{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cat vs coherent states in a Kerr resonator, and the role of measurement\n", "$\\newcommand{\\ket}[1]{| #1 \\rangle}$\n", "$\\newcommand{\\bra}[1]{\\langle #1 |}$\n", "$\\newcommand{\\braket}[1]{\\langle #1 \\rangle}$\n", "$\\newcommand{\\CC}{\\mathcal{C}}$\n", "Author: F. Minganti (minganti@riken.jp)\n", "\n", "In this notebook we show how the same system can produce extremely different results according to the way an observer collects the emitted field of a resonator. This notebook closely follows the results obtained in Refs. [1-3]." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from qutip import *\n", "from IPython.display import display, Math, Latex" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## The two-photon Kerr Resontator\n", "\n", "Let us consider a single nonlinear Kerr resonator subject \n", "to a parametric two-photon driving.\n", "In a frame rotating at the pump frequency, the Hamiltonian reads\n", "\\begin{equation}\\label{Eq:Hamiltonian}\n", "\\hat{H}\n", "=\\frac{U}{2}\\,\\hat{a}^\\dagger\\hat{a}^\\dagger\\hat{a}\\hat{a}\n", "+\\frac{G}{2}\\left(\\hat{a}^\\dagger\\hat{a}^\\dagger+\\hat{a}\\hat{a}\\right),\n", "\\end{equation}\n", "where $U$ is the Kerr photon-photon interaction strength, $G$ is the two-photon driving amplitude, and $\\hat{a}^\\dagger$ ($\\hat{a}$) is the bosonic creation (annihilation) operator.\n", "\n", "![cavity-1.png](./images/cavity-1.png \"The system under consideration is a single Kerr resonator, with parametric drive and one- and two-photon dissipation.\")\n", "\n", "The time dynamics of the density matrix $\\hat{\\rho}$ of this sytem is given by a Lindblad master equation $i \\partial_t \\hat{\\rho} = \\mathcal{L} \\hat{\\rho}$, where $\\mathcal{L}$ is the Liouvillian superoperator.\n", "The superoperator $\\mathcal{L}$ is made of an Hamiltonian part and \n", "a non-hermitian contribution, which describe the dissipation of energy, particle and information into the environment, as detailed \n", "in e.g. [5].\n", "\n", "Given the parametric drive, the dissipation processes include one- and two-photon dissipation, and the Lindblad superoperator become\n", "\\begin{equation}\\label{Eq:Lindblad}\n", "\\mathcal{L} \\hat{\\rho} = - i \\left[\\hat{H},\\hat{\\rho}\\right]\n", "+\\frac{\\gamma}{2} \\left(2\\hat{a}\\hat{\\rho}\\hat{a}^\\dagger\n", "-\\hat{a}^\\dagger\\hat{a}\\hat{\\rho}\n", "-\\hat{\\rho}\\hat{a}^\\dagger\\hat{a}\\right)\n", "+ \\, \\frac{\\eta}{2} \\left(2\\hat{a}\\hat{a}\\hat{\\rho}\\hat{a}^\\dagger\\hat{a}^\\dagger\n", "-\\hat{a}^\\dagger\\hat{a}^\\dagger\\hat{a}\\hat{a}\\hat{\\rho}\n", "-\\hat{\\rho}\\hat{a}^\\dagger\\hat{a}^\\dagger\\hat{a}\\hat{a}\\right),\n", "\\end{equation}\n", "where $\\gamma$ and $\\eta$ are, respectively, the one- and two-photon dissipation rates.\n", "\n", "We define the system parameters in the following cells. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "font_size=20\n", "label_size=30\n", "title_font=35" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "a=destroy(20)\n", "U=1\n", "G=4\n", "gamma=1\n", "eta=1\n", "H=U*a.dag()*a.dag()*a*a + G*(a*a + a.dag()*a.dag())\n", "c_ops=[np.sqrt(gamma)*a,np.sqrt(eta)*a*a]\n", "\n", "parity=1.j*np.pi*a.dag()*a\n", "parity=parity.expm()\n", "\n", "rho_ss=steadystate(H, c_ops)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This model can be solved exactly for its steady state [2,3].\n", "The corresponding density matrix $\\hat{\\rho}_{\\rm ss}$ is well approximated by the statistical mixture of two orthogonal states:\n", "\\begin{equation}\\label{Eq:MixtureCats}\n", "\\hat{\\rho}_{\\rm ss}\\simeq\n", "p^+\\,\\ket{\\CC^+_\\alpha}\\!\\bra{\\CC^+_\\alpha}\n", "+p^-\\,\\ket{\\CC^-_\\alpha}\\!\\bra{\\CC^-_\\alpha},\n", "\\end{equation}\n", "where $\\ket{\\CC^\\pm_\\alpha}\\propto\\ket{\\alpha}\\pm\\ket{-\\alpha}$ are photonic Schr\\\"odinger cat states whose complex amplitude $\\alpha$ is determined by the system parameters [2-4].\n", "We recall that the coherent state $\\ket{\\alpha}$ is the eigenstate of the destruction operator: $\\hat{a} \\ket{\\alpha}=\\alpha \\ket{\\alpha}$.\n", "The state $\\ket{\\CC^+_\\alpha}$ is called the even cat, since it can be written as a superposition of solely even Fock states, while $\\ket{\\CC^-_\\alpha}$ is the odd cat. \n", "In the previous equation, the coefficients $p^\\pm$ can be interpreted as the probabilities of the system of being found in the corresponding cat state.\n", "\n", "Below, we demonstrate this feature by diagonalising the steady-state density matrix, and by plotting the photon-number probability for the two most probable states." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The mean number of photon is 3.4606002041553974\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "vals, vecs = rho_ss.eigenstates(sort='high')\n", "print(\"The mean number of photon is \" + str(expect(a.dag()*a, rho_ss)))\n", "\n", "plt.figure(figsize=(8, 6))\n", "plt.rc('text', usetex=True)\n", "plt.rc('font', family='serif', size=font_size)\n", "plt.semilogy(range(1,7),vals[0:6], 'rx')\n", "plt.xlabel('Eigenvalue', fontsize=label_size)\n", "plt.ylabel('Probability', fontsize=label_size)\n", "plt.title('Distribution of the eigenvalues',fontsize=title_font)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "state_zero=vecs[0].full()\n", "state_one=vecs[1].full()\n", "\n", "\n", "plt.figure(figsize=(8, 6))\n", "plt.rc('text', usetex=True)\n", "plt.rc('font', family='serif', size=font_size)\n", "plt.plot(range(0,20), [abs(i)**2 for i in state_zero[0:20]], 'rx', label='First state')\n", "plt.plot(range(0,20), [abs(i)**2 for i in state_one[0:20]], 'bo', label='Second state')\n", "plt.legend()\n", "plt.xlabel('Eigenvalue', fontsize=label_size)\n", "plt.ylabel('Probability', fontsize=label_size)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Correctly, the two system have opposite parity. Indeed, for sufficiently intense pumping ($G> U,\\gamma,\\eta$ and $|\\alpha|\\gg1$), it was shown in [2] that $p^+\\simeq p^- \\simeq 1/2$.\n", "However, in this strong-pumping regime, the steady-state can be recast as\n", "\\begin{equation}\\label{Eq:MixtureCoherent}\n", "\\hat{\\rho}_{\\rm ss}\\simeq\n", "\\frac{1}{2}\\ket{\\alpha}\\!\\bra{\\alpha}\n", "+\\frac{1}{2}\\ket{-\\alpha}\\!\\bra{-\\alpha}.\n", "\\end{equation}\n", "Hence, the steady state can be seen as well as a statistical mixture of two coherent states of opposite phase.\n", "Since $\\hat{\\rho}_{\\rm ss}$ is anyhow a mixture of two (quasi-)orthogonal states, the steady state is bimodal. \n", "Such a bimodality can be visualised, for instance, through the Wigner function [2,3].\n", "Now, the pivotal question is: if one monitors the evolution of the system, in which states can it be observed?\n", "The orthogonal cat states, the two coherent states with opposite phases, or none of them in particular?\n", "As we will show in the following, the answer dramatically depends on the type of measurement scheme employed to monitor the trajectory of the system." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "xvec=np.linspace(-4,4, 500)\n", "W_even=wigner(vecs[0], xvec, xvec, g=2)\n", "W_odd=wigner(vecs[1], xvec, xvec, g=2)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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YXErqpHMEAgAAtEErAqCZ9czsWzPrTdmls9YbAgAAqFErAmBwJekusy0NhDdrvhcAAIDatCIAuvtY0kXOQwNJL8LjAAAArdCaaWDc/YWZnZjZrqTXknYlnbn7ac23BgAAsFatCYBSMrVL3fcAAACaI0wHty9prKRr2NjdLwscmw4k3ZE0ilsVwyDTvejx21lZxMw6koZhurpKtSoAAgAApMLg0KG7H0bbzsxsPK97WLqwRBzWzGyopHtZGg4VrzhmZkdmdjIjBA4ldZd+QgW0og8gAABAjr6SOYFjIyVBbKq8Sl0IhEfxubOVRHc/V1iNLOecPa0p/EkEQAAA0F5HejgTyJXeDXJ5PpN0Hm/ICXf7U6afmzb13IHyB6xWggAIAABaJ1TxespMERdWCtOMuYMl6UTSy+zGTLPxpaSLeMnZUCU8y7mXA0lfFbn/VdEHEAAAtFFXug98OXpKBobk6Ugam9mJogAZqoDpvwch2F2b2SA915T+fx13n5hZ8WexJAIggHe8fvN9KefZeczHC4BGW2oVsKgy2IvDnJkNzawbb3P3Z2Z2oaRP4Y2kj3LOdxQHx3XhExpoubIC37zzEggBTPPod39HO3/4H1Zx6qdmdhX9fFrClHDTguOXkr6WFIfCEyUDTXpKmn6vzewwbSoOzdDTKpCV4hMZaImqgt4q1ycUAqjYK3ffn7WDmXVmNAPnGWe+S5Lc/cbMOmbWc/exmY2UjBQeK2ku/kBJCLxQshiFJH1c1xzFfPoCW67u4DdLem8EQQA1SANcV1EVLlTl4sffEfXVm9p30Mzuwr7j+DhJh2Z2HfoG3ikZcVwLPnWBLdXk4JcV3ythEMA6hCA31sMm3a6kyZyJoN+uGjLlsX1J11OOHYVr9iTtmtkn0WN7SgLkUNLLKvsG8kkLbJlNCn55qAoCWKNLJWEtngtwL2yfZZTdL0z3Mg7Nv5J0POXYjqTLvIBpZs8lfejug4WfwZKYBxDYEq/ffL/x4S+2Tc8FQGMN9DCo9cN2SUmTsJndhgEdqdOwX2yYbosGeRzEO4QRxDszqos7hZ/BkvgTG9hw2xyUXr/5nkoggMqEZuBBqLylzbrDnIDWzTnuMDTVvlYyqGMYL/3m7n0zO4n2kZKm5QfVvRAMB5I+ltQJA0hG7p5dpaQ0fLICG2ybw1+KJmEAVQoha2rQCoM3nuRsHyuqFE45dqERvuFcfT2sKlaGJmBgQ7Uh/MXa9nwBoEoEQGADtTUMbVs/RwCoCwEQ2CAEoASvAQCshgAIbAhCz7t4PQBgeQRAYAMQdvLxugDAcgiAQIPR5Dsfrw8AFEcABBqKYLM4XisAKIYACDQQgaY4qqUAsDgCINAwhJjV8PoBwHwEQABbhxAIALOxthLQIHUHl1e/Ku/6T9/j4wUAmopPaKAh6gp/ZYa+aeetIwy+fvM96wcDwBQ0AQMNUEf4e/Wr7ysLf3VeK1Z3RRUAmoo/j4GWqSOIZa9N8zAA1IsKIFCzdVWp6qrC5VnnfVAFBICH+DMcqNE6w1/TUA0EkPrh7/5AH/zhj0o/7/9U+hm3BxVAYMs1MfzF1nF/VAEB4F0EQGBLNanJd55NuU8A2BYEQKAmVValNjFQVX3PVAEB4B4BENgymxj+UptUtQSATUYABGpQVTVqW8JTVc+DKiAAJAiAwJoR/upFCAQAAiCwFbYx/G3jcwKApiAAAmtE9akYQiAAVIMACGy4bQ9JVTw/gjiAtmvVFPxmdiSpJ2k3fB+5+3m9dwUsb9vDHwCgGq0JgCH8jdPAZ2YdSddm1nX303rvDm2wiVWn27s3C+23231c6X28+tX3LBkHACVq0ydqL672ufvEzIaSRpIIgNg4VVX/Fg19s46pOhCW4fWb77XzuE0fgQBwrxV9AEO175PwPXYZHu+t/66AZrm9e7NU+Jt2rrLR3A0A5WlFAHT3iZI+fwQ91KLs5t+yw1AVga2KcwIAytGKAChJ7v7E3W8ym/ckTdx9XMc9AU1QZVAjBAJAM7UmAE7xmaTP674JoC7rCGhlXqPsyucmDswBUC4z2zOzEzM7SL8vcY6OmY0y24bh3NnuZ4XOU5XW9oA2sxNJd+7+YsbjJ5L0k5/8ZJ23BsxUVghaZ3Xu9u7NRgwMAdAuYQzA0N0Po21nZjYu2Do4lNTNbNuT9DycM7v/2N13FzxPJVpZAQxveD9+w7Pc/dTd9919/+n776/x7rBtqDIlaA4G0EB9JbOBxEZKgthCQqbIC21jSYeSnimZfzj96ks6LnCeSrQyACp5Yz+q+yaAuhDGAECSdCQpOz7gKmxf1IGki5zt1+5+6e437j5OvyQpZ0zCrPNUonUBMLStfxpGBgOtU2f4I3gCaIrQN68n6S7enuaDRaaIC/0Fv8p7LG+RCTM7mbJ96nmq0qoAGPr1DePwFzp9Mj0MAADt0pXuA1+ORbJBZ9GCkpntKakurnSesrQmAIal4NJ/98LInANJx0wDg7ZoQgVu1XtgJDCAkiw8OjePmR3FK4wt4CCv6XeJ85SiFaOAQ5n3bMrDhD9sDFbDALCNfu93f6D//D/6URWnfmpmcdXtNK8JtqiQKxau2IUi1IO8UfQ8ZWpFAAxl1QdjsAEAwFZ75e77s3Yws2WaXz8uGCQ/U/7g06LnKU1rmoCBOtC8CACNlVbk3pl6JZq4ObeFcE5fvrz9O5L2siGz6HnK1ooKIIBm9P8DgKZw94mZjfWwL2BXs5eJ3Ze0a2afRNv2JPXMbCjpZaZP34Hym3mLnqdUBEAAANBWl0qCWDw4Yy9szzVlGpfnkj5090HOIR8qp5q4xHlKRRMwAABoq4EersrRD9slvV2f9zZMJTfNzozHHsw1uOR5SkUFEAAAtFJoBh6EyttYSVgb5jT/5i7RFuYRHkj6WFInLDYxykz3ktfMvMx5SkUABFpit/uYfoAAkBFC1tSgFQZvPJny2FhJxbA/4/i5zbmLnKdsNAEDFdp5zN9YTcd7BKCNCIAANsrT9whsALAqAiCAtdrtPq77FgCg9QiAwAZZtfpF+AIASARAAGtEAAWAZiAAAi1DCAMAEAABrEUTgycjgAG0FQEQaKF1h7GyrscIYAAoBwEQqFhTq0xNrMgBANaDAAhsmDKrYOsIgU0Nmk0N5gCwDgRAoOWqDGhlnpvmXwAoDwEQWIOyq01lh6GyQ+Bu93FjK38AAIk/qQFIug+Bt3dvVj5H2coOvDT/Amg7PgWBDfX0vUd69avvSz9vHOIWCYNVV/po+gWA8vHJCqzJzuNHev2m/MBWJZpxAWA7EQCBDVZVFbApqqj+0fwLNM8PH/2OevzBuVYMAgE2HE2kAICiCIDAGlVVfdrGEEj1DwCqQwAEtsQ2hcBtei4A0EQEQGDNqELNVlX443UHgHsEQGCLbHrljPAHAOtBAARqUGUg2dQQuKn3DQCbiAAIbKFNC1Obdr8AsOkIgEBNqm6WfPreo8YHq3XcI82/APAQARDYck0Ngeu4L8IfAOQjAAI1WldAaVoIbNr9AEDb8CkMtEQauupcOm6dwY/qHwBMRwUQqNm6g0pdfQMJfwDQHHxKAg2w8/iRXr9Zb2VuHRVBmnoBoJn4dAYaoo4QKOWHtGVCYVPCHtU/AJiPT0qgQeoKgVlNCXNFEf4AYDF8WgIN05QQuGkIfwCWYWZ7kvYljSX1JI3d/XKB447C/rvh+8jdz6ec/yD8uBP2G0ePH0g6lPQ6nOva3U9XelIL4BMTaCBCYDGEPwDLMLOepKG7H0bbzsxsHIe0nOOOlATF8/BzR9K1mXXj8Bb2O3T3frRtKGkQ/n0gSe4+iB6/NrOOu78o7YnmYBQw0FCEmsXwOgFYQV/SKLNtJGk457ieu9+kP7j7JBzz9lwhFA4z4e9I0lHm+lmXU7aXqnUB0MyO0sQNNB3hZjZeHwArOpJ0k9l2pXdD2jtCsPskfI9dhsd74efPJL3TJBwqhoeZ47I/S9Jk9m2vrlUBMAS/L+q+D6AIQk4+XhcAqwgBrifpLt4eqnlxkFPO473wNcuJpJc5x4+jfx/Hzb/BkaQv593/qlrxCRrexIGka2XeaGAT0CfwXYQ/ACXoSveBL0dPycCQB9z9Sc7mPUmTKOB1JI3N7ERR9sgbKJIK+95U3f9PakkADG9GX5LMLJu0gY1ACEwQ/gAU8NTMrqKfT6NBGtkm3FV9Julz6Z3qYS8zKGSYHSgSth8pNAW7+3HJ95WLT1Jgg7Q5BBL8gO31w0e/o93u4ypO/crd96s4cSyt8kWVu2nh8ktJX0t6JwCGquC5mXXM7FrSp/Egkyq0qg8gsA3aGITa+JwBrEfOYI6ix/ck9eOpZHTfdPxOE3IIdZ05/QtHSkJipQiAU5jZiZldmdnVq1/8ou7bAd6x8/hRa0JRW54ngLVLw1k33hgFwqnzAGYMJX0Ub4j6Fc7qXzjNpZKQWOmMJQTAKdz91N333X3/6fvv1307QK5tD0fb/vwA1CeEtLEeNtd29e5gjqnMbKSkuTYv6KUri+QZm1nPzL6dVg3Mua9SEQCBDbeN1cBtfE4AGulSyTJwsb2wfabQ728Yhz8zO4gC3SicKz5mT8kKImm4vNLD2UnS4+kDCGC+bQhMBD8AazaQlB112w/bJSVNwmZ2GwJfuu0o+nfPzPZCk+1xFO5O9XBFj2G6Lex3MeWeXixSgVwFn7TAFknD0yaOFCb4AVg3d5+Y2cDMnuu+yXaYE77e9hMMfQTPppwynuR5YmaHYe3f15J2w7kvo31ehDEHu9E+Z9lpYqrAJy6whTYpCBL8ANQpjMyd2twamnifZH62Bc89VlRNnLJP5WEvTxs/ebuquGMl0BRxuGpKGCTwAUD9WvFJHMq1nykp7XYkDc3sUNLFrCVZgG1Sd1WQ4AcAzdGKT+RQrmUJOEAPg1hVgZDABwDNxSc00HJlBkJCHwBsBj6tAbyDEAcA2495AAEAAFqGAAgAANAyBEAAAICWIQACAAC0DAEQAACgZQiAAAAALUMABAAAaBkCIAAAQMsQAAEAAFqGAAgAANAyrPkEAABq9chMT98jkqzTyq+2mf2RpANJu5J6kjqSuuH7WNJE0p2kW0k37v4/rnpNAAAALG+pABhC308lnUj6saRvlIS9cfj367DrjpIguCPpQ0n/xMx+LOlS0sjd/8UK9w4AAIAlFAqAIfidSnom6QtJx+7+dcFz9CR9JOmnZvaFpOfu/s+LnAMAAADLW3gQiJn9t5IulFTudtz9Z0XDnyS5+9jdv3D3P1XSbPx3zOylmf3HRc8FAACA4hYKgGb2ryS9cve/4+5/UdbF3X3i7j+T9ImkL8zsH5R1bgAAAOSbGwDN7L+X1Hf3f1rVTYSq4J9K2jWzP6nqOgAAAJgTAM3sA0kDd/9mHTfj7n8m6dt1XAsAAKCtZg4CWVfwy1zz5+u+JgAAQJuUthKImX1EHz4AAIDmKy0AhhHBZmZfmdmfm9mPsvuY2Y/D439U1nUBAABQTKlrAbv7X7j7x5L+TNI/M7PPM4//Mjw+LPO6AAAAWFypATAVRvV+LOnKzL7MmeOvU8V1AQAAMF+pKy+HZt/PJO0pWRdYStYFHpvZWPdrBJ+XeV0AAAAsrrQAaGb/UNJIkk3ZZTd8P3X3n5Z1XQAAABRTSgA0s7+nZI3gUyXLxd1IusvuJsIfAABA7cqqAP5M0u68eQPNbGBmf+7u/6ik6wIAACzNzPYk7UsaK+m+Nnb3y1WPM7OOpBNJ5+4+NrOepCNJN5n9DiQdSnqtpLX02t1Py3p+05QVAL9dZNJod//GzH5pZn/k7v9nSdcGAAAoLISyobsfRtvOzGzs7uMVj+sqmfVkaGaSNJH0aU74k7sPom3XZtZx9xflPMt8ZY0C9gL7fi6pX9J1AQAAltVXMn4hNtL86eoWPe5Q0hMlraRP3D07CDYvD11O2V6qsgLg7vxdEu7+S92PEAYAAKjLkZJxC7GrsL2U49x9MquaqCQkZk3mXH9lZQXAMzP78wL7TxspDAAAULnQR6+nzKBVd5+Ex3OLVcsel8fdj+Pm3+BI0peLnmNZpQRAd/9C0qGZ/TcLHvK6jOsCAAAsqSvdB7cc04JckeM6ZnYUvk7MbGZl0cxOlAwSqbT/n1QXqah4AAAgAElEQVTuRNDpyh8Hkkbu/s/zdgqTRe+UeF0AAIA8T83sKvr5NBphu+yqZIsedyepG4/oDQNFlO0LGILhoZRUBZe8r0JKC4DufmNmfyrpX0l6ZmanSlb8eKlkiPRYyXDpQfgCAADQox+Ydh6XujhZ6pW771dx4nlChTA7ncsofJ1n9j2XdG5mHTO7VjJaONvHsFSlvtrufmlm/4mSJ/eRpGM97BD5Z+7+L8q8LgAAwDLClCuFB10sedxYUm/ase4+MbORpK+VjB6uTFmDQN5y93GYF+eZpBdKnsTXkr6QtO/uPyv7mgAAAAXF8/W9FQZ5xI8vdZyZPc85Nh04MmugyKWSvoMHM/ZZWSX1Vkly959L+nlV5wcAAFhWqLaN9bBPX1fS1KlbFjkunSjazM4z50lDY7rPtaRnU661bB/FhVQWAJto2eVeAADAVrpUkgvi/nZ7YfvSx4UQ2M8JdgdKRvlOzKyrZO7Au8w+aXWw0j6ApTcBN1W0bMupu1+GUTn9IvP1AACArTJQMl4h1lc0WDUMzLgNU7QsfJykuzhjhCbivqRPpSQkSrqYck8v5kwevbKZFUAz+0DSR+7+z6q8ieh6P5J04u7/tILTz1q2ZS1DrgEAQHOEStwg9NdLWweHOeGrW/Q4dz9P5wBUMv1dR9JxZp8XYX7AXSVzJO9KOounjqnKzADo7t+Y2TdhlY/n7v5XVd2ImX2kJPx9UtEljvQwAF4pP30DAIAWCNOtTG1uDaN1H4zInXdc2Ce79m/ePpWHvTxzm4DdPR3B+3Mz+6/KvgEz+5GZfSXpqKrwV+ayLQAAAJtuoT6AIeXuS/rQzP4PM/uHobl2aWb2d0Pwu5b0P7j7P1rlfHMsu9wLAADA1ll4FHAITz8N1bLnkk7DbNWXkm6VNKdOJN25+/+XHheCYlfJ6JiepA+VjIIZK1mS5eOSnssslQ6lBgAA2CSFp4EJnRd/qiQM/hdK1q77me6raG5m2cPSDZdK+tz9zN2/WeqO1ySM9jmRpJ/85Cc13w0AAEB5VpoH0N3/QtJfpD+b2Y+VVPs64fudkkkRGxH2iizbEjplnkrS3rNnXumNAQAArFHZawH/UtIvyzxnSeJlW94GwAWWewEAANg6rZgIOlT9Ci/3AgAAsI1qCYBm9kc1XDZdtiW2yHIvAAAAW6WuCuBZDddcZNkWAACArVdqH0BpoepeOinzWhVY7gUAAGCrlRYAzexzJfMDNtYiy7YAAABsu1ICoJn9YyXNqX+mZFLoWZ5I+ryM6wIAAKC4siqAh5I+CNPAzBUmWQYAAEANyhoEcrNo+Av6JV0XAAAABZVVAXxVZGd3/7qk6wIAgA1n33+nR7/8f+q+jVYpqwL4SzP70aI7m9mflHRdAAAAFFRKAHT3LyT9kwITPA/LuC4AAACKK20aGHf/mZn9uZl1lcyzN200cEfJChwAAACoQVnTwPxYyZJqzxY8xMu4LgAAAIorqwI4lPStkqXWxpImM/Z9IullSdcFAABAQWUFwJ67/+mC+35jZj8v6boAAAAoqKxRwBcF9z8u6boAAAAoqKwAWKhPn7t/U9J1AQAAUFBZAfAbM/u7i+5sZv91SdcFAABAQWXNA/gXkg7N7B8seAhLwQEAANSkrGlgPg//PDCzLyRdKRkNnKcrqVfGdQEAAFBcWaOA+5J+LMnCz4dz9mceQAAAgJqU1QdwLOmn7v47i3xp9jyBAAAAqFBZAfBO0pcF9mcUMAAAQE1KaQIuMAl0uv9+GdcFAABAcWVVAAEAALAhFg6AZvYnZV20zHMBAACgmCJNwENJH5Z03TLPBQAAsFZmtidpX8lA2J6ksbtfFjj+SNIke4yZdSSdSDp397GZ9SQdSbqJ9zWzA0l74ccdSbfufrro9YsEwDLn7mMeQAAAsJFCKBu6+2G07czMxu4+bR7k+PgDSV9IOs55uKukUDY0MymZOeXTTPjbkyR3fxFtOzKzk0VDYJEA+MTMfhNu5K7AcbGupM6SxwIAADRBX9Ios22kJLjlhTpJb4PjQNK1ZmepQyWLanSnBMq+u7+zqpq7n5vZmaTSA6CUTPT8JHytgomgAQDApjrSwwB4Jeli1kEhzPUlycwGc/adaPq8yftm1ssJhwsX2YoGwD2tPoffrqSXK54DAABg7UIfvZ4yFTx3n5iZpgSzsl1KujCzY3e/Cfd1JOls0RMUCYBjd/9fCt5gnhszYyJoAAAgSbLf/Fo/+OW/q+LUT83sKvr5tMhAiSm60tsKXZ6ekoEhq+iEQJde787dz9MH3X0Q+hFeh0riOGyvZBBIttS5ijLPBQAAkOdVBYtPVD2W4U5J37+3YS4MMFEmBD4zswsl/Q5vJH1U5CILzwPo7n9W5MTrOhcAAMC2cPdJTiUvHWDylpmdKOlPeKik6ngdBpkspJSl4AAAADZNkcCkpBn2bbOvmXVmNAOXbSypl17TzEZKpqEZSxqb2QdK+v9dKBlrMRcBEAAAtE46l1+BQ15KeqH7/n1dRaN0w+AQacX+f2b2PJ7fL0gHnPTMLO3v9/Y6IYgemtm1mR0sMiE1ARAAALROCFBT5+ybcdwkhLBsX8CukpU9lg6AaSg1s/PMebrh+1jJ6iPXU04xyrmvXAv3AQQAAICkZBqW7OCSvbB9aek8gTkh8kDJUnATJSHw2ZRTdJQMCJmLAAgAAFDMQA+rh/2wXVLSJGxmt2GwRp5pq6PdxX0TQ9NyX9Kn0n3Tb5gGRtF+PUk7i1YgaQIGAAAoIDQDD8zsucIADd0Pyoh14x9CmPss7N9R0tx7KOkineIlLOl2FOYB3An7HWf6/PXN7MTMhpJeh80Td5+5ukiMAAgAAFBQWIFjanNraK59krNtbkiL5/ubsc9KE1oTAAG0xus33y913M5jPioBbBc+1QBsrWUD3yLnIRQC2GR8ggHYKmWFvqLXIRAC2CSMAgawFV6/+X5t4W/a9QFgU/AnK4CN1MTARVUQwKZo1adTGFI9WWSJFADN1MTgN016rwRBAE3TmibgMGHiF3XfB4DlbVL4i9XdPA0AWVsfAM2sZ2YjJZMu3s3bH0DzbEuA2obnAGA7bH27RLquniSZ2cIzZAOo3zYGJpqFATTB1lcAAWymbQx/sW1/fgCajQA4RVhj78rMrl794hd13w7QKm0JR9vStA1g8xAAp3D3U3ffd/f9p++/X/ftAK3Q1kDUxucMoF4EQACN0PYQ1PbnD2C9NqYXspn1Cux+5+6Tym4GQKkIP4nXb75ncAhayb/7G/36//7Xdd9Gq2zEJ00If8MCh7yU9KKi2wFQIsLfuwiBANZhIz5lwlQux3XfB4ByEf7yEQIBVI0+gABqQfibjdcHQJXaFgC7kjp13wTQdoSbxfA6AajK1gdAM+uY2dDMzpSEv6GZjczsqO57A9qIUFMMrxeAKmx9J5MwGpgl4IAGIMwshz6BAMrGJwqAtWhK+Hv1q+L38fS9+j8qCYEAysSnCYDK1Rn+lgl8s85RZxgkBAIoC58kALZKGYGvyPmbUB0EgKK2fhAIgHqts/pXdfibds11XrcpTekANht/ugKozLrCSh3Bb9o9UBEEsAmoAALYWOuuvi1iHfdDFRDAqgiAACpRdUhpWvCLEQIBNB0BEEDp2hz+UuuoThICASyLAAhgo2xC+Itt2v0CaAcCIIBSVVmV2tQwVeV9UwUEsAwCIIDSEP6m2/T7B7BdmK8AQOMRnmZjhRBg/cxsT9K+pLGknqSxu18ucNyBpENJryXtSrp299Mp5z8IP+5IGrn7OHOevejx27zzTMMnBoBSVFX926bw9+pX3zNPILAFzKwnaejuh9G2MzMbxyEt57gDSXL3QbTt2sw67v4i2nYk6dDd+9G2oaRB+PdeOM87x5jZyaIhkCZgAI21TeEvtY3PCWihvqRRZttI0nCB47Iu4+1m1lESLuNtR5KO4vNkq43ufq6ksrgQAiAArFkVIZDBIMBaHUm6yWy70rshbZq8kDaJ/v2ZpPP4wZxwtx+qkFmdBa4viQAIoARVhA8qZQCaKFToepLu4u3uPgmP5wWzdJ/juPk3OJL0ZfTziaSXOcfGTcuXki7SpuBw3SNJZws+DfoAAmin27s3c/fZ7T6u7PpV9AdkMAg21W+/+05/+2++qeLUT83sKvr5tMhAiSm60n3gy9FTMjBkLjM7kXQT9+VTUsUbh8fehsxQBUz/PQj9Ca/NbJBej0EgADZaVdW/RULftP2rDIMAKvPK3fdLPufCzazTpIM8pKQqGG1Pq4e9OMyZ2dDMuvE2d39mZhdK+h3eSPqoyD3QBAxgJWU3/1YR/m7v3hQOf3nnKBvN3EA7uft5GOQxCKOA06bcaeHyS2UGmIQKYV9JkOwpqQZObX7OogIIYGuVHdrS8zW5GkgzMLC4IoFJ0l3c7BumbpnWDLwQd5+Y2UjS15Ke6L7peJzZ78bMOmbWc/dxOGYY+gWOzewDJf3/LpTMLTgXnxIAltbk6l8VFbv43GWFQOYGBOqRzuVX4JCXkl7oPpx1FY3eDYNDpAX7/0UuJXXM7MDdL81MendUcKxnZnfSu4NCQhA9DNXEg0UmpOZTB8DWqTL8xddociUQwGwhQB3P3fHhcRMzG+thc21X0mTaRNAhcF5LejZlnzhAThtIMlay+sj1lNsb5dxXLvoAAmiETewPt46gCaCRLpUEsdhe2D7LlTLTxygJe9L9vIIj3S/xJuntyh/pKiNjSc+mnL+jh/MT5iIAAtgq6w5lhECglQZ6WD3sh+2SkiZhM7sNgzXSiuPFlHO9iKqCp3q4Ysgw3Zbuly4rF12vJ2ln1lJ0MZqAASyliStPbGoYox8gsFlCM/DAzJ7rvsl2mBO+upnjXpjZiZntSnqtZMDGWWZ6l4mZHYa1f9N9hnG/Pnfvh/Ok+0hJ83N2kump+MQBULtNbP6N0R8QaB93v9GM5tYwMONJzva5kzWHIDkzzK06oTVNwAC2wqZW/wCgDgRAABtvG8LfpldBAWwWAiAAAEDLEAABYMs0cYAOgGYhAAIorMyAQdMnAKwfARAASrAN/RABtAcBEAAAoGUIgAAAAC1DAAQAAGgZAiAAAEDLEAABoAQsBQdgkxAAAWDL7DxmmXcAsxEAAdTq6XuEFYnXAcB68YkDAABq9Zu//U6Tf/1v6r6NVmlFBdDMjszsuZmNzOzCzI7qvidgkzWtiZH+dwBQTLM+xSsQwt7Y3c/Dzx1J12bWdffTeu8OwDYggALYNG2oAPbc/Sb9wd0nkoaSRvXdEoCy1RXCyrgu/f8ArNtWB8BQ7fskfI9dhsd7678rAFllBSAqcQCwmK0OgKHa1wtfhZjZiZldmdnVq1/8ovybA1CJdYZAAieATbXVAVCS3P1J3AQc7EmauPt4xnGn7r7v7vtP33+/2psEUKp1BLOyrkHzL4A6bH0AnOIzSZ/XfRPAJit7JHDZQajKEEjlD8Cma10ANLMTSXfu/qLuewFQrSqCWtPDX9Om6AHQTBvzSVFwwMZd6P+Xd46+uz8r784AlOXpe4/06lffl3rO3e5j3d69KeU8ZaP5F0BdNuLTJwS3YYFDXkrKq/ANJX1Uyk0B0M7jR3r9ptzAVoU4vBUJg02v9gHAsjYiAIbBGsernMPMRpI+zasMAmiOKqqAsW0OdTT/AlhUK/oAhn5/wzj8mdkB8wACqAvNvwDqtPUBMF7318x6ZrZnZgeSjmdNAwNgMVVUnbY9HG378wPQfFv9KRRWADmb8jDhD2iwqpuC61JV+KP5F0ARW/2JEZp8re77ALCcbQuBhD8ATbH1TcAAqkcAmY9mXwBNQgAE0GjbEJyqfA6EbwDL4JMDQCmqnBNwk5uCtyHAAnjIzPYk7SsZU9CTNHb3yznHdCSdSDp393GYjeRI0k16rJkNJX0Zzjd16rpw/b6kW0k7kr5095tF759PJgAbYRNDYNXhj+ofUI90gQp3P4y2nZnZeM4MI10li1IMzUySJkrmKI6D456k5+Gc2ePH7r4bZjMZZK5/bWYLz3BCEzCA0lQdSDapmrZJ9wqgsL6kUWbbSIutWnYo6YmkXXd/4u7nmcfHYZ9nknajr77uF8XIu9bnYZ+F8AkFYKOkwaqp1cB1BT+qf0CtjvQwAF5Juljk4NC0O6159zqvKdnM5O43oRm5p4fT2d0omfpusMg9UAEEUKp1BZMmVtiaeE9Ayz01s6vo62TVE0YB7C7envbXW3WVMXc/zbnmSbQ9Pf9dZre76P7m4tMKQOmqHBASa0o1cN3Bj+ofts1v/vbX+vb231dx6lfuvl/yObvSfeDLkVedi3WiVcq6ku5ymoHfCoM9rqJN6bm7ereK2J2yPRefIgA2Xl1BsI6KH+EPqN1CFbYp7iR14ypfGDyiGSHwwN1fpD+4+8TMLpUMFomDZi/6PncgCE3AACpRR1B5+t6jtYUymnsBFOXuk5wm3qmDR0KlMC/M9RUN+Mg0+2abhnPxCQagMutqCs6Kw1mZVcG6Qx/VP6BcBfvr3cXNvmbWmTVPXwFjSb0p5/tM0kfZA8IcgsdRU/JE90FxoWlg+DQBsNXqDm1lIfwB5Urn8itwyEtJLzSlD15UhZsawMzsedycG6QVu56Skbzx+famhcyw/Tzafy/aPhefKAAqVVcVcJsQ/oDyhQmTj+fu+PC4iZmN9bAvYFfSZNpEzGngNLPzzD7p4I3scQdaYDBHZF9RIJyHPoAAKkeAWR6vHdBIl0oCV2wvbM8VQl8/JyAeKFkKLhv2PtSUaqKZXeRMaTPQgnMASgRAAGtCkCmO1wxorIEeVg/7igKYmXXM7DYT1O7ifoehmbcv6dOcazyYazAyURQ2zey5pNGiy8BJNAEDWCOagxdH+AOaKzQDD0LwGisJa8OcANbNHHduZkdh8MaOkmbkaev35jUzpwaSjsxsJ/x8mzeB9Cx8wgBYK0LgfIQ/oPnc/UbRoI2cxydK1vzNbl+on567T23ODYExO5ikEJqAAawdAWc6XhsA60AABFALgs5DvCYA1oUACKA2BJ7EzuNHvBYA1ooACKBWbQ8/bX7uAOpDAATQCG0MQm18zgCagU8fAI2RBqJtHyVM8ANQNz6FADTOtgZBgh+ApqAJGEBjbUtgans/RwDNQwAE0GibHp42+d4BbC8+mQBshDhIbULTMMEPQJPxCQVg4zS5jyDBD8Am4JMKwMZqSlWQ0Adg0/CpBWArTAthZQVDQh6AbcInGoCtRnADmu/7v/ler//313XfRqswChgAAKBlCIAAAAAtQwAEAABoGQIgAABAyxAAAQAAWoYACAAA0DIEQAAAgJYhAAIAALRMK2ZINbMDSYeSXkvalXTt7qf13hUAAEA9tj4AhvAndx9E267NrOPuL+q7MwAAgHq0oQm4n7Ptcsp2AACArdeGACglzb9Zk7XfBQAAQANsfROwux/nbD6SNFr3vQAAADRBWyqAb5nZiaSbef3/zOzEzK7M7OrVL36xprsDAACo3tZXAFNmdqTQFDylKviOMEr4VJL2nj3zau8OAABgfVoTAN39XNK5mXXM7FrSp+5+U/d9AQAArNvGBEAz6xXY/c7dcwd5uPvEzEaSvpb0pJSbAwAArWJme5L2JY0l9SSN3f1yzjFDSV+GfacORg1T2O2FH3ck3WbnLw7X70u6Dft8WaSwtREBMIS/YYFDXkqa1cfvUlLHzA7mvVkAAACxNJe4+2G07czMxu4+nnHonqTnYf/sY2N33w3BTvFYBTM7MrOTNASGgDjIXP/azI7nXP+tjQiA4cnM7beXFd6ga0nPprwgnVXvDQAAtE5fD2cTGSkpVs3KK2Ml4xHu9O50dAeSrtJzu/s7cxW7+7mZnSmMTQjXys5n/HnYNtAC2jAK+ErJCx1Lm5PpAwgAAIo60sMMcRW2z3Lt7pfufuPu4/RLkqLm2/0p3d46kmRmHYUm58zjNwrVxUVsdQAML+pFzkMDSS8WLZMCAABI7wSwd4pLaZ++WWMWsv34wv4nme2Xki7SpuCwz5Gks/Bjev5scesuur+5NqIJeBXu/iLM6bcr6bWkXUlneW8CAADYKk/N7Cr6+bSE//93pfvAlyOvOpcrhLz4/uTug9DH79rMBum5ovtOz93Vu83I3Snbc219AJTyEzcAAGiG7777rf7tv/urKk79yt33Sz5nmeMHDvIWpnD3Z2Z2oaRP4Y2kj6LHJmZ2qWRASRw0e9H3uQF0q5uAAQAAmig06+YGtbBqWV/JgJGekmpg3LTcVzQIJNPsm20aztWKCiAAAEDWKnMMm1ln1lx+C/hMUWUvOu9IyRQzY0ljM/tASf+/CyXd2OTuYzM7DiFSSpp80zC5PdPAAAAAlGmFOYZz++BFVbi5ASzsu5cNkOk54kGqYZ/DMM/f2/mLw/bz6Ni9aPtcBEAAANA6y84xHPrgjfWwL2BX0mTBGUYOlD9QY1/J/MV5RjnXzB57PuPxd9AHEAAAoJhLJYErthe2L+JD5VcKx5KeTTmmozD3oJldhH6CsYEWnARaIgACAAAUNdDD6uE7q3CYWcfMbnOCmpQzj6B03/QbpoF5KzRX70TVxYmisGlmzyWNisxvTBMwAABAAaEZeBCC11hJoBvmBLDuw6OlcExuc66798P8xUMl8xdLSdNyXN0bSDoys53w823RKe8IgAAAAAWFpdumLikbBmM8mfLYzKbaeWEuBM0H8wcWQRMwAABAyxAAAQAAWoYACAAA0DIEQAAAgJYhAAIAALQMARAAAKBlCIAAAAAtQwAEAABoGQIgAABAyxAAAQAAWoYACAAA0DIEQAAAgJYhAAIAALQMARAAAKBlHtV9AwAAoN3+5re/1f/2V9/VfRutQgUQAACgZQiAAAAALUMABAAAaBkCIAAAQMsQAAEAAFqGAAgAANAyBEAAAICWIQACAAC0DAEQAACgZQiAAAAALUMABAAAaBkCIAAAQMsQAAEAAFqGAAgAANAyBEAAAICWIQACAAC0zKO6b2DdzKwjaeju/brvBQAAbDYzO5I0cffLBfffk7QvaSypJ2mcPbasfWZpXQCUNJTUrfsmAADAZjOzA0lfSDpecP+ekiLUYbTtzMzG7j4uc595WtUEHF4wwh8AAFiamfXMbKSk8nZX4NC+pFFm20hJcarsfWZqVQCUdCDpou6bAAAAm8vdx+7ed/fTgoceSbrJbLsK28veZ6bWBMBQpv2q7vsAAADtE8YgPKgYuvskPN4ra59F7qdNfQA77j4xs4V2NrMTSSfhx799/N57/2tld4YqPZX0qu6bwNJ4/zYX791m++N1Xuzf+3f/8vPvxk8rOPXvmdlV9PPpElW7snSl+6CW421wK2Gfuf0AWxEAzezI3c+LHBN+QU7D8Vfuvl/JzaFSvHebjfdvc/HebbZMaKqcu//9dV6vJp017jPX1jcBh1LptJQMAADQOhtTAVy0TTu4i0qjH9dY7gUAAA21QrZY5Zqdeecpa59ZNiIApvPdFDjkpaQXYZLEMsrYBMjNxXu32Xj/Nhfv3Wbb+vdv2WyxwiXTfnldRS2ToaUyffyupH3mMncvcO+bJQzk2M1s3lPSQfJc0suifQMBAABSZnYrqb/IKhxh32N3v4m29SRdu/uTMveZZyMqgMvKa/o1s+eSPnT3QQ23BAAA2utSyfJt8Rx+e2F72fvMtPWDQHLs1H0DAABga3SVMzLXzDpmdhtaI1MDPVw2rh+2l73PTFvdBBwLpdGBpI+VvFGnkkZx+RRA/VZd4Bz1MrMjJe/bbvg+oqvNZgp9yobu3q/7XpomvDafKfkdP1LyeXUp6SL9fQ/7fCNpELdIhs+4A91/xt1kP+PK2mfmc2hLAATQfOEPtVF2gXMlH6ALdWxGfUL4G6d/WIf/AV4rCRFbP6hg24S1brvunq00YQu0sQm4NKG8m12MGQ1mZkdm9tzMRmZ2Ef6HheZYeYFz1KoXt6qEKSqGevieouHCH2Pduu8D1dnqQSBrMBT/gWyMqDoRl+evzaxLdaIxjvQwLFxJuqjhXlBA+O/pEzM7zcxNdhke71HF3SgHSv67O5y3IzYTFcAl8dfRRqI60WBlLXCOeoT3qadorVJsJjM7kPRV3feBahEAl5f+dYQNEFUnsiO13lYn1n9XyFh4oXQ0k7s/yRlYtydpQvVvo6y0wgQ2AwFwCfx1tHmoTmyEUhY4R+N8Junzum8CizGzI0ZttwN9AJfTcfeJmdV9HyhgyuzoVCeAioT5z+7cfZXls7AmoYWEyl9LUAEsiL+Otg7ViYbJaabHBgrdKvrxlD5ovI+Zc7M9CIAF8NfRdqE60TjxQulvFV3gHI0xlPRR3TeBxYRJha/qvg+sTyubgAt2+L+LOsN+zHQh9Vvh/cueo+/uz8q7M6widKsY62FfwK5opt8oYX7UTxlIsFH2Je2a2SfRtj1JPTMbSnpJ69d2aV0ADP/jLzKp7EtJL/jrqBmWff9ytlOdaKaVFzhHvUJlfRiHvzBwbkyIb6684oaZPZf0obsvvL4sNgdLwS0ofKjtZjbvKRlVei7+OtoYoToxoDrRPKG59yyzFNyFkmot4aHhwmTrXd0H9k74+Zj1ZDdPqPz1WApuOxEAVxD9dcR/HBsiBPnLOExQnWiWVRc4Rz1CeP92ysNjd8/+AY2GCi0tA0kfKwnxp0rW6M7O8YgNRgBcAX8dbRaqEwAAJAiAS+Cvo81DdQIAgHsEQAAAgJZhHkAAAICWIQACAAC0DAEQAACgZQiAAAAALUMABAAAaBkCIICNUHAN6MacGwCaiAAIoPHCai0HFV7iLiwRCACtQAAE0GhhabjjvMXqyxLWhR6GdYcBYOsxETSAt8JyeUMla/CmxpIm0c934fuNpM9DeKrqfjqSriU9q/I60fWeS9px90HV1wKAOhEAATwQ+sTdSpq4+5OcxzuSTiR9JumrqtZSDs2y11VW/3KueSvp0HZTo1oAAARrSURBVN3H67omAKwbARDAA9HayTPXSY6C4qW7H5Z8Dz1JF+tepzlUQftlPx8AaBL6AAJ4YNHm1lAlO5V0EJpPyzRQ0hy9Vu5+LmmfkcEAthkBEMCqrsP3spuBTyR9VfI5F3Wq8p8PADQGARBA44Rm2Jt1DPyY4kJJAAWArUQABLCqZ+H7eYnnPJR0WeL5CnH3S0kdmoEBbKtHdd8AgM0VAtKJksEiM6dOMbO0P99rSTuSOpIGU6p8B1qi/5+ZnUg6VjJ1jSR1lUxVc1P0XOEcB0qagwFgqxAAARQWRgl/rCSknUv6dMa+PSVNqv1QWUu3H0n6xsye5Uy50pN0VeB+9iSdKTMaOR2lbGb97FQyZnYQ30+OsaS1jkAGgHUhAAKYpZsZ3bujpCq2J+mFpI8WqK5dSBplw5a7n5tZX0lwS5uR03ApvTv59FRhmbgLSS+yVUh3H5vZqaSRmX2VVhtD+JxnrHcnxAaArUEfQACz3Ln7i+hr4O7PlAS2PUn7sw4O4bGn6c2oI0l7oYKX6qbXnndzUXXxZkYTdLq822fRtk/CdC+zTJQ0UwPA1iEAAigsVP2OlayfO6uvXl/JaiLTqnlp028cJDvhGotUAEeZ73nSCuWe9DY0zg2XSvoqdufuBQAbiCZgAEtx94mZfSXpuZl9OaUpuCdpHAZn5OkoGe0bB7KFQleoGh6Ee5k1UCM9d9qcO9SMPos59wcAW4cACGAVt+H7J7qvtEl6W2mTkgrgrID2IvPzItW59JpSgelnQt+/8YLVxR3dVygBYKsQAAGsIg1SezmPLRrkcs9pZp05QS295ssFz9tV0vfveMH9O1pwIAoAbBr6AAJYRbZ59a0Q3gqPpI2mhFm0/92iVbqOkvWFF9XV8iEWABqNAAhgFWmFbFrIGypZUSOvQigpaSqeMi3L1GOCceb7POOc+QZn6em+iRsAtgoBEMAD0Vx887wNVPGyaSHUHYS+fzeavapHP2dKlkvNrxymI3+nTkUT7umL8GM32r7I8+sp068RALYFARBAnm7me65QUUsHeMRVvKNo4uePlEwo/WCqljBP4Jc5p76Q9OGca98oGUAyyAY6M+uE6WkGoc/fqd4d0fuFZgjBsTNnpRAA2Fjm7nXfA4CGCE2xnympfsUrcowlHU9rQg3TvPSVVO5eK5mY+TJnn0Ml/erSpuNR3jlDALt29ycL3vMn4bxpYB1nz21mZ7of2DGY1RycrikcLysHANuEAAigkczsWtKnCyw1V8W10+XrFp5iBgA2CQEQQCOlFcMC07aUdd2OpG8WqT4CwKYiAAJoLDO7lfRswYmby7rmUNLtnMmrAWCjMQgEQJMNNGfARplC38MDwh+AbUcABNBYoQ/enZkdrOmSI0lrbXIGgDrQBAyg8cII3k+rbAoOU9KMGfgBoA2oAAJovDAQ5KSq84eVSm4IfwDaggogAABAy1ABBAAAaBkCIAAAQMsQAAEAAFqGAAgAANAyBEAAAICWIQACAAC0zP8PEf98xxI++3EAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "W_ss=wigner(rho_ss, xvec, xvec, g=2)\n", "W_ss=np.around(W_ss, decimals=2)\n", "plt.figure(figsize=(10, 8))\n", "\n", "plt.contourf(xvec,xvec, W_ss, cmap='RdBu', levels=np.linspace(-1, 1, 20))\n", "plt.colorbar()\n", "plt.xlabel(r'Re$(\\alpha)$', fontsize=label_size)\n", "plt.ylabel(r'Im$(\\alpha)$', fontsize=label_size)\n", "plt.title(\"Steady state\", fontsize=title_font)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "W_even=np.around(W_even, decimals=2)\n", "plt.figure(figsize=(10, 8))\n", "plt.contourf(xvec,xvec, W_even, cmap='RdBu', levels=np.linspace(-1, 1, 20))\n", "plt.colorbar()\n", "plt.xlabel(r'Re$(\\alpha)$', fontsize=label_size)\n", "plt.ylabel(r'Im$(\\alpha)$', fontsize=label_size)\n", "plt.title(\"First state: even cat-like\", fontsize=title_font)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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Hf09vvfOf1X7ev5Hum9mzaNNxFNJWqsK5+wMzO1XSz+9C0vvRY1dmdqZklHAcIqfR55mSiuBGPHo4DEJR0yGQJmAAADBUL9x9O/o4XnxIOWa2p2RAx0Mlge4802y8r2jAR6bZ91J63fcve09lBqGsjAAIAABGa5n+eGZ2JOnM3dM5A99VUtE7TfcJgzoehelhdnU916BU0LQcPTZtup8gARAAAIxR3E/vtSh45Ya09PF41G6o5D2UdBX6BsbbT8LHmUKzczTQ5NaIYF0PHJk3CGVlBEAAADA6IYTNdLsv4IakedOybEs6L3jsKOd82WNPpOtJqHNGG6eBtNFpYQiAAABgrM6UhLLYVtheZCbpQcFjE4V5Bc3sNPQTjB2Ej7SCuJ8TNHeULAVXNDq5FgRAAAAwVgeSHmW27YftkpImXzN7noa5NLDFTb3h66mke1Ggu1IUJENz71Em8F3GFcDQvLwv6aNVn9giTAMDAABGKUzXchDC2UxJv7vDnKrcRua4fTPbM7NDSS/D5it3P4h2O5C0a2b3wtfPsyN+3f0kGiRyT0kF8dGc5ufaEAABAMBoufuFbi8HFz9+pWSt3uz2uVPKhBD3pMT117L2bxZNwAAAACNDAAQAABgZAiAAAMDIEAABAABGhgAIAAAwMgRAAACAkSEAAgAAjAwBEAAAYGQIgAAAACNDAAQAABgZAiAAAMDIEAABAABGhgAIAAAwMgRAAACAkbnT9g0AAIBx+/7v/I4mP/yPaj/vv6v9jMNBBRAAAGBkRlUBNLMdSQ8lvZS0Kenc3Y/bvSsAAID1Gk0ADOFP7n4QbTs3s4m7P2nvzgAAANZrTE3A+znbzgq2AwAADNaYAqCUNP9mXa39LgAAAFo0miZgd3+Us3lX0tG67wUAAKBNY6sAvmZme5Iu6P8HAADGZjQVwJSZ7So0BRdUBdP99iTtSdI777yznpsDAABYg9FVAN39xN33JR2EUcBbBfsdu/u2u2/ff/vtNd8lAABAc0YXAFPufqWk/98Xbd8LAADAOo02AAZnkibpHIEAAABjMIoAaGZTM/vazKYFu0zWekMAAAAtGkUADJ5JusxsSwPhxZrvBQAAoDWjCIDuPpN0mvPQgaQn4XEAAIBRGM00MO7+xMz2zGxT0ktJm5Keuvtxy7cGAACwVqMJgFIytUvb9wAAALojTAe3LWmmpGvYzN3PKhybDiS9J+koblUMg0y3osefz8siZjaRdBimq2vUqAIgAABAKgwOPXT3h9G2p2Y2W9Q9LF1YIg5rZnaopHtZGg4VrzhmZrtmtjcnBB5K2lj6CVUwij6AAAAAOfaVzAkcO1ISxArlVepCINyNz52tJLr7icJqZDnnnGpN4U8iAAIAgPHa1e2ZQJ7pZpDL87Gkk3hDTrjbLph+rmjquR3lD1htBAEQAACMTqjiTZWZIi6sFKY5cwdL0p6kL7MbM83GZ5JO4yVnQ5Xwac697Ej6vMr9r4o+gAAAYIw2pOvAl2OqZGBInomkmZntKQqQoQqY/vsgBLtzMztIz1XQ/2/i7ldmVv1ZLIkACOCGl9++quU8997k7QVApy21ClhUGZzGYc7MDs1sI97m7g/M7FRJn8ILSe/nnG83Do7rwjs0MHJ1Bb5F5yUQAihy53e+p3s//A+bOPV9M3sWfX1cw5RwRcHxM0lfSIpD4Z6SgSZTJU2/52b2MG0qDs3QRRXIRvGODIxEU0FvlesTCgE07IW7b8/bwcwmc5qB88wynyVJ7n5hZhMzm7r7zMyOlIwUnilpLn5XSQg8VbIYhSR90NYcxbz7AgPXdvCbJ743wiCANUsD3IaiKlyoysWP3xD11SvsO2hml2HfWXycpIdmdh76Bl4qGXHcCt5xgYHqcvDLk94vQRDAOoQgN9PtJt0NSVcLJoJ+vWpIwWPbks4Ljj0K15xK2jSzD6PHtpQEyENJXzbZN5B3WmBg+hb8sgiCANboTElYi+cC3Arb5znK7heme5mF5l9JelRw7ETSWV7ANLPHkt5z94PSz2BJzAMIDMTLb1/1PvzFhvRcAHTWgW4Htf2wXVLSJGxmz8OAjtRx2C92mG6LBnnsxDuEEcT35lQX71V+BkviT2yg54YclF5++4pKIIDGhGbgg1B5S5t1D3MC2kbOcQ9DU+1LJYM6DuOl39x938z2on2kpGn5VnUvBMMDSR9ImoQBJEfunl2lpDa8swI9NuTwl6JJGECTQsgqDFph8MbdnO0zRZXCgmNLjfAN59rX7apiY2gCBnpqDOEvNrbnCwBNIgACPTTWMDS0fo4A0BYCINAjBKAE3wMAWA0BEOgJQs9NfD8AYHkEQKAHCDv5+L4AwHIIgECH0eS7GN8fAKiOAAh0FMGmPL5XAFANARDoIAJNdVRLAaA8AiDQMYSY1fD9A4DFCIAABocQCADzsbYS0CFtB5cX39V3/ftv8PYCAF3FOzTQEW2FvzpDX9F52wiDL799xfrBAFCAJmCgA9oIfy++e9VY+GvzWrG2K6oA0FX8eQyMTBtBLHttmocBoF1UAIGWratK1VYVLs8674MqIADcxp/hQIvWGf66hmoggNTv/s739e4Pf1D7ef/X2s84HFQAgYHrYviLreP+qAICwE0EQGCgutTku0hf7hMAhoIACLSkyapUHwNV0/dMFRAArhEAgYHpY/hL9alqCQB9RgAEWtBUNWoo4amp50EVEAASBEBgzQh/5RACAaA5BEBgAIYW/gAAzSIAAmtE9akagi0ANIMACPTc0ENSE8+PIA5g7EY1Bb+Z7UqaStoMn4/c/aTduwKWN/TwBwBoxmgCYAh/szTwmdlE0rmZbbj7cbt3hzHoY9Xp+eW3pffd3Hizsft48d0rlowDgBqN6R11Glf73P3KzA4lHUkiAKJ3mqj+VQl8845tMgzW5eW3r3TvzTG9BQLAtVH0AQzVvg/D59hZeHy6/rsCumWV8NfkuVI0dwNAfUYRAN39SkmfP4IeWlF382/dYaiJwPb88ttGzgsAWN0oAqAkuftdd7/IbN6SdOXuszbuCeiCpkNaneenCggA9RhNACzwsaRP2r4JoC3rqtB1tRLYx4E5AOplZltmtmdmO+nnJc4xMbOjzLbDcO5s97NK52nKaHtAm9mepEt3fzLn8T1Jeuedd9Z5axiYrjb/djWUAcC6hDEAh+7+MNr21MxmFVsHDyVtZLZtSXoczpndf+bumyXP04hRVgDDD3w//oFnufuxu2+7+/b9t99e490BzWsj/BE4AXTQvpLZQGJHSoJYKSFT5IW2maSHkh4omX84/diX9KjCeRoxygCo5Af7fts3AYwNIRBAx+xKyo4PeBa2l7Uj6TRn+7m7n7n7hbvP0g9JyhmTMO88jRhdAAxt6x+FkcHA6BDCAOD1FHFTSZfx9jQflJkiLvQX/DzvsbxFJsxsr2B74XmaMqoAGPr1HcbhL3T6ZHoYoCcYCQygJhvSdeDLUSYbTMoWlMxsS0l1caXz1GU0ATAsBZf+expG5uxIesQ0MOiLVcNPF6p/XbgHAJBUenRuHjPbjVcYK2Enr+l3ifPUYhSjgEOZ92nBw4Q/YMRYEg5o39/7ne/rP/+Pf9DEqe+bWVx1O85rgq0q5IrSFbtQhLqVN6qep06jeNcLZdVbY7CBpjHPXL7nl9/2Yr1gAL33wt235+1gZss0v35QMUh+rPzBp1XPU5vRNAEDY0fTKwDckFbkbky9Ek3cnNtCuKAvX97+E0lb2ZBZ9Tx1G0UFEAAAIObuV2Y20+2+gBuav0zstqRNM/sw2rYlaWpmh5K+zPTp21F+M2/V89SKAAhg1Oj/B4zamZIgFg/O2ArbcxVM4/JY0nvufpBzyHvKqSYucZ5a0QQMAADG6kC3V+XYD9slvV6f93mYSq7IvTmP3ZprcMnz1Io/fQEAwCiFZuCDUHmbKQlrhznNv7lLtIV5hA8kfSBpEhabOMpM95LXzLzMeWpFAAQAAKMVQlZh0AqDN+4WPDZTUjHcn3P8wubcMuepG03AQIO61L+sS9OudOleAGCMCIAAAAAjQwAEsFZU/wCgfQRAoEfuv7Fak/IQwteq34NYl5roAWCdCIAAAAAjQwAERqbNKuAQKpAAMAQEQABrQfgDgO4gAAIjtO4w1sXwR/8/AGNGAAQa1tWgsa5Q1sXwBwBjRwAEeqbOUbBNI/wBQDcRAIER29x4s7GQ1sR56wq/Xa3KAsC6EACBNag7cNRdBawzrDUZKgEA9eDPYACSbobA55ffLnVcH1D9AwACINBb99+4oxffvWrk3F0MdX3q+wgAXUcTMLAmVJ7ax88AABK8GwI91mQVsEuo/gHD9rt3vqdpB1sehowKINBzQw9HQ39+ANAGAiCwRk01QRKSFqP5FwCuEQCBNSOIlEewBYBmEACBgSAsFSN0A8BNBECgBTQFLzak5wIAXUMABAZmCMFpCM8BALqMAAi0pMlmyT4GqPtv3Hn9AQBoFu+0wED1YY5Awh4AtIN3X2DAuhQCCXsA0B28IwMtuvfmHb38ttmA1kYI7FLYYwQwANxGH0CgZesIKOsKZPThA4B+4J0aGImmKoEEPgDoHyqAQAesq5myzrBGtQ8A+ot3b6Aj1tEfULoZAqtUBAl7ADAcvKMDHbKuEJhKQ11RECT0AcAw8e4OdMy6Q6BE0AMwXma2JWlb0kzSVNLM3c9KHLcb9t8Mn4/c/aTg/Dvhy3thv1n0+I6kh5JehnOdu/vxSk+qBN71gQ5K+wSuOwgCwJiY2VTSobs/jLY9NbNZHNJyjttVEhRPwtcTSedmthGHt7DfQ3ffj7YdSjoI/96RJHc/iB4/N7OJuz+p7YnmYBAI0GHMYbc6QjSAOfYlHWW2HUk6XHDc1N0v0i/c/Soc8/pcIRQeZsLfrqTdzPWzzgq212p0AdDMdtPEDfQBIRAAGrMr6SKz7ZluhrQbQrD7MHyOnYXHp+HrjyXdaBIOFcOHmeOyX0vS1fzbXt2oAmAIfp+2fR9AVYRAAKhXCHBTSZfx9lDNi4Occh6fho959iR9mXP8LPr3o7j5N9iV9Nmi+1/VKH6rhB/igaRzZX7QQF+0MThkVUXBtW/PA8AgbUjXgS/HVMnAkFvc/W7O5i1JV1HAm0iamdmeouyRN1AkFfa9aLr/nzSSABh+GPuSZGbZpA30Rh8Gh5SpVvbheQAYhPtm9iz6+jgapJFtwl3Vx5I+kW5UD6eZQSGH2YEiYfuuQlOwuz+q+b5yjSIAAkPT1Wpg1aZqgiAASfrdO9/T5sabTZz6hbtvN3HiWFrliyp3ReHyM0lfSLoRAENV8MTMJmZ2LumjeJBJE0bVBxAYkq71C1zlfrr2XACMR85gjqrHTyXtx1PJ6Lrp+EYTcgh1kwX9C4+UhMRGEQALmNmemT0zs2cvfvnLtm8HyHXvzTudCE913EOTz4MKI4AcaTjbiDdGgbBwHsCMQ0nvxxuifoXz+hcWOVMSEhudsYQAWMDdj919292377/9dtu3A8zVZgjsQgAFgKpCSJvpdnPthm4O5ihkZkdKmmvzgl66skiemZlNzezrompgzn3VigAIDMQQghhVQABrdqZkGbjYVtg+V+j3dxiHPzPbiQLdUThXfMyWkhVE0nD5TLdnJ0mPpw8ggHLWHQKbuN4QgiyA3jiQlB11ux+2S0qahM3seQh86bbd6N9TM9sKTbaPonB3rNsrehym28J+pwX39KRMBXIVvNMCAIBRcvcrMzsws8e6brI9zAlfr/sJhj6CTwtOGU/yfGVmD8Pavy8lbYZzn0X7PAljDjajfZ5mp4lpAgEQGJiuThFTRVPP4eW3rypVGO988+8lSa/e+mHt9wKgG8LI3MLm1tDEezfztZU890xRNbFgn8bDXp4xBsANNdyxEmhbl0JgGqKy6ghVL767+Rzvv1HfW1p83wRBAEMzij6Aof3+0MyeKgl/h2Z2FLfhA0PThb50ReFv0WPLevHdq1uhsE5N3DMAtKH93xBrEMq1LAEHrFGZsDSvsraoijkv6L347lVhNbBMM/Ci4EolEEDfjaICCIxVF6qAZfStsta3+wWALAIggNp1ISA12RQMAH1HAAQGrs9VwKJ7LxvuivarY4BMF0IuACyLAAigM5oaGNIgniB/AAAgAElEQVQUQiCAviIAAqjV2ELR2J4vgGEgAAIj0JVm4O9/85c3PvJkA1Ud955XBezKPIkA0AYCIIClVQlReYGvKAT2DVVAAH1DAATQuHlBL++xdfUFpAoIYKwIgABaN5RKIAD0BQEQGImu9AMskg2BcRWwrntnRDAAJLr9GwFAK/KCUtHSaotUqe59/5u/1G/f+v2lrgMAKI8ACOCGoipZ0fq6ZdbWXZfnl9/e2ra58eaNr7PPo877Z51gAH3RjXdtAGtx7807nRj48Jt/+/PX//6d/+SPbjwWVwHjQLXo3vPCX7o9GwIBdMsds6VbGbCclb/bZvYjSTuSNiVNJU0kbYTPM0lXki4lPZd04e7/etVrAmhHURUw9uqtH87tDxeHv/TrbAhc5P4bd1bqz7foeSx6DvNQBQTQB0sNAjGzH5nZn5hZGux+KumBpK8l/UzS55KOw7+/lnRP0n8p6cTMfmtmf25m/6SOJwCgPmVCVRMDKbKhsO5RwUXVwVQXqqIAsE6VKoCh2nesJOx9KumRu39R8RxTSe9L+omZfSrpsbv/T1XOAaBdy/ajywa97GN5lcAyFbVFAS/dJ24KLlPNXBZVQABdV7oCaGZ/IulU0pG733P3n1YNf5Lk7jN3/9Tdf6yk2fgPzexLM/tPq54LwLDEATGvCtiVwSYA0HelAqCZ/StJL9z9D939z+q6uLtfuftPJX0o6VOahYHm9WFOvaZkK4Xxc6AZGMCYLAyAZvY/Stp393/e1E2EquCPJW2a2R83dR0AzakrQOVVAeucZLlMc7GklZtwmRgaQJfNDYBm9q6kA3f/ah034+5/qmTQCIAeKKoC5oWnvP5/v/rFV68/Fu0LAKjP3ADo7l+5+zfruplwzZ+t83oAEutu0s2GvuzXi6wygCOuAtIMDGCMalsL2Mzepw8f0J473/z71x+L1DmYos4AFYfAtAqYbQYue++zy281K9nc2xSagQF0VW0BMIwINjP73Mz+hZn9ILuPmb0VHv9RXdcFcDtodDF4VJ3suS6rhECmcgEwVLUFQEly9z9z9w8k/amkf2lmn2Qe/yY8fljndYExKwp7dQ+ciD+yqjYfz2vunVcFLJJd6i0b+vJCIM3AAMas1gCYCqN6P5D0zMw+y5njb9LEdQEsr6hPXV7gKzOSNq2epev6VlEUEFcJtW01B3exGgsAtQZAM/uBmX0Slnr7N5L+RMk6wTMz+zdm9tLMfqtkfWAADWsyfBSFwHVU0NJ+gFUHgmRDYNkpYQBgaOocBPJPlUzhciDpoZJVPjYl3ZVk0b8/dfcP67ouMGZlAl7RPmUGUywKSEXNqFVd/fwXuvr5L25sS6uAZZuByyqqBC5z/3WvWQwA61JLADSzf6RkjeBPJT3SddiLPzYknbj7T+q4JoBhiINfNgTmWUeTalzFrGMgCM3AALqmrgrgTyVtuvtPwkCQr8KAj/jjStKBmf2Lmq4JoKR1NQWnVbQ0QC0TnuIQmK0CxlaZyiauAq7aDEwVEOg3M9sysz0z20k/13GcmU3M7LGZTcPX0/B1dr8dMzsMjx2Z2V59z65YXZOBfV1mtRB3/8rMvjGzH7n7/1PTtQF03G/f+v1KQenq57/Q5I/eubX9+9/85a1BJfffuFPbJNYvvnu11ATTefcFoPtCODt094fRtqdmNnP32YrHbSiZ9eTQzKRk/MNH7n4WHbMjSe5+EG07N7OJuz+p51nmq6sC6BX2/UTSfk3XBVBSXhWwrgmhmxxMkTciOO+5ZKeCqSLv/pkOBhiFfUlHmW1HWjxdXdnjHirpBrfp7nfd/STnPFlnBdtrVVcA3Cy7Y1hablrTdQF0TLYZOFZlMuhsf8C61weuMi0ME0IDg7Ur6SKz7VnYXstx7n41r5qoJCRmNT5bSl0B8GnFvn1W03UBVNDGtDB54el333l36evETcl1LmmXWrY5eVETNwNBgG4xs4mSgtRlvD2MWUibeWs7Lo+7P4qbf4NdSZ+VPceyagmA7v6ppIdm9t+XPORlHdcFUK9l+r81Ka0Czls5JM90hebgKuj3B/TahnQd3HIUBbkqx03MbDd87JnZ3MpiGABy0XT/P6neiaA/kPRTM/vfzey/LtoprBF8r8brAlij2eW3rz+K5FXR6ghLcTNwXFFbNrguGg1c93QwANbuvpk9iz7iEbbLrkpW9rhLSRvufhI+jiV9mBcCQ0A8kvTA3R8teV+V1PbnvrtfmNmPJf0rSQ/M7FjSiaQvJc3Cx7aSiaKz5U4Aa3Lnm39/I8zce/NO6QEPeWvsxtW255ff3hiM8fLbV5Waab9+/leSpLubf3/ufkWjbjc33mR1D6CH7nzfGunSIemFu283ceJFQoXwOLP5KHycZPY9kXQSpo45VzJaONvHsFa1LgUXhjb/gaR/raSf3yMlI2KeSjpX8qT/zN3/lzqvC6A9ZQZTxIGzzECQNAhKi5uB2+4HGAdR+gEC/RP69K3ruJmkadGxITQeSfpimXuqotYAKEnuPgvz4jyQ9ETJk/hCySoh2+7+07qvCaA70gpcXXPzZa27GRjAYMXz9b0WhbOikbuljjOzxznHpgNH5g0UOVPSd7DUhNTLqj0Aptz9Z+7+U3f/cfj4ibv/rKnrASiv7krUvCpg3LwcV8sWjQTOqwJWUddAkDL9ABkMAvRPqLbNdLtP34akwqlbyhyXThSdMyI4DY2zsDLI13NGDS/bR7GUxgJgFy273AswdHEzah2VtCryVvwoEjcDF00Hs8qE0ABG50zJ+ITYVti+9HEhPO7nhMgdJaN80xHEz5SZTkbX1cH+9AHssmjZlmN3PwujcfarzNcDoJy8ZuCq/QClm1XA2Domha7ahF22Ckg/QKBTDpSMV4jtKxqsGgZmPM+MIF54nKTLOGOEJuJ9SR9Jr0PiacE9PVkwefTK5v6pb2bvSnrf3f9lkzcRXe8Hkvbc/Z83cPp5y7asZcg1ULdXb/1w6UCRHQ2cp0ujaovWB46fRx3rAmdHMks3RzOv8j0H0C3ufmVmB6G/3kxJ9e0wJ3xtVD3O3U/SOQCVTH83kfQos8+T0CK5qWSO5E1JT0ORqlFzA6C7f2VmX4VVPh67+183dSNm9r6S8PdhQ5fY1e0A+Ez56RvAErLTwqTiAPXbt36/cLTs3c2/f6vq9/Xzv7oxLcyvfvHV6/6Di6aDmW68uXTT9DLoCwj0T5hupbC5NTTX3q16XNgnu/Zv3j6Nh708C5uA3T0dwfuzeRM8L8vMfmBmn0vabSr81blsCzBUdU+nUmY08CpLwmW1PR0MAPRJqT6AIeVuS3rPzP6Nmf3T0Fy7NDP7hyH4nUv6n939v1nlfAssu9wLMGhFTZmrLAk3r+JW1ORcdiBIPBq4aDqYPujb/QIYntKDQNz9yt1/Ium/UBIGr8zsSzP7JATCf2hmP8oGw1Dh+5GZ/RMz+2dm9pmZvVRSVTx19z9cw8TQjQ6lBrBYdrWRsgNBpOLBIHmy4bXsdDCLmopZFg7AkFQeBRwmev6Ju39P0p8oaRf/qZJ28Jmkr83st+mHpK/D9hNJP1bS727b3d9z90/reiJ1C50yn5nZsxe//GXbtwO0ZpVpVYoGkMzrK7doGTipeDqYWBP3DQBDsdI0MO7+ZyEM/kEIhHeVLAW3rSTsbUv6A3f/Xvj4sbv/qbvnr+nUsCrLtoTpYrbdffv+2283eVvASlatRsXNkYv60S1bTSuaDka67gdYZT7AIg2tJQoAg1P3WsDfuPtXYRWQL8LnVsJexrLLvQBoUJVm4FSZfoDLNgPnKRoIQjMwgD4bxUTQyy73AgxJUVNpkVUGghTJ9gMsUqYZuIy6VwUpe/8A0HWtBEAz+1ELl112uRdgVJqaDiaryrrAecosCxera23gujASGECb2qoAPm3hmmWWbQEGragKuCiMxJW0JvoBpub1A6wyEnhdaAYG0Fe1t/GUqO6lkzKvVYXlXgA0KF4VREr6Aeat7Zu3Kkie3/zbn7/uS5i3LFyXlrMDgK6oLQCa2SeSHtd1viaUWbYFGLqi5dPy1LG27jzxsnC/+867N5p1m1Blabh4TeAX371qpE8kALSllnc0M/tvlTSn/qmk5wt2vyvpkzquCyDx6q0frtynLK6e3XvzTi0DHtK1geMwtcjkj955PdI3rgLGA0Oufv4LTf7oncJ1gefd/6rrA2crmHV87wFg3er6k/ahpHfd/ZsyO5vZXk3XBbAmcVPqsiEqrqTFwamoGVgq3xScp0ozcNcGiQBAk+oaBHJRNvwF+zVdF0BJcbNvlSlh1jkdTNGk0FWmhSlTjSPsARi7ut7ZX1TZ2d2/qOm6AGoUNwOvS9wPcFnxQJBUthk4WwVcJQTSDAzUy179mv9Da1ZXBfAbM/tB2Z3N7I9rui6AoGpwWxS68ubTW2Y6mFReE2x8z9kAt8zScHnPicEbAHBbLQHQ3T+V9N9VmOD5sI7rAqim7OjfrDpD1KJRxctMCl1W3SuDAEBf1fau7u4/NbN/YWYbSubZKxoNPFGyAgeAEUhHAmfFzahFzcDxiOAqmmjKXjQVDM3AAPqkrmlg3lKypNqDkod4HdcFcFPd08HkqWM0cJF0NHBdcwKm/QDj+QyZGBoA6usDeCjpayVLrT2QtDnnI7seL4A1qtIMXPe6wHkWVerK9gUsmkamKXkjmVkaDkBf1BUAp+7+Y3f/M3f/mbt/NefjQtLParougDUpav6sMhgkrbzl9QPMBtO4L2A2BMZfZyuFRYNb4vunLyCAsasrAJ5W3P9RTdcFsIRlB4Ok6gpQeVW07GjgVNVRwWlT+DqqmDGqgAD6oK4AWKlPn7s3u+AnMGJ1BJC4H2GZALXqxMpl73nyR+8sNT1MnkUhdpWQW+b5EBQBtKmuAPiVmf3Dsjub2T+r6boAlrRMFbDpZtT0ntIqYJkpYapMG5Ntxl71OcxbL5mAB6DL6poH8M8kPTSzf1LyEJaCAwamqeXV6pgXsGozMH0EAQxdXdPAfBL+uWNmn0p6pmQuwDwbkqZ1XBdAvrrnpMsuq1Ykb1qYomCYzquXzgeYved0SphVlJkPsMmwV/RzoDoIoG119Y7el/SWJAtfP1ywP/MAAj21aE69OAQuUxXMmxS66ryA3//mLwubuOP7X4dsCCT8AeiCuvoAziT9xN2/V+ZD0lVN1wVQYNWgsUoFcbrxZi1NwvGI4CaXiGvaq7d++PoDALqgrgB4KemzCvszChjomaJ+dHU2oaYBqah6lw2BVUJhfP91rm1cpmkcALqmlndBd/9xxf1ZDQTosbqbUeN1gbOyfQH7XAkEgK6oqwIIoIPW1eS4bBVwnX3xsuqsAgJA35QOgGb2x3VdtM5zAWjOvH6ATQWovGbgotVByqg6qTUAjEGVCuBhjdet81wA1mRegGp67rxVQmARqoAAlmVmW2a2Z2Y76eeKx+/mHWNmEzN7bGbT8PU0fL2T2W8nbH9sZodmtlfl+lUCYJ1z9zEPILAm6xx5ukoIzBtMkR0MMi8ENhEQy2IgCDAuIZwduvuxu5+5+7Gk/TS0lTh+R9KnBQ9vKCmUPTczl3QuaebuZ9HxW5Lk7k/Cx4GkyyohsMqfv3fN7LdKpnC5rHBcbEPSZMljAXRMU3PqzZvIuo4JomNlnwPVQgCRfUlHmW1HSoLbo6KDQkA8UBLq5mWph0oW1dhw97yFNfbd/caqau5+YmZPJR0vvv3qo4BN0t3wsQomggZ6atGqIHmTQ68ib2LobAisUv3Lu/91Tw4NoPd2dTsAPpN0Ou+gEOb2JcnMDhbse6XieZO3zWyaEw5LF9mqBsAtrT6H36akL1c8B4AK6l4aLpYXnopC4KIm4qLpYIpCIACsm5lNlHRlu1HBc/crM1NBMKvbmaRTM3vk7hfhvnYlPS17gioBcObu/0fFG8xzYWZMBA30RJn1dPOsOiikztBa5jnMqwKWaf6dN5chgPnst7+59UdeTe6b2bPo6+PQX28VG9LrCl2eqZIV0lYxCYEuvd6lu5+kD7r7QehHeB4qibOwvfRzq/JulS11rqLOcwEooc5AlW1GXUcTal4VcN6+y0iDXvpc6PcH9N6LBhafaHosw6WSvn+vw5yZPTUzZULgAzM7VdLv8ELS+1UuUnoUsLv/aZUTr+tcAPptXnDMVu2WDXZZiyp199+4Q/gD0Ap3v8qp5KUDTF4LI373lQwYmSqpBpaeZYV3OGBE1t0XcBmLmlKrVAJT65wKB0B/VAlMSpphXzf7mtlkTjNw3WaSpuk1zexIyTQ0M0kzM3tXSf+/UyVjLRYiAAJYyqLRwHXJC63zQmBdVUIAw5bO5VfhkC8lPdF1/74NRaN0w+AQacX+f2b22N2fZDanA06mZpb293t9nRBEH5rZuZntxHMGFiEAAiPThypgGXkhsO3wx0AQoD9CgCqcs2/OcVchhGX7Am5IulplBHAaSs3sJHOejfB5JmlbyTyCeY5y7itXlZVAAGChJvrOFTXh/vat37/xUQVBDcAKzpQEsdhW2L60dJ7AnBC5I+kiVPpmkh4UnGKiZEDIQgRAYITq6hPXVIhiaTUAHXeg29XD/bBd0us1fZ/PWZ6taHW0y7hvYmha3pf0kXTd9JuzNvBU0r2yFUj+BAZQuyaagptsuq4TzcDA8IVm4AMze6wwQEPXgzJiG/EXIcx9HPafKGnufSjpNJ3iJSzpthvmAbwX9nuU6fO3b2Z7ZnYo6WXYfBXWBC6FdylgpJoOVGNeY5cQCAxfWIGjsLk1NNfezdm2MKTF8/3N2WelCa1pAgZGrI6m4HU2Ay9zv0wBAwC3EQABNGadA0K6hn6MALqMAAiM3KJAtWrgmhcCFwXEohBV9p76EhYBYN0IgAD06q0frhSW2lhabdE9dyH8UQUE0FX0UgbwWnZgSN0haoxNwgwIAdBFo3pXCkOqr8oskQKMVdcCVVMBap3VOUIggK4ZTRNwmDDx07bvAwAAoG2DD4BmNjWzIyWTLl4u2h/AcpqscA2hL90QngOA4Rh8AHT3mbvvrzphIoDhaCuMEQIBdMXgAyCAYRhKeBrK8wDQbwTAAmGNvWdm9uzFL3/Z9u0AvdD0QIc6wlMXAtjLb1914j4AjBcBsIC7H7v7trtv33/77bZvB0CwSnDqWujq2v0AGA8CIIBarWO6k2UqaF0NW129LwDD1puJqcxsWmH3S3e/auxmAHRCGp6KQmdfwtWi5wEMnf/6b/Wbf/vztm9jVHrxbhPC32GFQ76U9KSh2wHQMX0JeoswYTSAdenFO427zyQ9avs+AKBphEAA60AfQADomKFUNAF019gC4IakSds3AQwdFazVEQIBNGnwAdDMJmZ2aGZPlYS/QzM7MrPdtu8NAOYhBAJoyuD/TA+jgQ/avg8A/fLiu+Lwdf+N9b110icQQBMGXwEEgCpefPdqbvgru0+dqAQCqBsBEAC0XKhbZxAkBAKoE+0KAEapzuCWnqvppmGagwHUhXcSAKPRdLXuxXev1to/EACWRRMwgEFLm2nX1VTb9HVoCgZQB/5UBVC7NkPKOgdnzLuHJiuBNAUDWBXvIAB6qwthrwghEECX8e4BoDe6HPjy0CcQQFfRBxBA56173r06NXnf9AcEsCwCIIBa1R1K+hr8YkN4DgCGhQAIoLOGFJyaei5UAQEsg84pADppSOEvRZ9AYDjMbEvStqSZpKmkmbuflThuR9JDSS8lbUo6d/fjgvPvhC/vSTpy91nmPFvR48/zzlOEdyIAtaEa1Q5GBAPrZWZTSYfu/jDa9tTMZnFIyzluR5Lc/SDadm5mE3d/Em3blfTQ3fejbYeSDsK/t8J5bhxjZntlQyBNwAA6Z4jVv9SQnxswIvuSjjLbjiQdljgu6yzebmYTJeEy3rYraTc+T7ba6O4nSiqLpRAAAdSC6l95TYRAvv/AWu1Kushse6abIa1IXki7iv79saST+MGccLcdqpBZkxLXl0QABNAxVMgAdFmo0E0lXcbb3f0qPJ4XzNJ9HsXNv8GupM+ir/ckfZlzbNy0fCbpNG0KDtfdlfS05NOgDyAAtKGJASH0BURf/d2vf61f/eKrJk5938yeRV8fVxkoUWBDug58OaZKBoYsZGZ7ki7ivnxKqniz8NjrkBmqgOm/D0J/wnMzO0ivxyAQAL20rurf88tvK+2/ufFmQ3cCoGEv3H275nOWbmYtkg7ykJKqYLQ9rR5O4zBnZodmthFvc/cHZnaqpN/hhaT3q9wDTcAAVtaX/mfPL7+tHP5WOW4RmruBcXL3kzDI4yCMAk6bcovC5WfKDDAJFcJ9JUFyqqQaWNj8nEUFEMCg1Rnc0nN1uSJIMzBQXpXAJOkybvYNU7cUNQOX4u5XZnYk6QtJd3XddDzL7HdhZhMzm7r7LBxzGPoFzszsXSX9/06VzC24EO8SAFZSV/WviWpYE1W79Lx1hUAmhwbakc7lV+GQLyU90XU421A0ejcMDpFK9v+LnEmamNmOu5+ZmXRzVHBsamaX0s1BISGIPgzVxJ0yE1LzrgNgkJoKf/H5u1wJBDBfCFCPFu54+7grM5vpdnPthqSroomgQ+A8l/SgYJ84QBYNJJkpWX3kvOD2jnLuKxd9AAEMTtPhb93XAdA5Z0qCWGwrbJ/nmTLTxygJe9L1vIJHul7iTdLrlT/SVUZmkh4UnH+i2/MT5iIAAlhaF5t/1x3K6rgeg0GA3jnQ7erhftguKWkSNrPnYbBGWnE8LTjXk6gqeKzbK4YcptvS/dJl5aLrTSXdm7cUXYwmYACDQUUOwDqEZuADM3us6ybbw5zwtZE57omZ7ZnZpqSXSgZsPM1M73JlZg/D2r/pPodxvz533w/nSfeRkubn7CTThQiAAAahzfBHf0BgfNz9QnOaW8PAjLs52xdO1hyC5Nwwt+qE1jQBAwAAjAwBEMBSujT58xCafukHCGCdCIAAWkXwAYD1IwACwMB0qToLoJsIgAB6rSvNv125DwAogwAIAAAwMgRAAACAkSEAAgAAjAwBEEBlDDIAgH4jAAIAAIwMARAAAGBkCIAAeq0ra/B25T4k6d6bLPMOYD4CIAAAwMjwZyKAyu69eae2gSD337jDcnBKvg/AWP32V7/W1c9/0fZtjMoo3nHMbFfSVNJm+Hzk7ift3hWAumxuvMlKHABQweADYAh/szTwmdlE0rmZbbj7cbt3B2AIutT/DwDKGEMfwKm7X6RfuPuVpENJR+3dEoC69TmE0fwLYN0GHQBDte/D8Dl2Fh6frv+uADSljRDY5+AJYLwGHQBDtW8aPioxsz0ze2Zmz1788pf13xyA1/paASP8AeirQQdASXL3u3ETcLAl6crdZ3OOO3b3bXffvv/2283eJIDarCuU1XWdvoZfAP02+ABY4GNJn7R9E0CfdXmy4aZDIJU/AH03ugBoZnuSLt39Sdv3AuBa3ZWwzY03GwlqXQ9/XQ7mALqjN+8UFQdsXIb+f3nn2Hf3B/XdGYC6NDEpdJ1zBNYd/mj+BdCWXrz7hOB2WOGQLyXlVfgOJb1fy00BqHVFkCbFwa1KGOx6tQ8AltWLABgGazxa5RxmdiTpo7zKIIDuaHppuCGHOpp/AZQ1ij6Aod/fYRz+zGyHeQABtIXmXwBtGnwADEvBpf+emtmWme1IejRvGhgA5TRRdRp6OBr68wPQfYN+FworgDwteJjwB3RY003BbWkq/NH8C6CKQb9jhCZfa/s+AEAi/AHojsE3AQNoXlMBZEhNpUN6LgD6jwAIoNOGEJyafA5U/wAsg3cOALVock7APvcHHEKABXCbmW1J2lYypmAqaebuZwuOmUjak3Ti7rMwG8mupIv0WDM7lPRZOF/h1HXh+vuSnku6J+kzd78oe/+8MwHohT6GwKbDH9U/oB3pAhXu/jDa9tTMZgtmGNlQsijFoZlJ0pWSOYrj4Lgl6XE4Z/b4mbtvhtlMDjLXPzez0jOc0AQMoDZNB5I+VdP6dK8AKtuXdJTZdqRyq5Y9lHRX0qa733X3k8zjs7DPA0mb0ce+rhfFyLvWJ2GfUniHAtArabDqajVwXcGP6h/Qql3dDoDPJJ2WOTg07RY1757nNSWbmdz9IjQjT3V7OrsLJVPfHZS5ByqAAGq1rmDSxQpbF+8JGLn7ZvYs+thb9YRRALuMt6f99VZdZczdj3OuuRdtT89/mdntMrq/hXi3AlC7JgeExLpSDVx38KP6h6H57a9+o6+f/1UTp37h7ts1n3NDug58OfKqc7FJtErZhqTLnGbg18Jgj2fRpvTcG7pZRdwo2J6LdxEAvddWEGyj4kf4A1pXqsJW4FLSRlzlC4NHNCcE7rj7k/QLd78yszMlg0XioDmNPi8cCEITMIBGtBFU7r9xZ22hjOZeAFW5+1VOE2/h4JFQKcwLc/uKBnxkmn2zTcO5eAcD0Jh1NQVnxeGszqpg26GP6h9Qr4r99S7jZl8zm8ybp6+CmaRpwfk+lvR+9oAwh+CjqCn5StdBsdQ0MLybABi0tkNbXQh/QL3SufwqHPKlpCcq6IMXVeEKA5iZPY6bc4O0YjdVMpI3Pt9WUcgM20+i/bei7QvxjgKgUW1VAYeE8AfUL0yY/GjhjrePuzKzmW73BdyQdFU0EXMaOM3sJLNPOngje9yOSgzmiGwrCoSL0AcQQOMIMMvjewd00pmSwBXbCttzhdC3nxMQd5QsBZcNe++poJpoZqc5U9ocqOQcgBIBEMCaEGSq43sGdNaBblcP9xUFMDObmNnzTFC7jPsdhmbefUkf5Vzj1lyDkStFYdPMHks6KrsMnEQTMIA1ojm4PMIf0F2hGfggBK+ZkrB2mBPANjLHnZjZbhi8cU9JM3LR+r15zcypA0m7ZnYvfP08bwLpeXiHAbBWhMDFCH9A97n7haJBGzmPXylZ8ze7vVQ/PXcvbM4NgTE7mKQSmoABrB0BpxjfGwDrQAAE0AqCzur3x6EAAA/9SURBVG18TwCsCwEQQGsIPIl7b97hewFgrQiAAFo19vAz5ucOoD0EQACdMMYgNMbnDKAbePcB0BlpIBr6KGGCH4C28S4EoHOGGgQJfgC6giZgAJ01lMA09n6OALqHAAig0/oenvp87wCGi3cmAL3Qt2Zhgh+ALuMdCkCvxMGqi2GQ4AegD3inAtBbXQmDhD4AfcO7FoBBKAphdQVDQh6AIeEdDcCgEdyA7nv1t6/08v9+2fZtjAqjgAEAAEaGAAgAADAyBEAAAICRIQACAACMDAEQAABgZAiAAAAAI0MABAAAGBkCIAAAwMiMYoZUM9uR9FDSS0mbks7d/bjduwIAAGjH4ANgCH9y94No27mZTdz9SXt3BgAA0I4xNAHv52w7K9gOAAAweGMIgFLS/Jt1tfa7AAAA6IDBNwG7+6OczbuSjtZ9LwAAAF0wlgrga2a2J+liUf8/M9szs2dm9uzFL3+5prsDAABo3uArgCkz21VoCi6oCt4QRgkfS9LWgwfe7N0BAACsz2gCoLufSDoxs4mZnUv6yN0v2r4vAACAdetNADSzaYXdL909d5CHu1+Z2ZGkLyTdreXmAADAqJjZlqRtSTNJU0kzdz9bcMyhpM/CvoWDUcMUdlvhy3uSnmfnLw7X35f0POzzWZXCVi8CYAh/hxUO+VLSvD5+Z5ImZraz6IcFAAAQS3OJuz+Mtj01s5m7z+YcuiXpcdg/+9jM3TdDsFM8VsHMds1sLw2BISAeZK5/bmaPFlz/tV4EwPBkFvbbywo/oHNJDwq+IZNV7w0AAIzOvm7PJnKkpFg1L6/MlIxHuNTN6eh2JD1Lz+3uN+YqdvcTM3uqMDYhXCs7n/EnYduBShjDKOBnSr7RsbQ5mT6AAACgql3dzhDPwvZ5zt39zN0v3H2WfkhS1Hy7XdDtbSJJZjZRaHLOPH6hUF0sY9ABMHxTT3MeOpD0pGyZFAAAQLoRwG4Ul9I+ffPGLGT78YX99zLbzySdpk3BYZ9dSU/Dl+n5s8Wty+j+FupFE/Aq3P1JmNNvU9JLSZuSnub9EAAAwKDcN7Nn0dfHNfz+35CuA1+OvOpcrhDy4vuTux+EPn7nZnaQniu67/TcG7rZjLxRsD3X4AOglJ+4AQBAN/z613+nf/eXf93EqV+4+3bN56xz/MBO3sIU7v7AzE6V9Cm8kPR+9NiVmZ0pGVASB81p9HlhAB10EzAAAEAXhWbd3KAWVi3bVzJgZKqkGhg3Le8rGgSSafbNNg3nGkUFEAAAIGuVOYbNbDJvLr8SPlZU2YvOe6RkipmZpJmZvauk/9+pkm5scveZmT0KIVJKmnzTMDmcaWAAAADqtMIcw7l98KIq3MIAFvbdygbI9BzxINWwz8Mwz9/r+YvD9pPo2K1o+0IEQAAAMDrLzjEc+uDNdLsv4Iakq5IzjOwof6DGtpL5i/Mc5Vwze+zJnMdvoA8gAABANWdKAldsK2wv4z3lVwpnkh4UHDNRmHvQzE5DP8HYgUpOAi0RAAEAAKo60O3q4Y1VOMxsYmbPc4KalDOPoHTd9BumgXktNFffi6qLV4rCppk9lnRUZX5jmoABAAAqCM3AByF4zZQEusOcALZx+2gpHJPbnOvu+2H+4kMl8xdLSdNyXN07kLRrZvfC18+rTnlHAAQAAKgoLN1WuKRsGIxxt+CxuU21i8JcCJq35g+sgiZgAACAkSEAAgAAjAwBEAAAYGQIgAAAACNDAAQAABgZAiAAAMDIEAABAABGhgAIAAAwMgRAAACAkSEAAgAAjAwBEAAAYGQIgAAAACNDAAQAABgZAiAAAMDI3Gn7BgAAwLj97d/9nf6vv/5127cxKlQAAQAARoYACAAAMDIEQAAAgJEhAAIAAIwMARAAAGBkCIAAAAAjQwAEAAAYGQIgAADAyBAAAQAARoYACAAAMDIEQAAAgJEhAAIAAIwMARAAAGBkCIAAAAAjQwAEAAAYGQIgAADAyNxp+wbWzcwmkg7dfb/tewEAAP1mZruSrtz9rOT+W5K2Jc0kTSXNssfWtc88owuAkg4lbbR9EwAAoN/MbEfSp5Ieldx/qqQI9TDa9tTMZu4+q3OfRUbVBBy+YYQ/AACwNDObmtmRksrbZYVD9yUdZbYdKSlO1b3PXKMKgJJ2JJ22fRMAAKC/3H3m7vvuflzx0F1JF5ltz8L2uveZazQBMJRpP2/7PgAAwPiEMQi3KobufhUen9a1T5n7GVMfwIm7X5lZqZ3NbE/SXvjyV2++8cb/2didoUn3Jb1o+yawNH5+/cXPrt/+wTov9lf+6z//5Nez+w2c+u+Z2bPo6+MlqnZ12ZCug1qO18Gthn0W9gMcRQA0s113P6lyTHiBHIfjn7n7diM3h0bxs+s3fn79xc+u3zKhqXHu/o/Xeb2WTNa4z0KDbwIOpdKilAwAADA6vakAlm3TDi6j0ugHLZZ7AQBAR62QLVa55mTReeraZ55eBMB0vpsKh3wp6UmYJLGOMjYBsr/42fUbP7/+4mfXb4P/+S2bLVa4ZNovb0NRy2RoqUwfv6xpn4XM3Svce7+EgRybmc1bSjpInkj6smrfQAAAgJSZPZe0X2YVjrDvI3e/iLZNJZ27+90691mkFxXAZeU1/ZrZY0nvuftBC7cEAADG60zJ8m3xHH5bYXvd+8w1+EEgOe61fQMAAGAwNpQzMtfMJmb2PLRGpg50e9m4/bC97n3mGnQTcCyURg8kfaDkB3Us6SgunwJo36oLnKNdZrar5Oe2GT4f0dWmn0KfskN332/7XromfG8+VvIa31XyfnUm6TR9vYd9vpJ0ELdIhve4HV2/x11k3+Pq2mfucxhLAATQfeEPtaPsAudK3kBLdWxGe0L4m6V/WIdfgOdKQsTgBxUMTVjrdsPds5UmDMAYm4BrE8q72cWY0WFmtmtmj83syMxOwy8sdMfKC5yjVdO4VSVMUXGo2z9TdFz4Y2yj7ftAcwY9CGQNDsV/kN6IqhNxef7czDaoTnTGrm6HhWeSTlu4F1QQ/j99aGbHmbnJzsLjU6q4vbKj5P/dw0U7op+oAC6Jv456iepEh9W1wDnaEX5OU0VrlaKfzGxH0udt3weaRQBcXvrXEXogqk5kR2q9rk6s/66QUXqhdHSTu9/NGVi3JemK6l+vrLTCBPqBALgE/jrqH6oTvVDLAufonI8lfdL2TaAcM9tl1PY40AdwORN3vzKztu8DFRTMjk51AmhImP/s0t1XWT4LaxJaSKj8jQQVwIr462hwqE50TE4zPXoodKvYj6f0Qed9wJyb40EArIC/joaF6kTnxAulv1Z1gXN0xqGk99u+CZQTJhV+1vZ9YH1G2QRcscP/ZdQZ9gOmC2nfCj+/7Dn23f1BfXeGVYRuFTPd7gu4IZrpeyXMj/oRAwl6ZVvSppl9GG3bkjQ1s0NJX9L6NSyjC4DhF3+VSWW/lPSEv466YdmfX852qhPdtPIC52hXqKwfxuEvDJybEeK7K6+4YWaPJb3n7qXXl0V/sBRcSeFNbTOzeUvJqNIT8ddRb4TqxAHVie4Jzb1PM0vBnSqp1hIeOi5Mtr6h68A+CV8/Yj3Z/gmVvylLwQ0TAXAF0V9H/OfoiRDkz+IwQXWiW1Zd4BztCOH964KHZ+6e/QMaHRVaWg4kfaAkxB8rWaM7O8cjeowAuAL+OuoXqhMAACQIgEvgr6P+oToBAMA1AiAAAMDIMA8gAADAyBAAAQAARoYACAAAMDIEQAAAgJEhAAIAAIwMARBAL1RcA7oz5waALiIAAui8sFrLToOXuAxLBALAKBAAAXRaWBruUd5i9XUJ60IfhnWHAWDwmAgawGthubxDJWvwpmaSrqKvL8PnC0mfhPDU1P1MJJ1LetDkdaLrPZZ0z90Pmr4WALSJAAjgltAn7rmkK3e/m/P4RNKepI8lfd7UWsqhWfa8yepfzjWfS3ro7rN1XRMA1o0ACOCWaO3kueskR0HxzN0f1nwPU0mn616nOVRB9+t+PgDQJfQBBHBL2ebWUCU7lrQTmk/rdKCkOXqt3P1E0jYjgwEMGQEQwKrOw+e6m4H3JH1e8znLOlb9zwcAOoMACKBzQjPsxToGfhQ4VRJAAWCQCIAAVvUgfD6p8ZwPJZ3VeL5K3P1M0oRmYABDdaftGwDQXyEg7SkZLDJ36hQzS/vzvZR0T9JE0kFBlW9HS/T/M7M9SY+UTF0jSRtKpqq5qHqucI4dJc3BADAoBEAAlYVRwh8oCWknkj6as+9USZPqfqispdt3JX1lZg9yplyZSnpW4X62JD1VZjRyOkrZzPazU8mY2U58PzlmktY6AhkA1oUACGCejczo3ntKqmJbkp5Ier9Ede1U0lE2bLn7iZntKwluaTNyGi6lm5NPFwrLxJ1KepKtQrr7zMyOJR2Z2edptTGEz0VmujkhNgAMBn0AAcxz6e5Poo8Dd3+gJLBtSdqed3AIj1MVN6MeSdoKFbzURnrtRTcXVRcv5jRBp8u7fRxt+zBM9zLPlZJmagAYHAIggMpC1e+RkvVz5/XV21eymkhRNS9t+o2D5CRco0wF8CjzOU9aodySXofGheFSSV/FjYV7AUAP0QQMYCnufmVmn0t6bGafFTQFTyXNwuCMPBMlo33jQFYqdIWq4U64l3kDNdJzp825h5rTZzHn/gBgcAiAAFbxPHz+UNeVNkmvK21SUgGcF9CeZL4uU51LrylVmH4m9P2blawu3tN1hRIABoUACGAVaZDaynmsbJDLPaeZTRYEtfSaX5Y874aSvn+PSu4/UcmBKADQN/QBBLCKbPPqayG8VR5JG00JU7b/Xdkq3UTJ+sJlbWj5EAsAnUYABLCKtEJWFPIOlayokVchlJQ0FRdMy1J4TDDLfF5kljPf4DxTXTdxA8CgEAAB3BLNxbfI60AVL5sWQt1O6Pt3ofmreuznTMlypsWVw3Tkb+FUNOGePg1fbkTbyzy/qTL9GgFgKAiAAPJsZD7nChW1dIBHXMXbjSZ+fl/JhNK3pmoJ8wR+lnPqU0nvLbj2hZIBJAfZQGdmkzA9zUHo83esmyN6P9UcIThOFqwUAgC9Ze7e9j0A6IjQFPuxkupXvCLHTNKjoibUMM3LvpLK3UslEzOf5ezzUEm/urTp+CjvnCGAnbv73ZL3/GE4bxpYZ9lzm9lTXQ/sOJjXHJyuKRwvKwcAQ0IABNBJZnYu6aMSS801ce10+brSU8wAQJ8QAAF0UloxrDBtS13XnUj6qkz1EQD6igAIoLPM7LmkByUnbq7rmoeSni+YvBoAeo1BIAC67EALBmzUKfQ93CH8Af9/e3dUBSAIQwEUullFO1nKCEYwgz+rAHJ89waA33c2Nvg7ARBYVr3Be3rv26Qrz9ba1JYzwBe0gIHl1QTvPrIVXCtpboMfQAIVQGB5NQhyjDq/fiq5hD8ghQogAEAYFUAAgDACIABAGAEQACCMAAgAEEYABAAIIwACAIR5AdyNy3ugcc+vAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "W_odd=np.around(W_odd, decimals=2)\n", "plt.figure(figsize=(10, 8))\n", "\n", "plt.contourf(xvec,xvec, W_odd, cmap='RdBu', levels=np.linspace(-1, 1, 20))\n", "plt.colorbar()\n", "plt.xlabel(r'Re$(\\alpha)$', fontsize=label_size)\n", "plt.ylabel(r'Im$(\\alpha)$', fontsize=label_size)\n", "plt.title(\"Second state: odd cat-like\", fontsize=title_font)\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Quantum Trajectories\n", "From a theoretical point of view, the Lindblad master equation describes the out-of-equilibrium dynamics of a system coupled to a Markovian (i.e., memoryless) environment.\n", "Indeed, the density matrix $\\hat{\\rho}(t)$ solving the Lindblad equation encodes the average evolution of the system when no information is collected about environment state.\n", "However, one can imagine to keep track of the system state by continuously probing the environment.\n", "\tDoing so, the time evolution of the system would change at each realisation.\n", "\tHowever, $\\hat{\\rho}(t)$ can be retrieved by averaging over an infinite number of such \"monitored\" realisations.\n", " The Monte Carlo wavefunction method has been developed relying exactly on this idea.\n", "\tIt is based on the stochastic simulation of the system evolution when one continuously gathers information from the environment.\n", "Each simulation of the stochastic evolution of the system gives a single quantum trajectory.\n", "The results obtained by solving the master equation are recovered by averaging over many trajectories.\n", "In order to simulate the quantum trajectories, it is necessary to explicitly model how an observer measures the environment, thus affecting the system evolution itself (a detailed discussion on this subject is given in [5].\n", "Interestingly, several different measures can be associated with the same master equation.\n", "Depending on the chosen measurement, contrasting results and interpretations can emerge.\n", "Those incompatibilities are, however, harmonized once the mean value over many trajectories is taken.\n", "\n", "![measure_type-1.png](./images/measure_type-1.png \"Homodyne measure (left): the optut field is detected after being mixed with that of a local osillator. Photon counting (right): each photon escaping the cavity is detected by a photon counter.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\newcommand{\\ket}[1]{| #1 \\rangle}$\n", "$\\newcommand{\\bra}[1]{\\langle #1 |}$\n", "$\\newcommand{\\CC}{\\mathcal{C}}$\n", "### Photon counting\n", "\n", "The most natural way to observe the exchanges between the Kerr resonator and the environment is to just detect every leaked photon (both individually and by couples).\n", "This mechanism is described via the action of the one-photon jump operator $\\hat{J}_1=\\sqrt{\\gamma}\\, \\hat{a}$ and the two-photon one $\\hat{J}_2=\\sqrt{\\eta}\\, \\hat{a}^2$, which describe the absorption of one or two photons by an ideal photodetector (details in e.g. [6]).\n", "Indeed, in typical realisations (e.g. [4]) the one- and two-photon dissipation channels are discernible.\n", "Hence, we can assume that the photodetector is capable of distinguishing between one- and two-photon losses.\n", "The photon-counting trajectory is then obtained by using the \"mcsolve\" function of qutip. \n", "In conclusion, a photon-counting trajectory is characterised by abrupt jumps corresponding to the projective measure associated to the detection of one or two photons.\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100.0%. Run time: 0.38s. Est. time left: 00:00:00:00\n", "Total run time: 0.44s\n" ] } ], "source": [ "tlist=np.linspace(0,20,2000)\n", "\n", "\n", "sol_mc=mcsolve(H, fock(20,0), tlist, c_ops, [a.dag()*a, (a+a.dag())/2, -1.j*(a-a.dag())/2, parity], ntraj=1)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(18, 8))\n", "plt.subplot(311)\n", "plt.plot(tlist, sol_mc.expect[0])\n", "plt.ylabel(r'$\\langle \\hat{a}^\\dagger \\hat{a} \\rangle$', fontsize=label_size)\n", "plt.xlim([0,20])\n", "plt.subplot(312)\n", "plt.plot(tlist, sol_mc.expect[3])\n", "plt.ylabel(r'$\\langle \\hat{P} \\rangle$', fontsize=label_size)\n", "plt.xlim([0,20])\n", "plt.subplot(313)\n", "plt.plot(tlist, sol_mc.expect[1], label=r'$\\langle \\hat{x} \\rangle$')\n", "plt.plot(tlist, sol_mc.expect[2], label=r'$\\langle \\hat{p} \\rangle$')\n", "plt.xlabel(r'$\\gamma t$', fontsize=label_size)\n", "plt.xlim([0,20])\n", "plt.ylim([-3,3])\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As shown in [2], the Hamiltonian $\\hat{H}$ and the two-photon dissipation tend to stabilize photonic cat states.\n", "On the other hand, the annihilation operator switches from the even (odd) cat to the odd (even) one: $\\hat{a}\\ket{\\CC^\\pm_\\alpha} \\propto \\alpha \\ket{\\CC^\\mp_\\alpha}$.\n", "The operator $\\hat{J}_1$ thus induces jumps between the two cat states at a rate proportional to $\\gamma \\braket{\\hat{a}^\\dagger \\hat{a}}$.\n", "This picture is very well captured in the framework of photon-counting trajectories, an example of which is given in the previous figure.\n", "The cat states are, indeed, orthogonal eigenstates of the parity operator $\\hat{\\mathcal{P}}=e^{i \\pi \\hat{a}^\\dagger \\hat{a}}$ with eigenvalues $\\pm1$.\n", "As we can see, along a single trajectory the state intermittently and randomly switches between the two cat states.\n", "We stress that, instead, the mean values of the field quadratures $\\hat{x}=\\left(\\hat{a}^\\dagger+\\hat{a}\\right)/2$ and $\\hat{p}=i\\left(\\hat{a}^\\dagger-\\hat{a}\\right)/2$ are practically zero along the trajectory, as expected for any cat state.\n", "The parity, hence, appears to be the appropriate observable to detect a bimodal behaviour in a photon-counting environment.\n", "Thus, we may interpret \n", "$$\\hat{\\rho}_{\\rm ss}\\simeq\n", "p^+\\,\\ket{\\CC^+_\\alpha}\\!\\bra{\\CC^+_\\alpha}\n", "+p^-\\,\\ket{\\CC^-_\\alpha}\\!\\bra{\\CC^-_\\alpha}$$\n", "as the steady-state probabilities to find the system in one of the two cat states.\n", "\n", "The previous analysis seems to point in the direction of privileging the cat states over the coherent ones as the more truthful picture of the steady state." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Homodyne\n", "\n", "Another possible way to monitor a quantum-optical system is through homodyne detection, a widely-used experimental technique which allows to access the field quadratures [5-6].\n", "To implement this kind of measurement, the cavity output field is mixed to the coherent field of a reference laser through a beam splitter (here assumed of perfect transmittance).\n", "Then, the mixed fields are probed via (perfect) photodectors, whose measures are described by new jump operators.\n", "We stress that both the coherent and the cavity fields are measured simultaneously.\n", "\n", "In our case, we want to probe independently the two dissipation channels.\n", "To distinguish between one- and two-photon losses, one can exploit a nonlinear element acting on the cavity output field.\n", "Indeed, in experimental realisations such as [4], a nonlinear element is already part of the system and is the key ingredient to realise two-photon processes.\n", "More specifically, one-photon losses are due to the finite quality factor of the resonator.\n", "They can be probed by directly mixing the output field of the cavity with a coherent beam of amplitude $\\beta_1$ acting as local oscillator.\n", "Therefore, the homodyne jump operator for one-photon losses can be cast as $\\hat{K}_1=\\hat{J}_1 +\\beta_1 \\hat{1}$.\n", "Two-photon losses are, instead, mediated by a nonlinear element (a Josephson junction in [4]), which converts two cavity photons of frequency $\\omega_c$ into one photon of frequency $\\omega_{nl}$. Hence, the field coming out of the nonlinear element can be probed by a second independent oscillator.\n", "This whole process can be seen as the action of a nonlinear beam splitter which mixes couples of dissipated photons with a reference oscillator of amplitude $\\beta_2$.\n", "Therefore, the homodyne two-photon jump operator takes the form $\\hat{K}_2=\\hat{J}_2 +\\beta_2 \\hat{1}$.\n", "Without loss of generality, in the following, we assume the amplitudes $\\beta_{1,2}$ to be real [6].\n", "\n", "In the ideal limit $\\beta_{1,2}\\to\\infty$, the system evolves diffusively according to a homodyne stochastic Schr\\\"odinger equation.\n", "Using the ssesolve function with option \"method='homodyne'\", one can simulate the trajectory." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total run time: 636.04s\n" ] } ], "source": [ "tlist=np.linspace(0,8000,800)\n", "\n", "\n", "sol_hom=ssesolve(H, fock(20,0), tlist, c_ops, [a.dag()*a, (a+a.dag())/2, -1.j*(a-a.dag())/2, parity],ntraj=1,nsubsteps=9500, store_measurement=False, method='homodyne')" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(18, 8))\n", "plt.subplot(311)\n", "plt.plot(tlist, sol_hom.expect[0])\n", "plt.ylabel(r'$\\langle \\hat{a}^\\dagger \\hat{a} \\rangle$', fontsize=label_size)\n", "plt.xlim([0,8000])\n", "plt.subplot(312)\n", "plt.plot(tlist, sol_hom.expect[3])\n", "plt.ylabel(r'$\\langle \\hat{P} \\rangle$', fontsize=label_size)\n", "plt.xlim([0,8000])\n", "plt.subplot(313)\n", "plt.plot(tlist, sol_hom.expect[1], label=r'$\\langle \\hat{x} \\rangle$')\n", "plt.plot(tlist, sol_hom.expect[2], label=r'$\\langle \\hat{p} \\rangle$')\n", "plt.xlabel(r'$\\gamma t$', fontsize=label_size)\n", "plt.xlim([0,8000])\n", "plt.ylim([-3,3])\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the mean parity $\\braket{\\hat{\\mathcal{P}}}$\n", "is confined around zero along a single homodyne trajectory, in spite of the \n", "\"switching cat\" picture.\n", "These fluctuations are due to the diffusive nature of the homodyne trajectory, which rules \n", "the stochastic time evolution of the system wave function under homodyne detection.\n", "\n", "The bimodal behaviour, instead, is clear in the time evolution of $\\braket{\\hat{x}}$ and $\\braket{\\hat{p}}$.\n", "This appears compatible with the picture given by \n", "$\\hat{\\rho}_{\\rm ss}\\simeq\n", "\\frac{1}{2}\\ket{\\alpha}\\!\\bra{\\alpha}\n", "+\\frac{1}{2}\\ket{-\\alpha}\\!\\bra{-\\alpha}$: at the steady state the system switches between the coherent states $\\ket{\\pm\\alpha}$.\n", "We point out that the phase switches observed for homodyne trajectories have a much smaller rate than parity\n", "switches in photon-counting trajectories. This is a consequence of the metastable nature of the \n", "coherent states $\\ket{\\pm\\alpha}$ [1-4]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conciling the two points of view\n", "\n", "Summing up, we have shown that the behaviour of the system along a single quantum trajectory dramatically depends on the measurement protocol adopted.\n", "For photon-counting measurements on the environment, the system switches between the parity-defined cat states, while under homodyne detection, the states explored along a single quantum trajectory are the coherent ones.\n", "\n", "In other words, one may assign a physical meaning to the probabilities appearing in the mixed-state representation of $\\hat{\\rho}_{\\rm ss}$ only upon specification of the single-trajectory protocol.\n", "However, any possible controversy at the single-trajectory level is washed out by averaging over many of them." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10.0%. 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Est. time left: 00:00:00:42\n", "80.0%. Run time: 113.37s. Est. time left: 00:00:00:28\n", "90.0%. Run time: 127.39s. Est. time left: 00:00:00:14\n", "Total run time: 141.30s\n" ] } ], "source": [ "tlist=np.linspace(0,3,100)\n", "sol_mc_mean=mcsolve(H, fock(20,0), tlist, c_ops, [a.dag()*a, (a+a.dag())/2, -1.j*(a-a.dag())/2, parity], ntraj=50)\n", "sol_hom_mean=ssesolve(H, fock(20,0), tlist, c_ops, [a.dag()*a, (a+a.dag())/2, -1.j*(a-a.dag())/2, parity],ntraj=50,nsubsteps=350, store_measurement=False, method='homodyne')" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-2, 2)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(18, 8))\n", "plt.subplot(311)\n", "plt.plot(tlist, sol_mc_mean.expect[0], 'r', label='Conunting')\n", "plt.plot(tlist, sol_hom_mean.expect[0], 'b', label='Homodyne')\n", "plt.ylabel(r'$\\langle \\hat{a}^\\dagger \\hat{a} \\rangle$', fontsize=label_size)\n", "plt.xlim([0,3])\n", "plt.legend()\n", "plt.subplot(312)\n", "plt.plot(tlist, sol_mc_mean.expect[3], 'r')\n", "plt.plot(tlist, sol_hom_mean.expect[3], 'b')\n", "plt.ylabel(r'$\\langle \\hat{P} \\rangle$', fontsize=label_size)\n", "plt.xlim([0,3])\n", "plt.subplot(313)\n", "plt.plot(tlist, sol_mc_mean.expect[2], 'r')\n", "plt.plot(tlist, sol_hom_mean.expect[2], 'b')\n", "plt.ylabel(r'$\\langle \\hat{p} \\rangle$', fontsize=label_size)\n", "plt.xlim([0,3])\n", "plt.ylim([-2,2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "\n", "[1] N. Bartolo, F. Minganti 1 , J. Lolli, and C. Ciuti,\n", "Homodyne versus photon-counting quantum trajectories for dissipative Kerr resonators\n", "with two-photon driving, The European Physical Journal Special Topics 226, 2705 (2017).\n", "The European Physical Journal Special Topics 226, 2705 (2017).\n", "\n", "[2] F. Minganti, N. Bartolo, J. Lolli, W. Casteels, and C. Ciuti,\n", "Exact results for Schrödinger cats in driven-dissipative systems and their feedback control, Scientific Reports 6, 26987 (2016).\n", "\n", "[3] N. Bartolo, F. Minganti, W. Casteels, and C. Ciuti,\n", "Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions, Physical Review A 94, 033841 (2016).\n", "\n", "[4] Z. Leghtas et al., Confining the state of light to a quantum manifold by\n", "engineered two-photon loss, Science 347, 853 (2015).\n", "\n", "[5] S. Haroche and J. M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons\n", "(Oxford University Press, 2006).\n", "\n", "[6] H. Wiseman and G. Milburn, Quantum Measurement and Control (Cambridge University Press, 2010)." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "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: 1.15.4\n", "Scipy Version: 1.1.0\n", "Cython Version: 0.29.2\n", "Matplotlib Version: 3.0.2\n", "Python Version: 3.7.1\n", "Number of CPUs: 6\n", "BLAS Info: INTEL MKL\n", "OPENMP Installed: False\n", "INTEL MKL Ext: True\n", "Platform Info: Linux (x86_64)\n", "Installation path: /home/test/anaconda3/lib/python3.7/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()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }