu+xefNmtm7d6nOZdIvF4rdmGg4SMIKQOmcB8CatF2sCSt/a0c3btkYeWW0Z8sP+gSVT+OZzx6hpbic3LfA+kPFg0S8WRfX+hz9zOGL38vZwKC4uZsWKFX0eSNu3u962rVYrFoul55ynScvX8Wja9E++92Y3xcX7PZ+Ykur3fEpmlt/zw5Gfn091dXWf5iKLxcLWrVspLi6murp6yMuVl5WVYbPZ+gTz6upqzGZznwBisVgiWvMcUsBQSqUAFqAZaNRaj4vFj7LnLgXAURfY0No3Tl7F7tTcPS97yPd8cFkOH146hZR405DzECNP/85Sq9U6oD16w4YNAx5GnoeDzWajrKxsQO2g9wY8e/bs6Xlg9b6fr+MiODt27GDDhg1s2bIl5A/s4uLiAf+2lZWVbNy4sc+xSDdTBhQwlFKbgQ3AckADNsCz1rdFKZXmPrYL2K21Phv6okbfjKw52FIgrsEeUPpXjl9hQnwM+dOG/g+aFCeVQF8i+YYfav1HvXh7QPTX++FQXV3N8uXLB6TxNFkVFhZSXFxMXl4e69ev78nb13ERvMLCQrZt28aGDRsoLy/v8+D29HEMRXFxMRaLhS1btvQ5Xlpa2ueY1Wpl3boA28ZDxOfTyF2LeAJYBpQDG7TWLf4yU0qtBR53B5BSrfXLoSxstE1Omsyb6Yq0Js2NtqskJWb6TKu15pUT9ayZnUWMcXiD0d691Mo/PHuYf3lwEfMny8KE49FQHg5VVVVYrVbKy8spKCigqqrK73ERvK1bt5Kfn8/mzZuxWCxkZGQAsHPnzp6+CZvN1vOCUFxcTHFxMYWFhezevZvS0tKeobNFRUWkp6dTUlLC+vXre+ZfnD59GqvVOiAIlZeXD3jxCDut9YAvXEHiJ8BMb+cD+QI2A48N9fqhfBUUFOhw+89P5evKRfP0keN/9JvuaE2Lnl78nH6q4vyw71nf2qEf+OFe/batYdh5jVbHjh2LdhGGpaqqSpeWlvo8v3XrVr/Xb9mypc/npqYmbTabB6Tbs2dPz/16W79+vW5qavJ5XAxusH/DSGpqahr0d6a3wf7/AJU6gGfsgFdfpdRMwKK1/oLWesh7kmqtdwI7lVIPDTWPkciZk0ViF1w88ZbfdK+fugLAHXMGLmMerKwJcfzhS7cP2D9DjA/e2qnNZjNbtmzxOaGvsrKyzxtpenp6zzIU3o6L0aWsrKxPf1WkDGiScgeJkGxerV1NWM+EIq+RIi5vNnCOhlPH/Kbbd7qBvKwkslPiQ3bv9i4HGk1irPRrjDUrVqzwec7Xw2HHjh2UlZVRVlbWM6zW05mdnp5OdXU11dXVNDY29jRn+TouRpeKioqIzr/wCOrJo5RaqrU+EK7CjAZp8/MBK20XL/lMo7XmQlM7t1gyQnbf2uZ27vruK/zjAzfxiZunhyxfMTL4G37p7+HQv2N0sPyGOsxTuAQ7US8cmpubo1K7gOCXBhkwBk8plaqU+rpSammIyjSi5eYtoSsGVP11n2mUUuz56hr+74duCtl9J6fGMzElnj3HZDHC0WooD5toPhxEX/n5+SMi4JrN5qiVw2/AUEqdUkpVKKW+rZS621sarXWL1vpfgQxfacaSGWYLl9IgscHh6dz3SilFvMkYsvsqpbh7XjZv2Rro6HaELF8RGUN92ETz4SBEf4PVMDYALwH3AFZgizuAbFdK3e0eeguA1volYMz3npnjzVzNMJLdqLly47LXNI8/fYiSF98L+b3XzMmko9tJ5dmmwRMLIUSI+Q0YWuv9WuvHtdbLtdYGXMHjKaAAVwBpcgeQnyilHgHGRd25IzuRic1w9sLbEb3vLZYMYo0GXjt5JaL3FUIICL4Pw6a1/let9T3uALICVwDJwFULCc+iLSOMyp2EUUPtsTe9nv/Ow4vZeu+8kN83MTaG5TPSeO3E+AwY/poAhRDehfL/TbDjM/tsLaW1rgaqQ1aaUSJp9jzgJC2nBjY7ddmdYd1SdfXsLHa8+B71rR0hHbI70plMJtrb20lMlAUYhQhGe3s7JlNo1qIL6snm7qcY97IW3gpA18WBI5YeKz/IQ//xRtjuvWaOazmSvSevhu0eI1F2djY1NTW0tbVJTUOIAGitaWtro6amhuzsoS+A2tuAGoZ7pvcyrfWwJ9y5O8U3aq1/Nty8RpLpuQu5mggxVwbu0V19volFOalhu/f8SSlkJsfy2skrPFyQG7b7jDQpKa7xFbW1tXR3d0e5NEKMDiaTiYkTJ/b8/xkurzO9lVJmpdRPgB16iCvPule4tWittw2zjCPOtJRpHE6H1KsOuh3dmIyu6l79tQ4uNrXzmVUzwnZvg0Hx7x9dFtT+4GNFSkpKyH7xhRDB89okpbXeDzwOPKqU+pNS6pHeQ2h9UUotVUr9VCn1J+D0WAwWALHGWJozTExuggut53uO7z/v2s8gf3p4RxffNiuTqeMwYAghostnp7d7HajHAZRSDwM/U0rl49oPoxnw7E2YB3j2w6jEtaz5/nAWeiSwT0zGfLCJc+cqsaS59uitPt+EyahYMCV8TVLgapssr7xI5oRY7p43Maz3EkIIj4BGSWmtnwae9nxWSqXSd8c9v/tkjEWm3ClAE1cOvwlLXdNP9p9rZsGU1JDO8PZGKUXpa6eZPzlFAoYQImKGtOypO0CM+VqEP679vY9y/fRJALodTg7VNPPxlZFZGHBX0SoykmIjci8hhIDgJ+4Jt8mL1+BU4Kx1TaJ791IrHd1Olg1jO9ZgZCbHoZSKyL2EEAIkYAzZjIkLqE+FuCvtABy86GqVi1TAcDg1xbsP8du3zw+eWAghQmDIAUMp9ZB7/ahxKTsxm8sZiswGBy2dLSybauZr6+aQY06IyP2NBsXBi808f9j3vhxCCBFKQQWMXsNmK3B1eqcppSrdiw+Oi/0wPAzKQFuGicmNcK75DAtzUvnbtbMj2ky0Ki+DirONdNpluXMhRPgNGjCUUinuDZIqgW1AudZ6hdb6u+6FCJcDZbjmbFQopR4LZM7GWKAnphBnhzMnKnjL1kBblz2i9781L5NOu5MD7vkfQggRTj4DhlLqYaXUn3Etad7kXuJ8k7f1pNzLoD+qtV4BtAAvuyf8PRS+okdfwvSpANRU7+OjZW/x6vHIriK7cmY6BgVvnm6I6H2FEOOT14ChlPopsBwoctcmAl4LSmu9013reBRYqZTaFZqijjxpcxYDEFN7np9/bkVI9/AORGqCiYU5qeyzScAQQoSf13kYWutHh5ux1voM7pniY9W0ebfTHvsLjJcauWtuaFaDDNYqSwb/9cYZ2rscJMSGd8KgEGJ8k2G1wzB94mIupUPylQ4OXojOtqmr8jLodmiqzsm2rUKI8AppwFBK3R3K/Ea6CXEpNKQrJjVqdh86EpUyrJiRToxB8ebp8bU/hhAi8kJdw1gX4vxGvPZ0E5ktkJUUnW1Tk+Ji2LA8l5y0yMz/EEKMX0NaS8qPcbdWRVd6Cgauktp0Kmpl2P7Q4qjdWwgxfoS6hjHu9s68luraMlWfOxrVcnR0O2hpk53ohBDhI53ew3Qu3rU6bffZc1ErQ5fdyYpvWfmPV6NXyxFCjH1RDxhKqfVKqUKl1FYf53e4/9wS2ZINrtPu4Oi16TQmQ+yl6I1Sio0x8LV75lA4X/bGEEKET1QDhnsHP7TWVqDZ87mfLUqp07h29BtRjl++Rm3HTC6lQ+rVLjrsHVEry2dvm8mKGelRu78QYuwLdcAIttN7E65d+8AVEAq9pNmstc5zB5UR5XBNC05MtKYppjTAudboNUs5nJqqc43YrlyPWhmEEGObv7WkZgwhv9NBpjfz/t7gAN7W1rAM0mS1xb1ibuWVK5Ed2nqy7jorg8gmAAAgAElEQVSpCSbsWXFM6IALF6LX8d3tcPKxnW/zP+/I/hhCiPDwV8PYEWxmWuudwyiLrzxL3LWLDKXUgBqI1rrMvTDi8qysrFDf3q9/euAmXvraHcRPdsW5K8cPRPT+vcWbjCybapZ1pYQQYeMvYGxQSj2plHowjMuVNwOehncz0Odp5649rHd/bMC1B8eIoZQiMzkOs2UWAG0noju0dlVeBkdrW2V4rRAiLAbrw7gHeBpoUkqddG+UFMoAsov3g4AFsAIopTz7nFZ6jgF57s8jwom6a/z9Uwc4e/UGk+euxG4Afb4mqmVaZclAa3j7jNQyhBCh5y9g7NZapwOzgC8A+3F1Ug8IIEO9uda6GsDd1NTs+YxrDw7P+Y3uWsbpXuejrqa5nb0nr6IUzJx+O5fTIL7uOlpHb+7i0mlm4mIMvGVrHDyxEEIEyd/SII0AWmsbrh31ygCUUjNxrRlViCuAFCmlmoD1Wuu/BFsArXWZl2MF/s6PBHfNzabiHwpdAULPoj4dshscNHU2kR4fneGtcTFGCqanST+GECIsfNYwfO2JobU+4+5o3uiugeQBPwOsSqnpYSrniKWUQhkMtKcbmdQEZxujO11klSWDdy+10nSjK6rlEEKMPcOeh+EOIMXACqBk+EUa+brsTu75/qv8bn+vPovsZEwOqDm1P3oFw9XxDdKPIYQIvZBN3HP3L4yYTulwOlF3jRN11zEa3p+nmDRtCgCNR6PbzbI410yCyUj1+ebBEwshRBCGvby5UuohwKa1PsA4Wa32cE0LAItyUnuOTbopH3iXrhPHo1Qql9gYA3/+6hpyZX8MIUSIhaKGUQK85A4cLSHIb8Q7XNPChPgYpmck9hyblbeaKykQezH6TUFT0xNRatxtTSKECLNQBIwC4HFctYyQz/QeiY7UtLBwSmqfh3JOzs3UZkJ2XRctndGNm81tXRTvPsSrJ6KzC6AQYmwKRad3i9Z6p7tJaszrsjt579I1FuWm9jluMMVzPUOR0wCnrka3WSopLobXT13lQmNbVMshhBhbQr1F65h3ou4aXQ4nC3NSB5xTk5IwOa5z5r0KCnJWRqF0LiajgdeL75JmKSFESIV0eXOl1COhzG8kOuLu8F7sJWCkTJsEQOOxgxEtkzeeYBHNmedCiLEl1Pth5IU4vxHnkJcOb48pc5fgBOwnT0a+YP3UNrez9nuv8MdDl6JdFCHEGBHtDZRGnXmTJvDRFVO9NvfMsqyhLg0SLlyN+pt99oQ46ls72Xc6+qO2hBBjQ6j7MMZ8+8enV83weS4752asmTCx3k5DRwOZCZmRK1g/MUYDK2am87asKyWECJFhBQyl1MO4lgTRuGoXa91v3sp9rEJr/cxwCzlStHc5UMq1WZE3KiGV9gzF5FOak3XHyJyxJsIl7GuVJYOX36unrrWDiSnxUS2LEGL0G1bA0Fo/jWu5cwCUUt/RWm8bdqlGqN8dqOH//O4Ie7fexRSz95nUhknJGPU1ao9WQLQDhntdqX2nG/irZTlRLYsQYvQLdR/GmG6SWpSTypfumsXkVN9v6+aZuQC0vHc4UsXyaf7kFFLiY3hLmqWEECEg8zCCsDAn1ev8i96mzi3AbngX58lTESqVb0aDYuXMDN6Ujm8hRAj4rGEopWYMIb8xu9Vbl93JO2caaeuy+003e8YaajIg6UITDqcjQqXz7fZZGZxvbON8g8z6FkIMj78axg5cO+oFY0TujhcKxy9fY2PpPn788XzuXzzZZzpzznLqsmDWeSfnr51nZurMAWm01pw7fID33niVpku1xJhMTJ49jwV3riVt0pSQlnvNnCwAXj15hU9ljLv9rYQQIeSvD2ODUupJpdSDSqmUQDLTWo/Z1WoP1bj2l1ic679JClMCXdkG0q/DidMV3tNozdvP7uJUxT6MRiOdbTd45/flWHf+KMSlhpmZSfzt3bO8zkwXQohgDNaHcQ+wEdBKKRtgBf4MvKS1bg134UaSIzUtpCaYAtpnIjE3DWig7uA+yN/Yc7zOdooJmVkkpqTy4b9/AlN8AjEmEwA3mpvouHEdgK6Odrra20lOG/7e4EopvnbP3GHnI4QQ/moYu917ds8CvgDsx9VE9TTQpJQ6qZT6iVLqwQiUM+oO17SwKCc1oAX9Js+dB0Dn0Xd7jjVcPE/5t/6Bl39eCkDChJSeYAGQZE4jI2cqAC/++Ps8+Y9f53pjaDqrHU5N9fkmWb1WCDEs/gJGI4DW2qa1LtNab3QHkDz6BRClVINS6q7wFzc6Ou0Ojl8euKS5L/Msq6hPhXjbJbTWdFy/zjPf+QYxpljWfPyzg16/4iMP09bSwjM7/pmu9uE/5K932Fn/kzd5qvLCsPMSQoxfPgOG1vpRH8fPeAkgPwOsSqkx2at6/PI1uh26z5as/kyeejsXs2HK5S7qbtSx52c/5npjAx957P+QkpU9+PWz5vLA32/j6vmzvPDj/2/Y61KlJpr4xedX8vnbBnbACyFEoEKxgdIZrXUxriVCSoZfpJHn0MWBe3j7ozJn0ZbpZFIj7HvhKU7s28utGz7B5NmB9yXMXFrAmk98jlMVb7H/xeeGVO7eVs/OIi0pdtj5CCHGr5BN3NNaVyulKkOV30hy8EIz6UmxAXV4A2AwEjslGQNtXG+tZcWHH2bFRx4O+r4F9/8V1xuvMm3h4qCv7a+9y8Gv3zrHotxUbrFkDDs/IcT4M+wahlLqIaXUUvfHMbk0yP4LzSybag5qB7usPFfzT+f546z5xOcwGLwvWOiPUoo7P72ZzKmulr7hNE2ZjIofvHySZ6ovDjkPIcT4FooaRgmQppTaDIzJeRhlnyqgy+EM6ppJ2Yt5K+8qnBz+A9re1cWesh+SPXMWBfd/ZEh5xBgN3D4rk9dOuPbqkO1bhRDBCsXigwXA44BNa70zBPmNOJasZOZNCmjuYo/aox00JSUysbadls7hxVGjyUT79Wu8setXwxpqe+fcLC63dvDupWvDKo8QYnwKRad3i9Z6p9b6QCgKNNJYj9Xx5Dvng2oOaqi5wPH9h4mNaWFmnYPDF4fXtaOU4u7PPYrTYWfv//xiyPncNc81Quuld+uGVR4hxPgU6uXNx5xnD9Twn6+fCaoJ562nn8QUG0fi1HaMGs5X/GXY5TBPnETB/X/Fsdde5tLJ40PKI3tCPEtyU3npvfphl0cIMf54DRhKqa8rpe4ebuZKqaVKqceGm080/ehjy9hVtCrg9I21Nbz35mssvfdD5M5zdVbfOBCaytfND24kyZzG608OvZaxdv5EDl5s5sq1zpCUSQgxfviqYewGNrqX/9gezFLnSqkUd8CpBIqAl4ZfzOhRSpEexPyF+ORkbnlwIwX3fYQFs25zzfg+cWHYk+8AYhMSeeCr2/jgl4Yeg9fOz0Zr+MtxqWUIIYLjNWC4J+M9qrWeDVQCZUqpPymlHvKVkVLqYaXUn4FyoElrvVxr/QWt9f7wFD38Xn6vjsfKD9LS3h3wNYkpqdy26VMkmdOYMu12zk2G6Re7uHg9NMNZc+bdRHJaOlprtDO4kVsAN01OYUpqvPRjCCGCNmgfhtb6aa31PcCjwEql1Cn3ooNLlVIzlFLfUUpVAMuBIq31B7TWPwt3wSPhleNXeP7wJZLjAht9/N6br3Gq8u2ez2ryYjqzHGS1wrHjb4SsXO3XWtn1jWKOvvZy0NcqpXhgyRSSAvyehBDCI+Cnhtb6DK7hs48rpdYCT+CaqFemtX48TOWLqgMXmlmSa8ZoGLzD22G38+qv/pP0KbnMWn6z62BsIsm5yUA7lyr3wvKPhqRc8ckTsHd182b5b5h32x19Vr0NxLb75oekHEKI8WVIo6S01i+5Fx/cpLUe1X0UvrR12TlW20r+dHNA6U+89TrXGxsouP+v+hyfPvcmHArsR46GrGxKKW7/2Ke5dvUKh6wvDDmfYJrahBBChtX6sP98M3anZsWMwDYxOvCn/yVtcg4zlxb0Ob5w9lrOZUPqqSt0O0L3gJ6+aClTFyzmrWd20dXRHvT1/++5Y9zz/VdxOsfkai5CiDCQgOHD22caMSgomJ42aNqr589Se+JdFhfeizL0/ZGmTF9N3SRNXq2Td+uPhKx8Silu/+inaW9t4ZD1xaCvv3NuFptXW+geQse5EGJ8koDhQ8WZRuZPTmFC/OD9AzdamsnIncZNa7xMXcnIg8mahC54750/hbSMU+bM40NfeZwl6z4Y9LWrZ2fxyGoLcTHBL4oohBifJGB40WV3sv9CU8DNUdMXLeWz3/sPElO87JehFJNmTQGg5Z03Q1lMAOauuh1TXPyQ5nm0dnTz3KHakMwREUKMfRIwvDhS20JHt5OVMwcPGC31ddi7uvymWTrvNurMkHj0LE4d+iagC0cP8ettX6H9enCLClqP1fGl3+7nwIXmkJdJCDH2SMDwosvuJH+ameUzBu+/eP5H3+Opb27zm2bKzLs5mwOzznVzsulkqIrZIz55AvVnTlP13LNBXbd2/kRMRsULRy6HvExCiLFHAoYXt1gyeOZvbiN7QrzfdFcvnKP2+DFm33yb/wxzV2KfZCelHY5WhbYfAyBr+kzmrlpN9fN/oK018KXUUxNM3D4rk+cPX5JmKSHEoCRg9ON0ajq6HQGlPfzSnzAYY1hwx1r/CeOSyXI3bzW+9fpwi+jVqg0fx97VRcUfng7qug8umszFpnZplhJCDEoCRj/HLrWy+Bt/5tUTV/ym6+7q5NhrLzN75Srvnd39LJy/iqYkMB06GZa3+Yycqcy//Q4OvPgcN5qbAr7u3oWTiIsx8Oz+mpCXSQgxtkjA6GdCfAyfuXU68ydN8Jvu7IEqOm5cZ3HhvQHla5l9HyenwRxbB6caQ9+PAbBqwye494tfDSiAeaTEmyi8aSJ/PFhLl13mZAghfJOA0c/0jCT+4f6byE7x338xa8UqPv4v32PqTYsCyldNu4XunG7MN+DAW78PRVEHME+cxNxVqwdMHhzMQ8tyaGrrHrRWJYQY3yRg9NJpd/DOmcaA3rSVUkyeNTfwh3N8ClPyMgBo2vvKMEo5uIo/PM1rv/3vgNOvmZNFRlIsz+4PzRLsQoixSQJGL9XnmtlYum/QN+03nvoNL/3XT4Pui1gxbzUXMsF86BxdDv9zN4aj5Uo9Vc89S0t9YMNlTUYDH146hWsddllbSgjhkwSMXt44dRWjQXGLxfeEPXtXFwf+/L+0tTQHtc83QNac+zg/TTP3vIMDF98ZbnF9uvnBDSiDgX1PPxnwNf/3/pv41V/fjCGApdyFEOOTBIxeXj91lSW5qX7XjzpZsY+Oa60sWvuB4G8w7VZMU+zE2uH4K+HpxwCYkJ7J0nvu49hrL9NYG9joJ0+gaLwRvpqPEGJ0k4Dh1nC9k4MXm1kzJ8tvusPWF0nNnsj0hUuCv4kpnlnz8+g2Qucb+4ZY0sCs/MgGjCYT+3b/NuBrXn6vjpX/YuVITeCT/4QQ44cEDLdXjl9Ba1g7b6LPNI21NVw4dphFd38g6JFIHstv+gjvTgPL4QZqr9UOtbiDSkw1s/bzX2DZvR8K+JqCael8/vaZpCfFhq1cQojRSwKG28vH68meEMeCKSk+08SYTCxZdx8L7iwc8n3i5nyAlul2JjfBvn3lQ84nEAvvLGTKnMC3Y01NNPHEffOZYk4IY6mEEKOVBAyg2+HkteNXuGtutt9O35SsbAof+RuS0wJb9tyrjDxyZ7rmeDTsGfr2qoFqa21hT9mPqDtzOqD0Wmv2nrzCazInQwjRjwQMoPJsE9c67dw9P9tnmksnj1Pz3rGQLOtx68JCbJNgUvV5Wrtah52fPwajkeNv7eXN8t8EfM32599j+wvvyYKEQog+JGAAb9kaiDUauH1Wps80r+/6Fc//6LvoEOxnYV7wMDUzHeTVaPYden7Y+fkTn5TM8g89hK3qHS6dPD5oeqUUn1o1nXcvtfKWrTGsZRNCjC4SMICvFM7mpa/dQVJcjNfzDRcvcP7wARbd/QEMhhBsaTptFenTFQbg3HPh7ccAyP/gA8RPSOGNp34dUPoHl+WQkRTLzr22MJdMCDGaSMDA9VY9NT3R5/n9f3oOo8kU8EKDgzIYuW3pnVzMgKw33uNaV3A75QUrNiGRmz+ynnOH9nP2YPWg6eNNRj69agYvv1fPybrwlk0IMXpIwBhEZ9sNjr36EvNuXRPUKrCDmbxoE2fmOph3wcmrlbtDlq8vS+99gIL7P0LG1GkBpf/UqunEmwz8bO+ZMJdMCDFaSMAYxJXzZzGaTCy794HQZjxjNZNmujqVa599KrR5exFjMnHnpzczId13P01v6UmxbCiYyrP7a6hr7Qhz6YQQo4EEjEHkzltA0U9/yUTLrNBmbDRxx5IPcHIKTHv7HFfaIjOMtbH2Is+WfDOgTZa2rLHg1JqfvBLYkFwhxNgmAcOPttYWtNNJjMn32lLDkZr/WS7PtjO9XvOXv/w8LPfw5uyBal5/8leDppuansj6glx++/Z5LrW0R6BkQoiRTAKGH8/92w6e+n9PhO8GOQXMmZdMlxGulT8dkXkP6VNyyb/vwxz5y5+pee/YoOm/dPcsvlw4mxQ/CzIKIcYHCRg+XDp5nAtHD5GXvzJ8N1GK25d/kv3zYGl1K++ceS189+pl1fqPkZKVzZ9Lf4C9y//qtLlpiXzxrlk+hxwLIcYPCRg+vPP7cuKTkkM3lNaHmCUfxzS7ncQuOPibH4X1Xh6x8Qmse+SLNNZeZP+Lfwzomj8fvcy//O/gNRIhxNglAcOLhovnOVXxFkvv/RCxCb7nZ4REymTWLlnJ+SzItR6l/kZ9eO/nNmNpAff/3ddZ+oH7A0p/pLaVvSev0tZlD3PJhBAjlQQML46++hIxsXGhH0rrw6Rbv8LZhXZm1mlefPa7EbknwLzb7sAUF09XRzsOe7fftF+8K4/n/vZ2EmOlaUqI8UoChhe3f+zTbPrGd0I6Uc+vaau4ZVEmzUkQ/z8vhH3md2+dbW38qvjveGOX/2VD4mKMxBgNtLR3U3FW1pgSYjySgNGPvasLg8HIpLzZkbupUiy57cscXOpg0Wk7//vCDyN267jERKYtWELFH5/h/JGDg6bf9swh/vq/K6i/JpP5hBhvJGD0cvn0Scq++DlqT7wb+ZsveIjFN8XSFgf2XzxFuz1y8x7u/PQjpE/O4YUffY+2Vv/bs37tnrl02J184w9HI1Q6IcRIIQHDTWvN60/+Eq01GbnTI1+AmFhW3fl1Kpc6KTjWybPPfS9itzbFx3Pf332d9uvX+N9/34HT4fCZNi8rmS+vnc3zhy/z4pFLESujECL6JGC4na58m3OH9rPqoU3EJYZ5ZJQPaunHWbokltYEiPvpkzS0N0Ts3hNn5lH4yBexd3XT2d7mN+2WNRYW5qTw+DOHqW2WGeBCjBcSMIDurk5e+eVOMnKnseSewIaZhoXRxM1r/4HqlQ5uOuvgd7/6p4jefuGdhWz65++QkDzB76xzk9HADz+WT7fdyVeePIDdMfxNpYQQI58EDOB0xVu01Ndx9+cexRgT5WGjizZyV/5ELpthxn+/zLu1g3dEh5LBYKSz7QbPfOcbfjvBZ2Ym8a0HF/LO2Ua+bz0RwRIKIaJFAgau+Qif2vEDpi1cHO2igMHAvA/9O7bVnUxp1Lz67b/D7ozsZDnt1Fy7eoXff/db1J/1veveg8ty2bR8Kj/+y2l+f6AmgiUUQkSDBAy37BmWaBfhfTn5fHT1B3nnJrjt5XqefuH7Eb19fHIyDz/xTeISk3n62/9IY+1Fn2m/+VcLWDkjnVP11yNYQiFENEjAGKGS7vk2llVGrsdD2nd+ztGLg2+tGkoTMjJ5+IlvArDrG4/TcPG813RxMUZ+9chKvnbPXACczvCvuCuEiA4JGCNVfCqrN5ZxZG0nOVc07xQXRXQGOEBG7lQ2/uN2ktMyUAbfvypxMUYAjta2cN8P9nLm6o1IFVEIEUESMEay6bfy6Xs/y+srNbdUXecX3/5kxPszMnKn8snv/BvpU3LRTid1tlM+05qMBkxGAyqC5RNCRI4EjBEu7q7/wwfvuYkjM+HOXSf4z7K/ichGS70p5QoBB/Y8z2+e+Hv2v/hHr2WYM3ECf/jSbczITMLp1NKvIcQYIwFjpDMYmLbhF8y5L4UL2bDyx3v5+a8fi3jQAFhwx1pm5i/n5Z+X8vwPv0tn28AJfp7g8pNXT3P/D/ayu8p3h7kQYnSRgDEaxE1gyeeeI/GBeBpSYFnJ8/zs53+HU0d2wlxsfAIfeewfuG3Tpzj+5l5+ve3LPpuoPrpiKvnT0nis/CBPPHuYjm7fy40IIUYHCRijRXIWdxS9QOyD8Vwxw83fs/KTb62PeEe4wWDkloc2sfGfvo3T4cBh996nkpEcx6/+eiWP3pHHb98+zwM/fJ3955siWlYhRGipaDRthMvy5ct1ZWVltIsRXm2NvP3fD3HhD3UsOAtv3pLKrdvLmD858pMOHXZ7z8z4N8t/S0pmFjetuRuD0dgn3SvH63nimcNcbu3gs7fO5MtrZ5OaaIp4eYUQ3imlqrTWywdLJzWM0SYxnZu3/ImVRXewt0Bz61stXFz/UX5d/o90OboiWhRPsLB3dXH2YBV/+um/84uvf4nj+17H6Xy/CerOudn86atr+NjKafz8zTPc8d2/8F+vn4loWYUQwyc1jFGs7ejv+O2vHmfuS4r06/BOfiJTvvwY61ZswqAi+y6gteZUxT5e/59f0lh7kdSJk7j3b75K7rwFfdIdq21l+wvvEhdj5Gefcb3QtHc5SIg1estWCBEBgdYwJGCMdm2NVPzhKxz44zvcsl/hMEBlwQQyPvNZPrD6sySaIrtUu9Pp4HTF21S/8Ac++KWvkZKZRe2Jd+m8cYPpi5f1NFfd6LSTFBfD2as3uP8He/n+pqXcs2BSRMsqhHCRgDHOOOqO8sKzX+eq9Qz574LRAUctRlrXLGLug5/llll3YzJGp9/guX/bwfF9e4lPSmb6knws+SuYsSSfxJRULjS2Ufraaf7mzllMMSfw4pHLvHK8njvnZnP77EyS46K8erAQ44AEjHHK3nCal1/8Bmeslcw7Btkt0GWE49MMNC+YjHn1Wuas/ABzMudFrPbhsHdj21/J6Yq3OXOgkraWZiZaZvHJ7f8GwOmqd5iQkUn6lFx+8U4N/7bnBNc67ZiMioU5qeRPSyN/WhpLp5mZkhrfM9dDCBEaoyZgKKXWA81Avta6JNjzvUnA6MVh5+zRct60/pK2qnNMO6eZetV1qsME57OhYUoCzumTiJ+Zh3n2YiZaFjHFPJWM+AziY+LDUiztdFJ35jQdN64zY/EynA4HP/zcRuydnShlwDxpMum5U4mZXcCR2JlUnW3g/JmzNJCE3WBiQlwMS6eZ+dVf3wxA1bkmEkxGbpqSEpbyCjEejIqAoZTKByxa691KqS1Apda6OtDz/UnA8EFrrtRWUvnOk9RWvA3nmkmrdzC9DhJ7DayyG6BxAjQnwY0kA53JMTgmxEFyPCQmYEhKwpScTEzSBEwTzMSmpGKKT8YYn0xM4gRi4idgio/HFBNHbEwcJoOJGEMMRmXEoAwYlAGllOvvuP6uUFyvv0LT+fO01NTSXFNDU81FZt1yKysf3kTH9ev8/NHPuwoYG48jNhFnXCIf3PQQc25bzSf+41VmXD7ApltnY4qLo2zfRW5oI8bMKSSmZZIWB2bdQVJ8HIkJcSTGm8jJmEBBXjYGgxHb1RukJpjITIpDa01rh6tmE2NUxBgMGAyu2ozyskJW/2NS8xHRpFBD/h0cLQFjB7BHa21VShXSrxYx2Pn+hhow9j51gqsXxte6R07tpL2zhc4bzXS3t+Hs6oJuBwa7RjkhxqGJcYDRSdCLCWpAq/f/pNefnvOeTHv/9nlLo7WdbmcdTt2OpgOtu9C6C5NxGrHGKTicrVzvfm1AGRJiFmMyTsPhbOJG9xtezudjMk7B7rxKW3cF4Fk0UQGKBNMyYgyZ2J31tHcfBtU3cCSYlmE0mOl21NFpP+7O9f1vIMG0DIMhmW5HLV320wPvH7scg0qg23GRLvvZAecTY1eiVCxd9nN0Oy54Ob8KpYx02W10Oy71OadQJMbdCkCn/RQOR13fi1UMibGuGlpn93Eczr57xysVS0Ks69nR0X0Mp7O53/kEEmKXuc8fxunsO3nUYEgm3uSaF9TefRDtvNHvfCrxJtfoufauarTu6HPeaEgnzjQPgLauCtDdfc8bs4iLme0+/xb0W/EgxjiJ2BgLWjtp73qL/mKMOcTGTEdrO+1d7ww4b4qZhsmYi1N30tFV5eX8DEzGKTidbXR0HxhwPjYmjxjjRBzOa3R2H/Zyfg4xxkwczmY6u48NOB9nmo/RkIbd2UBX93Ev5xdiNKRgd9TTZXettJCgU0j7ZCYbH/jGgPSBCDRgRLtH0Qw09vqcEeR53DWPLQDTpk0LdfnGLIMykBSfRlJ8mtfzdm3H7uim296Jo7sDp70bp70Lp8OBdn/hdLrWtBrwhftLo/pEhH4vJ7pfMHKfVn0+mzAac/E26NYBYEglyXg/YEdrh+tPHCiVgFMpUEnEsdSdmRONE7QTZUzBaVBAAqaY6e6yeb4AQxzaoIA4jAbPr53u+VMTg0YBMRhUAgNfu4y4Ht0xKBXnpfQG93dqRClvgxEM7ut9nVe9ru//0/GcA4UBBpw39JxHGVxfPs67ru93XvW6HkNPMPV+f4X2cx5UGK/3Vrbe571d2y/NkK6P/PneL2HhFO2AMWxa6zKgDFw1jKHksXrjnJCWSQgRKkXDPP/oIOe/GERZRLRnejcD6e6/m4GGIM8LIYSIkGgHjF2AZzNtC2AFUEqZ/Z0XQggReVENGJ4RT+4O7eZeI6BeGuS8EEKICIt6H4a7D6L/sQJ/54UQQkRetJukhBBCjBISMIQQQgREAoYQQoiASMAQQrYwRQgAAAO2SURBVAgRkKgvPhhKSqkrwLkhXp4JXA1hcYToTX6/RDgN9/drutY6a7BEYypgDIdSqjKQtVSEGAr5/RLhFKnfL2mSEkIIERAJGEIIIQIiAeN9MkFQhJP8folwisjvl/RhCCGECIjUMIQQQgREAoYQQoxC7i2se39er5QqVEptDdc9JWAQmR+0GL/cWw17docUYtjcK3iX9/qcD6C1tgLN/YNJqIz7gBGpH7QY17YopU4DtmgXRIwN7udV79+nTbg2nMN9vDAc9x33AYMI/aDFuLZZa53n/k8uRDiYgcZenzN8JRwOCRgR+kGLcc0iTZ5iLJCAIUSYaa1L3LWLDHfbsxCh1gyku/9uBhrCcRMJGBH6QYvxSSm1RSm13v2xgff3qBcilHbx/u+WBQhL86cEjAj9oMW4Vcn7v1N57s9CDIv7JWS552VEa13tPl4INHs+h/y+MtO7Z7ijDbDIHuIi1Ny/X424fr9Kol0eIYZKAoYQQoiASJOUEEKIgEjAEEIIERAJGEKEkQyjFWOJBAwhwsQ9gkWWmhFjRky0CyDEGLYJ2BztQggRKlLDECIISql890KCgTBrrZv7HwwyDyFGDAkYQgSn92KVPrmbo8p9nA4oDyFGGmmSEiI4hQS2GkARsGGYeQgxokgNQ4jg5AN7/CVQSpkBvDVHBZqHECORBAwhBuFemrxUKeV5yG9wf/Y1Amoj/ZqjhpCHECOOLA0iRIDc+1ls0loXDJJuD7DBR4d3QHkIMRJJDUOIwK1jkL4Hd3NUs5/mqEHzEGKkkhqGEAFSSmlgnb+tVt01CJvWenegeSilLLg6ybcCxbhGUJlx7f5Y4SsvISJNAoYQAXD3NVQBaX5qDyil9mit1wWbh7tm0qS1Vv2O7wAaZFl0MRJIk5QQgSkEqj0Pes9IqN7cNQV/8ysGzaM/rXUxsM2dtxBRJQFDiMCsoO9ueVu8pFkPlA4zD2+s7ryFiCoJGEIErgp6VqD11o+xyV//RoB5eNOIK9gIEVUSMIQIzHZgXf89lD3cTUaD7dftNw8/0oGK4IorROhJp7cQIeDunN4TQA3D1/VeO73d55qAtUEEGCHCQgKGECGglKoazmQ8P6OktgIZ7s5vIaJKFh8UYpjcw2UHa47yd71nHoYnQPSeh3FahtSKkUJqGEIMk1KqFCiVJiMx1kmntxDDly7BQowHUsMQQggREKlhCCGECIgEDCGEEAGRgCGEECIgEjCEEEIERAKGEEKIgEjAEEIIERAJGEIIIQLy/wM6tTikQcIvVQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "jmax = (0.5 * N)\n",
    "j2max = (0.5 * N + 1) * (0.5 * N)\n",
    "\n",
    "label_size = 20\n",
    "label_size2 = 20\n",
    "label_size3 = 20\n",
    "label_size4 = 15\n",
    "plt.rc('text', usetex = True)\n",
    "\n",
    "\n",
    "fig1 = plt.figure()\n",
    "plt.plot(t/td0, jz_t1/jmax, '-.', label = r\"$|\\frac{N}{2},\\frac{N}{2}\\rangle$\")\n",
    "plt.plot(t/td0, jz_t2/jmax, '-', label = r\"$|\\frac{N}{2},0\\rangle$\")\n",
    "plt.plot(t/td0, jz_t3/jmax, '-', label = r\"$|+\\rangle_\\mathrm{CSS}$\")\n",
    "plt.plot(t/td0, jz_t4/jmax, '-', label = r\"$|-\\rangle_\\mathrm{CSS}$\")\n",
    "plt.plot(t/td0,jz_t5/jmax, '-', label = r\"$|0,0\\rangle$\")\n",
    "plt.plot(t/td0,jz_t6/jmax, '--', label = r\"$|\\mathrm{GHZ}\\rangle$\")\n",
    "#plt.ylim([-1,1])\n",
    "plt.xlabel(r'$t/t_\\mathrm{D}$', fontsize = label_size3)\n",
    "plt.ylabel(r'$\\langle J_{z} \\rangle(t)$', fontsize = label_size3)\n",
    "plt.xticks([0,(tmax/2)/td0,tmax/td0])\n",
    "plt.yticks([-1,0,1])\n",
    "plt.legend(fontsize = label_size4, ncol = 2)\n",
    "\n",
    "# plot\n",
    "plt.title(r'Total Inversion', fontsize = label_size3)    \n",
    "plt.show()\n",
    "plt.close()\n",
    "\n",
    "fig2 = plt.figure()\n",
    "plt.plot(t/td0, jpjm_t1/j2max, '-.', label = r\"$|\\frac{N}{2},\\frac{N}{2}\\rangle$\")\n",
    "plt.plot(t/td0, jpjm_t2/j2max, '-', label = r\"$|\\frac{N}{2},0\\rangle$\")\n",
    "plt.plot(t/td0, jpjm_t3/j2max, '-', label = r\"$|+\\rangle_\\mathrm{CSS}$\", linewidth = 2)\n",
    "plt.plot(t/td0, jpjm_t4/j2max, '-', label = r\"$|-\\rangle_\\mathrm{CSS}$\")\n",
    "plt.plot(t/td0,jpjm_t5/j2max, '-', label = r\"$|0,0\\rangle$\")\n",
    "plt.plot(t/td0,jpjm_t6/j2max, '--', label = r\"$|\\mathrm{GHZ}\\rangle$\")\n",
    "#plt.ylim([0,1])\n",
    "plt.xticks([0,(tmax/2)/td0,tmax/td0])\n",
    "plt.yticks([0,0.5,1])\n",
    "plt.xlabel(r'$t/t_\\mathrm{D}$', fontsize = label_size3)\n",
    "plt.ylabel(r'$\\langle J_{+}J_{-}\\rangle(t)$', fontsize = label_size3)\n",
    "plt.legend(fontsize = label_size4, ncol = 2)\n",
    "\n",
    "# plot\n",
    "plt.title(r'Light Emission', fontsize = label_size3)    \n",
    "plt.show()\n",
    "plt.close()\n",
    "\n",
    "fig3 = plt.figure()\n",
    "djz1 = (jz2_t1- jz_t1**2)/jmax**2\n",
    "djz2 = (jz2_t2- jz_t2**2)/jmax**2\n",
    "djz3 = (jz2_t3- jz_t3**2)/jmax**2\n",
    "djz4 = (jz2_t4- jz_t4**2)/jmax**2\n",
    "djz5 = (jz2_t5- jz_t5**2)/jmax**2\n",
    "djz6 = (jz2_t6- jz_t6**2)/jmax**2\n",
    "\n",
    "plt.plot(t/td0, djz1, '-.', label = r\"$|\\frac{N}{2},\\frac{N}{2}\\rangle$\")\n",
    "plt.plot(t/td0, djz2, '-', label = r\"$|\\frac{N}{2},0\\rangle$\")\n",
    "plt.plot(t/td0, djz3, '-', label = r\"$|+\\rangle_\\mathrm{CSS}$\")\n",
    "plt.plot(t/td0, djz4, '-', label = r\"$|-\\rangle_\\mathrm{CSS}$\")\n",
    "plt.plot(t/td0, djz5, '-', label = r\"$|0,0\\rangle$\")\n",
    "plt.plot(t/td0, djz6, '--', label = r\"$|\\mathrm{GHZ}\\rangle$\")\n",
    "#plt.ylim([-1,1])\n",
    "plt.xticks([0,(tmax/2)/td0,tmax/td0])\n",
    "plt.yticks([0,0.5,1])\n",
    "plt.xlabel(r'$t/t_\\mathrm{D}$', fontsize = label_size3)\n",
    "plt.ylabel(r'$\\Delta J_{z}^2(t)$', fontsize = label_size3)\n",
    "plt.rc('xtick', labelsize=label_size) \n",
    "plt.rc('ytick', labelsize=label_size)\n",
    "plt.legend(fontsize = label_size4, ncol = 2)\n",
    "plt.title(r'Second-moment Collective Correlations', fontsize = label_size3)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have found very different time evolutions for different quantum states that experience the same dynamics, leading to superradiant light emission, subradiance, delayed superradiant decay (superfluorescence), and macroscopic quantum correlations. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### References\n",
    "\n",
    "[1] R. H. Dicke, Coherence in spontaneous radiation processes, *Phys. Rev.* **93**, 99 (1954) \n",
    "\n",
    "[2] R. Bonifacio, P. Schwendimann, and F. Haake, Quantum statistical theory of superradiance. I, *Phys. Rev. A* \n",
    "4, 302 (1971); ibid. 4, 854 (1971); \n",
    "R. Bonifacio and L. A. Lugiato, Cooperative radiation processes in two-level systems: Superfluorescence, *Phys. Rev. A* **11**, 1507 (1975)\n",
    "\n",
    "[3]  N. Shammah, N. Lambert, F. Nori, and S. De Liberato, Superradiance with local phase-breaking effects, *Phys. Rev. A* **96**, 023863 (2017)\n",
    "\n",
    "[4] N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance, https://arxiv.org/abs/1805.05129 and https://github.com/nathanshammah/piqs/\n",
    "\n",
    "[5] G. T. Noe II, J.-H. Kim, J. Lee, Y. Wang, A. K. Wojcik, S. A. McGill, D. H. Reitze, A. A. Belyanin, and J. Kono, Giant superfluorescent bursts from a semiconductor magneto-plasma, *Nature Phys.* **8**, 219 (2012)\n",
    "\n",
    "[6] T. Bienaimé, N. Piovella, and R. Kaiser, Controlled Dicke subradiance from a large cloud of two-level systems, *Phys. Rev. Lett.* **108**, 123602 (2012)\n",
    "\n",
    "[7] A. F. van Loo, A. Fedorov, K. Lalumière, B. C. Sanders, A. Blais, and A. Wallraff, Photon-mediated interactions between distant artificial atoms, *Science* **342**, 1494 (2013)\n",
    "\n",
    "[8] A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, Superradiance for atoms trapped along a photonic crystal waveguide, *Phys. Rev. Lett.* **115**, 063601 (2015)\n",
    "\n",
    "[9]  C. Bradac, M. T. Johnsson, M. v. Breugel, B. Q. Baragiola, R. Martin, M. L. Juan, G. K. Brennen, and T. Volz, Room-temperature spontaneous superradiance from single diamond nanocrystals, *Nature Commun.* **8**,\n",
    "1205 (2017)\n",
    "\n",
    "[10]  A. Angerer, K. Streltsov, T. Astner, S. Putz, H. Sumiya, S. Onoda, W. J. Munro, K. Nemoto, J. Schmiedmayer, and J. Majer, Superradiant hybrid quantum devices, arXiv:1802.07100 (2018)\n",
    "\n",
    "[11] P. Kirton and J. Keeling, Superradiant and lasing states in driven-dissipative Dicke models, New J. Phys. 20, 015009 (2018).\n",
    "\n",
    "[12] J.R. Johansson, P.D. Nation, and F. Nori, *Comp. Phys. Comm.* **183**, 1760 (2012) http://qutip.org"
   ]
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     "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"
     ]
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   "source": [
    "qutip.about()"
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