{ "metadata": { "name": "Lecture-3B-Jaynes-Cumming-model-with-ultrastrong-coupling" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP lecture: Jaynes-Cummings-like model in the ultrastrong coupling regime" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Author: J.R. Johansson, robert@riken.jp\n", "\n", "http://dml.riken.jp/~rob/\n", "\n", "Latest version of this ipython notebook lecture is available at: http://github.com/jrjohansson/qutip-lectures" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# setup the matplotlib graphics library and configure it to show figures inline in the notebook\n", "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", "For more information, type 'help(pylab)'.\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# make qutip available in the rest of the notebook\n", "from qutip import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction\n", "\n", "In the Jaynes-Cumming model, the dipole-interaction term between the atom and the cavity field is assumed to be weak, so that a rotating-wave approximation can be performed. For large coupling strengths between the atom and the cavity field the RWA is not justified, and for very large coupling strength interesting properties of the atom-cavity ground state is observed.\n", "\n", "To explore this using QuTiP, consider the Hamiltonian\n", "\n", "### $H = \\hbar \\omega_c a^\\dagger a + \\frac{1}{2}\\hbar\\omega_a\\sigma_z + \\hbar g(a^\\dagger + a)(\\sigma_- + \\sigma_+)$.\n", "\n", "Note that here we have not transformed the interaction part of the Hamiltonian using the RWA, for which the Hamiltonian would have been\n", "\n", "### $H_{\\rm RWA} = \\hbar \\omega_c a^\\dagger a + \\frac{1}{2}\\hbar\\omega_a\\sigma_z + \\hbar g(a^\\dagger\\sigma_- + a\\sigma_+)$.\n", "\n", "In this notebook we will calculate the ground state of the Hamiltonian $H$ as a function of the interaction strength $g$ (try to set `use_rwa = True` to use $H_{\\rm RWA}$ instead).\n", "\n", "The regime $g$ is large compared with all other energy scales in the Hamiltonian $H$ is called the ultrastrong coupling regime, and has been an active topic of research in recent years. See references below.\n", "\n", "\n", "References:\n", "\n", " * [P. Nataf et al., Phys. Rev. Lett. 104, 023601 (2010)](http://dx.doi.org/10.1103/PhysRevLett.104.023601)\n", "\n", " * [J. Casanova et al., Phys. Rev. Lett. 105, 26360 (2010)](http://dx.doi.org/10.1103/PhysRevLett.105.263603).\n", "\n", " * [S. Ashhab et al., Phys. Rev. A 81, 042311 (2010)](http://dx.doi.org/10.1103/PhysRevA.81.042311)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem parameters\n", "\n", "\n", "Here we use units where $\\hbar = 1$: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "wc = 1.0 * 2 * pi # cavity frequency\n", "wa = 1.0 * 2 * pi # atom frequency\n", "\n", "N = 15 # number of cavity fock states\n", "use_rwa = False" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup the operators and the Hamiltonian" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# operators\n", "a = tensor(destroy(N), qeye(2))\n", "sm = tensor(qeye(N), destroy(2))\n", "\n", "na = sm.dag() * sm # atom\n", "nc = a.dag() * a # cavity\n", "\n", "# decoupled Hamiltonian\n", "H0 = wc * a.dag() * a + wa * sm.dag() * sm\n", "\n", "# interaction Hamiltonian\n", "if use_rwa:\n", " H1 = (a.dag() * sm + a * sm.dag())\n", "else:\n", " H1 = (a.dag() + a) * (sm + sm.dag())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Find ground state as a function of coupling strength" ] }, { "cell_type": "code", "collapsed": false, "input": [ "g_vec = linspace(0, 2.0, 101) * 2 * pi # coupling strength vector\n", "\n", "psi_list = []\n", "\n", "for g in g_vec:\n", "\n", " H = H0 + g * H1\n", "\n", " # find the groundstate and its energy\n", " gnd_energy, gnd_state = H.groundstate()\n", " \n", " # store the ground state\n", " psi_list.append(gnd_state)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate the cavity and atom excitation probabilities as for the calculated ground states:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "na_expt = expect(na, psi_list) # qubit occupation probability\n", "nc_expt = expect(nc, psi_list) # cavity occupation probability" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the ground state occupation probabilities of the cavity and the atom as a function of coupling strenght. Note that for large coupling strength (the ultrastrong coupling regime, where $g > \\omega_a,\\omega_c$), the ground state has both photonic and atomic excitations." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 1, sharex=True, figsize=(8,4))\n", "\n", "axes.plot(g_vec/(2*pi), nc_expt, 'r', linewidth=2, label=\"cavity\")\n", "axes.plot(g_vec/(2*pi), na_expt, 'b', linewidth=2, label=\"atom\")\n", "axes.set_ylabel(\"Occupation probability\", fontsize=16)\n", "axes.set_xlabel(\"coupling strenght\", fontsize=16)\n", "axes.legend(loc=0)\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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utptlkcOnXwgPD+eaa66hatWqRXpISVNyU/L03omIVFD/+hdMnmwaEd93nxl1+M+OKGWZ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\nzSq8uGGMMcbYrPIX3TAheYyRUWgAAAAASUVORK5CYII=\n" } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plot the wigner functions of the cavity as a function of coupling strength" ] }, { "cell_type": "code", "collapsed": false, "input": [ "g_idx = where([g_vec == 2*pi*g for g in [0.0, 0.5, 1.0, 1.5, 2.0]])[1]\n", "psi_sublist = array(psi_list)[g_idx]\n", "\n", "xvec = linspace(-5,5,200)\n", "\n", "fig_grid = (2, len(psi_sublist)*2)\n", "fig = figure(figsize=(3*len(psi_sublist),6))\n", "\n", "for idx, psi in enumerate(psi_sublist):\n", " rho_cavity = ptrace(psi, 0)\n", " W = wigner(rho_cavity, xvec, xvec)\n", " ax = subplot2grid(fig_grid, (0, 2*idx), colspan=2)\n", " ax.contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-.125,.125), cmap=get_cmap('RdBu'))\n", " ax.set_title(r\"$g = %.1f$\" % (g_vec[g_idx][idx]/(2*pi)), fontsize=16)\n", "\n", "# plot the cavity occupation probability in the ground state\n", "ax = subplot2grid(fig_grid, (1, 1), colspan=(fig_grid[1]-2))\n", "ax.plot(g_vec/(2*pi), nc_expt, label=\"Cavity\")\n", "ax.plot(g_vec/(2*pi), na_expt, label=\"Atom excited state\")\n", "ax.legend(loc=0)\n", "ax.set_xlabel('coupling strength')\n", "ax.set_ylabel('Occupation probability')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "output_type": "display_data", "png": 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iZNtFkzRFkxgrE2LXg0iKsHGY4DjkgwnjMCs6owg0AAjDWWfCVaJkfZcposzm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\n26WIgGXCrGyumBopmzJVoDWTGaKPZTqvEiXTr20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ABVAUOHUOiEngiM8VnPt0CpY95KuF\nWQ8+LCnOgFmnVW8rgNL2yvfmFGPbEkFom2UGAlTnWBdm8lw6+f5EBNRRnuFqpU5TtLNuHqBK4yIK\nNTSZ88PbgsKAiHBio7QnhYJI6WyjHxpFqTH79zbZdlWEVh+AMvW3GHwS/R2VLKUB5JF2/ro+2i7a\nZOr3QiSn5nkp/t9GpKzJsYrFoQyiFzAOuKiZF+qgWZv9WzWIZvp+y9o1CbI5aDafDNALfQgGDsuF\nWVZydujZwAEK0QcTIuVRiDAAlUKMt7eZGKPo2MmgTJTFyRSi+iLfBtCFGQCDOLNwQ/b+gedk29QL\nMlV8CUwiTLzWhZhoP0BirEvooqZWlAH5aD3LRY947bIekhRS8JiOlx8rf099OIp2lDsiJQ9IYZrZ\nQ5+hXJgBuQMALNZe+dowqkpirDlNBgLknDL0Zpw3dRBAjXQKZ1lgmr8oXpc5ano7y1CFWVNM9lYa\nHZN9olx3a+oH/r2a23eXbXvewYDZAajZAR0ugpWBnZJlGoDi4E5T+1tWjBW+/5qerboANEXKmHZt\nC+GrD/AJ8Qu017+8TVXPmOLfy0CCbAlMoiwXZ/xM8nx1q5C3rgqzmwAZIRO/dYQAE6/3MsGlCjH+\ndx4VA2AUYzPfgcTYVlM2n0z932xVQhEtA4Qwi9KUCyVFnB14wCQL/QNcpDW9ZXisKMYAFEQYb1+9\nECu8R+Jr41SJMgCaEIPiJAO5MMuc5UycASUT5ssEjkGI8f+ZhZi6BpSITIjvwdT2KQ4tQy7MRPsS\nxfzmaa9om2hzk79N+9xV5h4IEM7xFHm6LCuKamfaAxw1/dQcsVIjnfzY5Y4a/9v8HUxFFFZV3a4o\nTgHViV13P5ykNNyFBqB6s5kBeX/PFgARmCLtvA3lAtj0Wm171ynMH9NEGQCz8E0xI8zq+lcfZODH\nq7Zr0b5V37dJkM2Jvg5ZE1EmEILpOEow9GwZFRMCS1RmPMqEm3g//zz/W0TLdCHG22fNRsSUK5Pm\njZ08TKIMgCz0AWAmWuZY2XtZxMxlDGEyLYgzAFKgCfSKRSbUyBiQCzDe1lyE8bbm30G2vyYqpv+P\nWC9lDjL/X7mzwkVO7iznYow/UMuOlb/Oj2d6MNaJMfG3SZTNRlmgCLPcCZinvXqbq/5W3yvb1y4z\n10CA8jp33vKIGaCmnVX38YywLnHU+Hvmv9dBc5Ewfz+oszDq+uGk2Xc7A1D8r3xuY54dAPCIe+nx\nDfZnGuSZNyrWpb7X+xfAUpkXQPH7zdu/4u9Fr+9l+pYE2QJUiTIzfB2PMEllxOw4SqWIOo6KToMQ\nakJ4qagiTP1bjYoZf1Oa4olGFV4CPVqmkqcxAqLwhyrOAEiBJlCFWn17itup9qbuoioipn6P4r7J\ndjdNU1EGQHFQMCPOxL5qj9dw5L1KjKnv14oytd0GQdmEYmpW+Xv6+/r3IDiNbU47b9AGAVRBndR0\ns1GM1Nig+p7a1rapmn+jiwbTYMiq++Gk2HebA1BSnCnZAZXHrun3KtvruhATiDbNK3zNg2XZ74Zf\nc9nru227JkG2IGWiTP3frOjJz74qxoS4Oo7Swv/ybfVIW1GEiWOafou26W0nTiZV0TLx/+rP56Iu\n/yz/n9vkCaKh67cZsTWHEDNtQ2wOk6MCoPAgVYVZ4QEL5A/Z2uMorxs6HvNgEmV1gnKeNuttrHPW\nu+g0dYWFBgJKHGSgmVMs9q0es+w9/X39f21TWRQBqHRql+mHpoMN2yIK6lh2AErvc7W/6+ajimOI\n46p/171Xtr86ygaz5mWe4jXLXNtl/TtP34pj6u83HURrAxJkS2ASZQAK0bI6YSYiZ8CsEDMfc1aE\nVb4mMbZzmErilwkz8xwzfX+Q287TBhOmYzURYlX7JDaH/hAFZh+kEv38NbSnWefC/L82HD19ZLbg\nBAALt5m3r8k2ZON1zDsQUBahFZ+pPFZD29P/Z/r/qjAVRQDKhZmoLgqgEKlucgz5dwMxetLse267\nA3KhUNHn9Wmz1f3bxgBPWwKsbr91Am3ha1vtIzTPvmg6kLKuezcJsiXRRRkwGy0DyoSZoFkamP75\nqr9NZe1JjO0OphRGoD5iViXQxBy0OuoFXsn+SYhtJWUpJwKTOJtxXGqPYXivRoyl2UK8zfZfrKgG\nzEb05m0z36/hvRPmqG6CqjQn/n9k/68W1KqjPHuMkvcrHDX9/+ukiTAT/y849qwntzPut8F3PMlC\nTGWeAagq26uyu+LxtL9XIBJWJcbKjtVElAFzXtv6oEKDa7BeyBo+s2LbXliQvfGNb8SnPvUpuK6L\nJzzhCfjwhz+Mg4OD1hq2TaiiS76nRMv0bRYVRqbPzYiyEkPcVTG263ZaJ8yAXJyp2+vINMY57KiJ\nkKqqnLhrQmzbbdX0IAVmHUW+7RLHmWME2CTKyhyCqtFZ/v+FmlvYV9lxt4ku2ek856xUUJdEiKrP\n2Xzbi7a2SVmVxkX6YCad2LC/mfc7PtiwKjstE2WCxv2+QGRS32/5Ns36fJ1iTD1mk1TGptf2Kvu2\nbDu1jW3SLDRj4Kd/+qfxH//xH/j617+OH/7hH8bb3va2Ntu1lRgFk9WbqWyo/pjeK/sx7aPsOPq2\nuwrZKYdXViyPTOk/ZZ+f52eR49S19SRzUmy17CHFrF7hp/H+Kj7X5IGY9ljhZ962L9LmJp/jlby2\nz867ZqemfjT1PesVf0zbNvlc2WfL2rWq81y373m+S1kfzNt/pvZtilXa6bL9rm83T9/rxzG1revM\nk7kw816LfbvIdS3atYp+XliQPf/5z4eVVVJ71rOehe9973utNWqbKRNAQjCZ5nTN+1O3z6p27Bpk\np0WqBJOKSTwt+9NGu04yJ8lWmziiTR6am4gsNXW2lmn3NjhNZXTVTudxkPn2zX6a7k9tx7rP7yLi\nLP/s/P3QRIhumnXY6Tz9XieMm/R9m/2+iejYIpR9r2Wv66pBmXnb0hatzCH7i7/4C7zsZS9rY1cn\nBlMao/yf4YSHDUKsZemIpuMSs5CdFjHNH9vUsYkiJ8lW1QdYG4vhrsvZK0vBXGZfJ42u2WndOStz\ntvTCFnNHQzt0fuuut6Z9ULVt3XG7xjrstMl9Tu/PRQqqVB33JFN1bc/br03tet19WynInv/85+O+\n++6bef/OO+/Ei1/8YgDAxYsX4boufumXfsm4jzsvXpSvz58/j/MXLizT3q1DFUgmcSa3W9JB3UUh\ndvnSJVy+fBl/ddddODoaAQCe8pSnyP/PY6cXL75Vvj5//gIu7JidAtUiaRGxRqKLc+nSJVy+fAkA\ncNdddwEo2imwO7aqP+DqxE4XnI1tbPOiCFu96667cDTa3nvqvIMA8wow/RhdZZ5+WKQP9GOsi67b\nqalP5hHHi+x/XprM41o0ijZPuft5WUT4LrLvNlCf/U3oTaeLD/995CMfwYc+9CH88z//M3zfn915\nr4fDo+NFd3+iqRJnTdhFAVbH/t4AJnNuYqdHx+N1NJEgsDfoG+0UIFslukWZrW6znS4a8dwGATYP\nJ6kfts1OF+n7rvT7vKXs18U29GnVsx9YImXxc5/7HN75znfiS1/6ktHQiWpIUK0HslNiWyBbJbaB\nbbfTrji2m+ak90OX7bRp5HIbzlHTqomr5iT06cIRsltvvRVhGOLMmTMAgB//8R/HBz/4weLO53sZ\njgAAIABJREFUKUJGrBFThKypnXZ1NJc4eZSNkpGtEl3DZKtkp+3RNCWsCw5vlyE7bc4yAqrMXpfd\n367Yd12EbKmUxTpIkBHrpCxlsY5dvCkTm6PuplwF2SqxTha1VbLTaro4N2ebITtthmp3i9hSld0u\ns79dses6O1247D1BEARBEATRnGXKjW9LqXKCqINseRYSZARBEARBEASxI8wriNoUUCTGzLSyDhlB\nEARBEARB7DpdrUSY9lihbZsoyNFlMbbp80aCjCAIgiAIgiCWxCQ42pwr1bZoaCrKdDG3SBtMn5+3\n/asSTas+b00gQUYQBEEQBEEQS7CJ6E8bUa6mwqPt6oxt7KfN779paA4ZQRAEQRDEGljGeexK6hsx\nSxOnflnHv+zz8+y3yoas/8fencdFVf3/A3/NMOwgSAqoqGhYggqCC2kumLnvZqamWWmplUXbr/rU\nN7HF+pTmR/OT2aJmftwzV7RyGdFUSHLfNVEgJXdZBhhmzu+PKyM7DMzcO8O8no/Hfdw7d+7cc2bm\nXDjvOeeeIwwWD05sJdgpjxzfW1WxhYyIiIhIJgysHJetTKRcEblancxJQ+nATo7vjS1kRERERETV\noHSwYG4eqhJYOML0DLaWT7aQEREREVlBTSfjreh8ljonkdzsqXVMLmwhIyIiIrKwkhVJa1QsHaWy\nSpWzpVay2sjanwcDMiIiIiILkjP4YsXZvlT3+7KH1tDadu+YnBiQEREREcnAkSqYjsDWvk9Lt5JZ\nmq0Elbb2vQEMyIiIiIiIHE5lAZKSgYulW9tsHQMyIiIishnWmA/J3tXmz8Oe35stBgTmfp6Weg+V\npWuLn5UtYUBGREREiisZiBU+lrPCLkd6thiAKPU5F6apxHetJFu7j6yyCaMrY+lgzFHKQVEMyIiI\niEhRlVXA5KiglRUM2oOaVNLLCoKtzRa+69quOp9hZUFZdQeVUSKIrIitBcOFGJARERGRYqpaQbJm\nRd3SIxhasvJmrfetxKiNtvBdU/mqck9ZyaUm5ysvDUfEgIyIiIgUYQuVLyXyYKk0rdVK4Kjfi5ys\nHewr/WMCgzHzMCAjIiIi2VWn8mVPwZMlRrCrTRXU2vReirLlwSqU+syt/ZnUtu6KAAMyIiIiogop\nEZRZ694cewqM7CmvcrLVgKcmr3X075oBGREREdkNe6u4Vee+nNo2hLi9fWfmsuUgxJZbhQrZ+oTW\ncmBARkRERFSJ2hBU1Ib3QBJzAhO5vndbDpZsPTCtcUA2a9YsqNVq3LhxwxL5IbIKllOyByynZA8s\nUU4dLTCwZKXOliu9tkbOv6m18Xsx5z3J0Uoo92csaythTV6cmpqK3377DU2bNrVUfogsjuWU7AHL\nKdkDWymnSgV0NUnXEpW7ms45poSaplvd1ytRVuUeWdAWW8nMYYt5UkqNArLXXnsNn332maXyQmQV\nLKdkD1hOyR6wnJLcqhuEsqyWZukJo805pqbk/jFC7tY4TXVfuH79egQFBSE8PLzC42Z8/LFpu2vX\nrujarVt1kyQqZndCAnbv3l3hMVUtpx9//JFpu2vXbujGckoWkpCQgN27Eyo8pqrlFGBZJeuprKxa\nspwaVU4O+et4Td63PbaOWYMl/6Za4+9pdb5jtTBU+/s1N73qpFVRGuyqWLaqlNOiVEIIUd6TvXr1\nwpUrV0rt//jjjzFjxgz8+uuvqFOnDpo1a4YDBw7gvvvuK35ylQqZ2TlmZJ/IfIMHDURGRgZOHD+O\n1q1bm/abU06zc3RyZ5sczKCBA5CRkYHj1SynAMsqWV9hOQVQrKxao5zWNEiwVCVN7l/P7SEgs2QF\n2Frfc03/plr776ncn7lcAU5hOvZSHpUs+0V5erijgpCr4oCsPMeOHUPPnj3h4eEBAEhLS0OjRo2Q\nlJQEf3//eydnQEYy8vb0KFbYzSmnrOSSXEr+Ua5qOQVYVkleRcuqNcqprQRkgG1XEJVI0x4CskLV\n/Zsqx99TOVuBbCXwqExtDVQrY5WArKRmzZohOTkZfn5+xU/OgIxkVDIgK6micspKLsmlsj/K5ZVT\ngGWV5FVRWbVEObXngKym6dt6AKhk66O5+aju31Q5/55W9XOo7UGZEmVRrs++MpWVU4vMQ6ZSqSxx\nGiKrYjkle8BySvbAEuVU7sonOSZb+Jtqq0Piy3kN2WowZlQ52cT3Y5EWsnJPzhYyklFlLWTlYasD\nyamyX8kqwrJKcqpuWTWnnDpqK5nc9/uYQ+nP1Nx8yFFOLamiz8QSn73S33lZlJqU2dqftTlkaSEj\nIiIiMpct/DKtBEd933SvRaZkGVCyTFizpUypYKysc5T32duCag97T0REZIts5Z4Bqhp7HgK/JsOV\nV4WjDnXvKNemNd5nda8nS4yeWN45zWXJPNhLWWILGRER1QpqYTB7Ph6yDbZQabLHuY7KYwsV4eqy\nhTzYO6UDeXP/FhMDMiIicmCsNNgOe62IW+s+KXv9PGrCEd+zLSoMqKozwbUt3RdqT9hlkYiI7B4D\nq9rBnO5Wttbdq7r5KStNe5vnrKJzsguxMizVFVjOv62OXAZsuoVsd0IC03agtG0h/epIUDDPjpq2\n0ukr/d6rw5E/r4SE3Qqm7bife3Vpd/+uWNpKfWZGlRO0u3+v8YAD1a08K3uN7LbLirg9XNvWGMDC\nGmWlqvlU+m+aNdO37YBst3J/IJi2Y6ZfHbt3KxhAO2jaSqev9HuvDkf+vBIU/ZvquJ97de3enVDh\naGjWHCWtMO3qqGlLgpLf1649e6x27sq+R2umbU32dG1b8pqx5N9Tc/Ol9N80a6bPLotEROTQrD1S\nHtWMEt+NEl0Xa8qWuioqmQ6Vr+R3oERXb5aDsjEgIyKyI/YQPJT8J6+q5kTYtUV5lR5b/h55T559\nBWW2HoyRbarO9y9UKpYbK1CJ6kxvXtWTq1TWOjVRmapTnFlOSW7V/bPLskpy499Usgcsp2QPKiqn\nVg3IiIiIiIiIqHw2PagHERERERFRbcaAjIiIiIiISCEMyIiIiIiIiBRiNwHZrFmzoFarcePGDdnS\nfPPNNxEaGoqIiAgMHz4ct2/ftnqaW7duRcuWLdGiRQv8+9//tnp6RaWmpqJHjx5o1aoVWrdujblz\n58qavsFgQGRkJAYNGiRrupbEcmp9SpdTwP7LqhLlFHCssspyahn8m2pdLKeWwXJqfUqXVauXU2EH\nLl26JPr06SOCg4PF9evXZUv3119/FQaDQQghxFtvvSXeeustq6ZXUFAg7r//fnHhwgWRn58vIiIi\nxIkTJ6yaZlGXL18WBw8eFEIIkZmZKR544AFZ0581a5YYM2aMGDRokGxpWhLLqTyULqdC2HdZVaqc\nCuFYZZXltOb4N9X6WE5rjuVUHkqXVWuXU7toIXvttdfw2WefyZ5ur169oFZLH1F0dDTS0tKsml5S\nUhJCQkIQHBwMZ2dnjBo1CuvXr7dqmkUFBgaibdu2AAAvLy+Ehobi77//liXttLQ0xMfHY+LEidUe\nElxpLKfyULKcAvZfVpUqp4BjlVWW05rj31TrYzmtOZZTedT2OqrNB2Tr169HUFAQwsPDFc3HwoUL\n0b9/f6umkZ6ejsaNG5seBwUFIT093appliclJQUHDx5EdHS0LOm9+uqr+Pzzz01/XOwNy6ljlFPA\nvsuqrZRTwLHKKsup+WylrLKcWhfLqWU4UjkFamcdVWO1M5uhV69euHLlSqn9H3/8MT755BP8+uuv\npn2WjkzLS3vGjBmmfqIff/wxXFxcMGbMGIumXZKtTFKYlZWFESNGYM6cOfDy8rJ6eps2bYK/vz8i\nIyOh1Wqtnl51sZxKHLWcAvZRVpUspxWl76hlleW0fPybKmE5ZTk1N21HLadALa6jWqUjpIUcPXpU\n+Pv7i+DgYBEcHCw0Go1o2rSpyMjIkC0PixYtEp07dxY6nc7qae3bt0/06dPH9HjGjBni008/tXq6\nReXn54vevXuL2bNny5bmO++8I4KCgkRwcLAIDAwUHh4eYty4cbKlX1Msp45RToWw77JqC+VUCMcq\nqyyn1WMLZZXl1PpYTmvOkcqpELW7jmrTAVlJct8wuWXLFhEWFiauXr0qS3p6vV40b95cXLhwQeTl\n5cl+w6TRaBTjxo0TsbGxsqVZklarFQMHDlQsfUtgObUuWyinQth/WVViUA9HKqssp5bDv6nWw3Jq\nOSyn1mULZdWa5dSuOu3K3Vw6depUZGVloVevXoiMjMQLL7xg1fQ0Gg3mzZuHPn36ICwsDE888QRC\nQ0OtmmZRv//+O5YuXYqdO3ciMjISkZGR2Lp1q2zpF7KVZvHqYjm1Llspp4B9l1Ul8u5IZZXl1HL4\nN9V6WE4th+XUumylrFrre1YJYafD2hAREREREdk5u2ohIyIiIiIiqk0YkBERERERESmEARkRERER\nEZFCGJAREREREREphAEZERERERGRQhiQERERERERKYQBGRERERERkUIYkBERERERESmEARkRERER\nEZFCGJAREREREREphAEZERERERGRQhiQERERERERKYQBGRERERERkUIYkMnMYDAgMjISgwYNKvP5\nl19+GS1atEBERAQOHjwoc+6IiIiIiEhODMhkNmfOHISFhUGlUpV6Lj4+HufOncPZs2fxzTffYMqU\nKQrkkIiIiIiI5MKATEZpaWmIj4/HxIkTIYQo9fyGDRswfvx4AEB0dDRu3bqFjIwMubNJREREREQy\nYUAmo1dffRWff/451OqyP/b09HQ0btzY9DgoKAhpaWlyZY+IiIiIiGSmUToDjmLTpk3w9/dHZGQk\ntFptuceVbDkr2bWxrK6ORERERESWUlZPLrIeBmQy2bt3LzZs2ID4+Hjk5ubizp07eOqpp7BkyRLT\nMY0aNUJqaqrpcVpaGho1alTqXLxIyBbFxcUhLi5O6WwQlcKySbaI5ZJsjRBAQgIQE8Mf/+XGLosy\nmTFjBlJTU3HhwgWsWLECjzzySLFgDAAGDx5s2rd//374+voiICBAiewSERERkQMoKABWrQI6dgSe\nf17p3DgmtpAppLDr4YIFCwAAkyZNQv/+/REfH4+QkBB4enpi0aJFSmaRiIiIiGqp7Gxg4UJg9myg\nYUPgvfeAQYMAJyelc+Z4VIL93+yKSqVil0WySVqtFjExMUpng6gUlk2yRSyXpJQrV4B584AFC4Bu\n3YA33gA6dbr3POua8mNAZmd4kRARERGRuU6cAL74AvjpJ2DMGCA2FmjRovRxrGvKj10Wawk/Pz/c\nvHlT6WyQA6lbty5u3LihdDaIiIioHEIAu3YBM2cCBw4AL74InD0L1KundM6oKLaQ2ZnyfrXgrxkk\nN5Y5IiIi26TXA6tXSy1iWVnA668DY8cC7u6Vv5b/3+XHFjIiIiIiolrg9m3g22+BuXOB5s2BadOA\nAQMANcdVt2kMyIiIiIiI7NjFi8CcOcDixUDfvsDPPwPt2imdK6oqxstERERERHYoKQkYNQqIipJa\nwQ4dApYtYzBmbxiQkV1r3bo1EhISlM4GERERkSwMBmDtWqBLF+CJJ4DoaODCBWngjiZNlM4dVQcD\nMpLNsmXL0L59e3h7e6Nhw4bo378/fv/99xqd89ixY+jWrRsAIC4uDuPGjbNEVomIiIhsSmamdG9Y\nixZS8BUbK42Y+OqrQJ06SueOaoIBGcniiy++wKuvvor33nsP//zzD1JTU/Hiiy9iw4YNSmeNiIiI\nyGZdugS8+SbQrBmwZw/wv/8Be/cCI0YAGo4GUSswICOru337NqZNm4avvvoKQ4cOhbu7O5ycnDBg\nwAD8+9//RlJSEjp16oS6deuiYcOGmDp1KvR6PQBgypQpePPNN4udb8iQIfjPf/4DAAgODsb27dux\ndetWfPLJJ1i5ciW8vb0RGRmJNWvWoH379sVe+8UXX2Do0KHyvHEiIiKiatq/X+qSGBkpdVP84w9g\n1SqgUyelc0aWxoBMJrm5uYiOjkbbtm0RFhaGd955p9QxWq0WPj4+iIyMRGRkJD766CMFcmp5+/bt\nQ25uLoYNG1bm8xqNBnPmzMH169exb98+bN++HV999RUAYMyYMVi5cqXp2Js3b+K3337DqFGjAEhz\nZahUKvTt2xf/+te/MGrUKGRmZuLgwYMYPHgwLly4gFOnTple/+OPP2L8+PFWfLdERERE1VNQIM0f\n1qkTMGaMtL5wQZpPrFkzpXNH1sKGTpm4ublh586d8PDwQEFBAbp06YI9e/agS5cuxY7r3r271brx\nqVSWOY+5cwVev34d9erVg7qcSTCioqJM202bNsXzzz+PXbt24ZVXXkGXLl2gUqmwe/dudO3aFWvW\nrEHnzp0RGBhYRr5EsYkMXVxcMHLkSCxduhQfffQRjh8/josXL2LgwIHmvQEiIiIiK7p1C/juO+DL\nL6WBOd58ExgyBHByUjpnJAe2kMnIw8MDAJCfnw+DwQA/P79Sx1hzZnQhLLOY67777sO1a9dgNBrL\nfP7MmTMYOHAgGjRoAB8fH7z77ru4fv06AKkFbNSoUVi+fDkAaWCQJ598ssppjx8/HsuWLQMgtY49\n8cQTcHZ2Nv9NEBEREVnY2bPA1KnSJM6HDgE//QTs3g0MH85gzJEwIJOR0WhE27ZtERAQgB49eiAs\nLKzY8yqVCnv37kVERAT69++PEydOKJRTy+rUqRNcXV3x888/l/n8lClTEBYWhnPnzuH27dv4+OOP\niwVvo0ePxpo1a3Dx4kUkJSXhscceK/M8qjKaAB966CG4uLggISEBy5cv5yiMREREpCghgO3bgUGD\ngIcfBnx8gGPHgKVLgRK3vpODYJdFGanVahw6dAi3b99Gnz59oNVqERMTY3o+KioKqamp8PDwwJYt\nWzB06FCcOXOm1Hni4uJM2zExMcXOYYt8fHzwwQcf4MUXX4RGo0GvXr3g7OyMbdu2QavVIisrC97e\n3vDw8MCpU6cwf/58+Pv7m17ftm1b1KtXDxMnTkTfvn1Rp5yxXQMDA7Ft2zYIIYoFZ+PGjcNLL70E\nFxcXdO7c2ervl4iIiKgknU4aIXHuXMBolIatX7UKcHdXNl9arRZarVbZTDg4lbBmHzkq14cffgh3\nd3e88cYb5R7TrFkzJCcnF+vaqFKpyuzWWN5+W7Js2TLMnj0bJ0+ehLe3N9q3b493330Xer0ezz//\nPNLS0hAZGYkePXpg586dxSZ8/uijjzBt2jSsWrWqWAtZs2bN8P333+ORRx7BjRs3MGTIEBw/fhzN\nmzfHgQMHAACXLl1Cs2bN8P7772PatGmyv+/ayh7KHBERkdLS0oCvvpLuEYuOBl55BejZ03L39lsa\n/7/LjwGZmebOnYtx48ahbt26Zr3u2rVr0Gg08PX1hU6nQ58+fTBt2jT07NnTdExGRgb8/f2hUqmQ\nlJSEkSNHIiUlpdh57DkgU4pOp0NAQAAOHjyI+++/X+ns1Bosc0REROXbvx+YMwf45Rdg7FjpXrEW\nLZTOVeX4/11+7LJopoyMDHTo0AFRUVF49tln0adPnzLvXSrp8uXLGD9+PIxGI4xGI8aNG4eePXti\nwYIFAIBJkyZhzZo1mD9/PjQaDTw8PLBixQprvx2HMH/+fHTs2JHBGBEREVlVfr40bP3cucDVq8DL\nLwNffy3dJ0ZUHraQVYPRaMSvv/6KxYsX48CBAxg5ciQmTJggS4WfLWTmCQ4Ohkqlwrp16xAREaF0\ndmoVljkiIiJJRoYUeH39NdCqldQtsX9/+xwpkf/f5ccWsmpQq9UIDAxEQEAAnJyccPPmTYwYMQKP\nPvooPv/8c6WzR0WU7PJJREREZCkHDkitYRs3AiNHAr/9BrRurXSuyN6whcxMc+bMwZIlS3Dfffdh\n4sSJGDZsGJydnWE0GtGiRQucP3/equmzhYxsBcscERE5ovx8ab6wuXOBv/8GXnwRmDgRKGN6WbvE\n/+/yYwuZmW7cuIG1a9eiadOmxfar1Wps3LhRoVwRERERkTVduQJ8843ULbFlS+D//T9pLjENa9NU\nQ5wY2kznz58vFYwVTjZccqJnIiIiIrJvSUnAuHFAaCiQni6NmrhjBzBsGIMxsgwWIzMdP3682OOC\nggIkJycrlBsiIiIisrS8PGnS5i+/BK5dA154QRrCvrZ0SyTbwoCsimbMmIFPPvkEOp0O3t7epv3O\nzs54/vnnFcwZEREREVlCWprUJfHbb4G2bYH33wf69bPP0RLJfnBQDzO9/fbb+PTTTxVLn4N62Kb+\n/ftj9OjRpu6rNaVWq3Hu3Dk0b97cIuezBpY5IiKqDYQAEhKAefOA7dulSZxffBF48EGlc6YM/n+X\nH+8hq6JTp04BAB5//HH8+eefpRaqmpiYGPj5+SE/P7/Y/uDgYOzYsUOhXNVcfHy8KRhbvHgxunbt\nKnsezE03JSUFarUaRqPRirkiIiKyTVlZUmtYmzbA5MlA9+7AxYvS6ImOGoyRMthlsYpmzZqFb7/9\nFq+//jpUKlWp53fu3KlAruxLSkoKkpKS0KRJE2zYsAEjRowwPcdfY5TDz52IiBzJ6dPAV18BP/4I\nxMRIAViPHkAZ1TsiWbCFrIq+/fZbAIBWq8XOnTtLLVS5JUuW4NFHH8W4cePwww8/mPaPGzcOly5d\nwqBBg+Dt7Y2ZM2cCADZs2IBWrVqhbt266NGjh6mVEpBa1GbOnInw8HB4e3tjwoQJyMjIQL9+/eDj\n44NevXrh1q1b5eZl06ZNaNu2LerWrYuHH34YR48eBQCsXLkSzZs3R2ZmJgBgy5YtaNCgAa5fvw4A\nWL9+Pdq2bQsfHx+EhITg119/BSC1/H3//fc4deoUJk+ejH379sHb2xt+d+/+zcvLwxtvvIGmTZsi\nMDAQU6ZMQW5urik/n3/+ORo2bIigoCAsXLiwws9x8eLFuP/++1GnTh00b94cy5YtKzfdzZs3IzIy\nEj4+PmjSpAmmT59uOk+3bt0AAL6+vvD29kZiYiIAYOHChQgLC4Ofnx/69u2LS5cuVZgfIiIiW1dQ\nAKxbB/TuDXTrBnh5AYcOAWvXAo88wmCMFCaoStasWSN++umncpfK6HQ60bFjRxERESFCQ0PF22+/\nXeZxU6dOFSEhISI8PFz8+eefpZ4v7yuzh6/y/vvvF0uXLhVnzpwRzs7OIiMjw/RccHCw2L59u+nx\n6dOnhaenp9i2bZsoKCgQn332mQgJCRF6vd50fKdOncQ///wj0tPThb+/v4iMjBSHDh0Subm54pFH\nHhHTp08vMx9//vmn8Pf3F0lJScJoNIoffvhBBAcHi/z8fCGEEE8++aR4+umnxbVr10TDhg3F5s2b\nhRBCJCYmCh8fH7Ft2zYhhBDp6eni1KlTQgghYmJixPfffy+EEGLx4sWiS5cuxdKMjY0VQ4YMETdv\n3hSZmZli0KBB4p133hFCCLFlyxYREBAgjh8/LrKzs8Xo0aOFSqUS58+fL5X3rKwsUadOHXHmzBkh\nhBBXrlwRx48fLzddrVYrjh07JoQQ4siRIyIgIECsW7dOCCFESkqKUKlUwmAwmI5ft26dCAkJEadO\nnRIGg0F89NFHonPnzmV+jvZQ5oiIyLFlZAjx8cdCNG4sxEMPCbFkiRA6ndK5sm38/y4/dlmsoo0b\nN5bZVbHQ8OHDK3y9m5sbdu7cCQ8PDxQUFKBLly7Ys2cPunTpYjomPj4e586dw9mzZ5GYmIgpU6Zg\n//79FnsPqumW+flHTDO/i9uePXuQnp6OwYMHw9vbG2FhYVi2bBliY2PLPH7lypUYOHAgevbsCQB4\n4403MGfOHOzdu9fUsjN16lTUr18fANC1a1cEBAQgIiICADBs2DBs3769zHN/8803mDRpEjp06AAA\neOqppzBjxgzs27cP3bp1w3//+1+Eh4ejR48eGDx4MPr37w8A+P777zFhwgRTnho2bFj251OiC6AQ\nAt9++y2OHDkCX19fAMA777yDJ598EjNmzMCqVavw7LPPmuaxmz59OlasWFHuZ6lWq3H06FEEBQUh\nICAAAQEBZaYLAN27dzdtt2nTBqNGjcKuXbswZMiQMo//+uuv8c477+DBu53n33nnHcyYMQOpqalo\n3LhxuXkiIiKyFUIA+/ZJ3RI3bwYee0xqHYuKUjpnRGVjQFZFixcvrvE5PDw8AAD5+fkwGAymbmWF\nNmzYgPHjxwMAoqOjcevWLWRkZJgq3DVVnUDKUn744Qf07t3bNGXA448/jh9++KHcgOzy5cto0qSJ\n6bFKpULjxo2Rnp5u2lf0c3F3dy/22M3NDVlZWWWe++LFi1iyZAm+/PJL0z69Xo/Lly8DAHx8fDBi\nxAjMnj0ba9euNR2TlpaGAQMGmPO2AQBXr15FTk4O2rVrZ9onhDANpnH58mVTcAig2PsuydPTEytX\nrsTMmTMxYcIEPPzww5g1a5YpgCopMTERb7/9No4fP478/Hzk5eVh5MiR5Z7/4sWLeOWVV/D6668X\n25+ens6AjIiIbFp2NrBsGTB/PpCZCUyZIs0jVreu0jkjqhgDsipaunQpxo4di1mzZpkGoCi6fu21\n1yo9h9FoRFRUFM6fP48pU6aYWkQKlaz0BgUFIS0tzWIBmVJ0Oh1WrVoFo9GIBg0aAJDuqbp16xaO\nHj2KNm3alGp9bNiwoem+LkAKYFJTU9GoUaNy0ymrxacsTZo0wbvvvot//etfZT5/6NAhLFq0CGPG\njMHUqVOxZcsWAEDjxo1x7ty5Ss9f8r3Uq1cP7u7uOHHihOn9F9WgQYNi92lVds9W79690bt3b+Tl\n5eHdd9/Fc889h4SEhDJbcMeMGYOXX34Zv/zyC1xcXPDqq6/i2rVrZeYTkD6b//u//8Po0aMrfZ9E\nRES24NQpKQhbuhTo2hX49FPg0UcBNUdKIDvBolpF2dnZAIDMzExkZmYiKyvLtF04AERl1Go1Dh06\nhLS0NCQkJECr1ZY6pmRQUValOS4uzrSUdQ5bs27dOmg0Gpw8eRKHDx/G4cOHcfLkSXTOueV2AAAg\nAElEQVTt2tU0uEdAQADOnz9ves3IkSOxefNm7NixA3q9HrNmzYKbmxs6d+5c4/w899xz+Prrr5GU\nlAQhBLKzs7F582ZkZWUhNzcXY8eOxSeffIKFCxciPT0d8+fPBwBMmDABixYtwo4dO2A0GpGeno7T\np0+XOn9AQADS0tKg1+sBSN/7c889h9jYWFy9ehWAFHwXDggycuRILF68GCdPnkROTk6xgTdK+uef\nf7B+/XpkZ2fD2dkZnp6ecLo7W2XJdAEgKysLdevWhYuLC5KSkrBs2TJTmapfvz7UanWxz33y5MmY\nMWMGTpw4AQC4ffs2Vq9eXe3PmoiIyBr0euCnn4CePaWREr29gYMH7w3cwWCs6rRabbG6JSlAoXvX\nHN4HH3wgPv/882L7Jk2aJJYvX256/OCDD4orV64UO6a8r8yWv8q+ffuKN954o9T+VatWiQYNGgiD\nwSDWr18vmjRpInx9fcWsWbOEEEL8/PPPIiwsTPj4+IiYmBhx4sQJ02tLDgIyduzYYoN4fPfdd6JX\nr17l5mnr1q2iQ4cOwtfXVzRo0ECMHDlSZGZmitjYWNG/f3/TcYcPHxZ+fn7i3LlzpjyFh4cLb29v\nERISIn799VchRPFBPfLz88WAAQOEn5+fqF+/vhBCiNzcXPGvf/1LNG/eXNSpU0eEhoaKL7/80pTO\np59+KgIDA0WjRo3EwoULhVqtLnNQj8uXL4vu3bsLHx8f4evrK3r06CFOnjxZbrpr1qwRTZs2Fd7e\n3mLgwIFi6tSpYty4cabzvf/++6J+/frC19dXJCYmCiGE+PHHH0WbNm1EnTp1ROPGjcWECRPK/Axt\nucwREVHtlJoqxPvvC9GwoRBdugixfLkQeXlK56p24f93+amE4CRE5jh//jxiY2Oxb98+qFQqdO7c\nGbNnz0bz5s0rfN21a9eg0Wjg6+sLnU6HPn36YNq0aaYBIgBpUI958+YhPj4e+/fvR2xsbKlBPcqb\nr4vzeJHcWOaIiEgORiOwbZvULXHXLmD0aOn+sNatlc5Z7cT/7/LjPWRmGjNmDF566SXTYA8rV67E\n6NGjTXM4lefy5csYP348jEYjjEYjxo0bh549e2LBggUAgEmTJqF///6Ij49HSEgIPD09sWjRIqu/\nHyIiIiJbdO0asHgx8PXXUpfEKVOkyZy9vJTOGZFlsYXMTOHh4Thy5EixfRERETh8+LAs6bOFjGwF\nyxwREVmaEMDevVIQtnEjMGSIFIhFR3PyZrnw/7v82EJWRTdu3IAQAv369cMnn3xiGoVu5cqV6Nev\nn8K5IyIiIrJft29LoyR+/TWQnw9MngzMmQOUmCGIqFZiC1kVBQcHlzniobg77P2FCxdkyUd5v1r4\n+fnh5s2bsuSBCADq1q2LGzduKJ0NIiKyY8nJUhC2Zg3Qq5cUiPXowdYwJbGFTH4MyOwMLxIiIiKy\nZ1lZwIoVUiB27Rrw3HPAs88CZUzVSQpgXVN+DMiq4dixYzhx4gRyc3NN+5566ilZ0uZFQkRERPbo\nyBFgwQJg+XJpAudJk4A+fYC702mSjWBdU368h8xMcXFx2LVrF44fP44BAwZgy5Yt6NKli2wBGRER\nEZG9yMkBVq2SArHUVGDiRODwYaBxY6VzRmQ72EJmptatW+Pw4cOIiorC4cOHkZGRgSeffBLbtm2T\nJX3+akFERES27tgxKQhbtgx46CGpNax/f0DDpgCbx7qm/HhZmMnd3R1OTk7QaDS4ffs2/P39kZqa\nqnS2iIiIiBSl0wGrV0uBWEoKMGEC8OefQNOmSueMyLYxIDNThw4dcPPmTTz33HNo3749PD090blz\nZ6WzRURERKSIY8eAb74B/vc/oGNH4M03gYED2RpGVFXsslgDKSkpuHPnDsLDw2VLk83IREREpLTC\ne8O++Qa4eFFqDZswga1htQHrmvLjbxdmEkJg7dq12LNnD1QqFbp27SprQEZERESklEOHgG+/lYat\n79QJePtt3htGVFNqpTNgb1544QUsWLAA4eHhaN26NRYsWIAXXnih0telpqaiR48eaNWqFVq3bo25\nc+eWOkar1cLHxweRkZGIjIzERx99ZI23QERERFRlmZlSENaxIzB4MFC/PnDwILBpk/SYwRhRzbDL\noplatmyJEydOQK2WYlmj0YiwsDCcOnWqwtdduXIFV65cQdu2bZGVlYV27dph3bp1CA0NNR2j1Wrx\nxRdfYMOGDeWeh83IREREZG1CAAcOSIHY6tVATIw0gTPnDav9WNeUH3/TMFNISAguXbqE4OBgAMCl\nS5cQEhJS6esCAwMRGBgIAPDy8kJoaCj+/vvvYgEZAF4AREREpJibN6XBOb77DrhzR5o37MQJoEED\npXNGVHsxIKuiQYMGAQAyMzMRGhqKjh07QqVSISkpCR06dDDrXCkpKTh48CCio6OL7VepVNi7dy8i\nIiLQqFEjzJw5E2FhYRZ7D0REREQlCQHs3i21hm3cCPTtC8yaBfToAah5cwuR1TEgq6LXX3+92GOV\nSgVAatEq3K6KrKwsjBgxAnPmzIGXl1ex56KiopCamgoPDw9s2bIFQ4cOxZkzZ0qdIy4uzrQdExOD\nmJiYqr8RIiIiIgAZGcCSJVJrmJOT1CVx9mygXj2lc0Zy0mq10Gq1SmfDofEesmq4cuUK/vjjD6hU\nKnTs2BH+/v5Vep1er8fAgQPRr18/xMbGVnp8s2bNkJycDD8/P9M+9uslIiKi6jIYgF9+Ab7/Hti+\nHRg2TArEOnUCzPh9mWox1jXlx4ZoM61atQrR0dFYvXo1Vq1ahY4dO2L16tWVvk4IgQkTJiAsLKzc\nYCwjI8N0ASQlJUEIUSwYIyIiIqqOlBTg/feB4GAgLk4anOPSJWDRIqBzZwZjREpiC5mZwsPDsW3b\nNlOr2NWrV9GzZ08cOXKkwtft2bMH3bp1Q3h4uKmL44wZM3Dp0iUAwKRJk/Df//4X8+fPh0ajgYeH\nB7744gs89NBDxc7DXy2IiIioKvLygHXrpNawP/8ExoyRJm+OiFA6Z2TLWNeUHwMyM7Vp0wZHjhwx\nBVVGoxERERE4evSoLOnzIiEiIqKKHD0qBWH/+x8QHi4FYcOGAe7uSueM7AHrmvLjoB5m6tu3L/r0\n6YMxY8ZACIGVK1eiX79+SmeLiIiIHNidO8CKFdIAHX//DTzzDJCYCDRvrnTOiKgybCEzgxACqamp\n+OOPP/D7778DALp27Yphw4bJlgf+akFERETAveHqv/8eWL8e6NlTag3j5M1UE6xryo8BmRmEEGjT\npg2OHTumWB54kRARETm2v/8GfvgBWLgQcHGRgrCxY4EqDvpMVCHWNeXHURbNoFKp0K5dOyQlJSmd\nFSIiInIg+fnAzz8DgwYBrVoBFy4AP/4IHDsGvPYagzEie8YWMjM9+OCDOHfuHJo2bQpPT08AUqBW\n2SiLlsJfLYiIiBzH8eNSS9jSpUDLltK9YY8/DtytghBZHOua8uOgHmb65ZdfAMA0yiILLBEREVnS\n7dvAypXSvWFpacDTTwN79gAtWiidMyKyBraQVUNycjL27NkDtVqNhx9+GFFRUbKlzV8tiIiIah+j\nEdBqpYmaN268N0BH796Ahj+fk4xY15Qf7yEz0wcffICnn34aN27cwNWrV/HMM8/gww8/VDpbRERE\nZIcuXgSmTwfuvx949VWgfXvg3Dngp5+A/v0ZjBE5AraQmemBBx7AkSNH4ObmBgDQ6XSIiIjAmTNn\nZEmfv1oQERHZt5wcaYCORYuAQ4eA0aOle8MiI4G7d0QQKYZ1TfnxdxczNWrUCDqdzhSQ5ebmIigo\nSOFcERERkS0TQpqoedEiYPVqIDoaeP55YPBg4G6VgogcFLssmqlOnTpo1aoVnn76aTz99NNo3bo1\nfHx8MHXqVLz88svlvi41NRU9evRAq1at0Lp1a8ydO7fM415++WW0aNECEREROHjwoLXeBhEREcng\n8mXgs8+AsDDgqaeA4GDg6FFgyxZg5EgGY0TEFjKzDRs2DMOGDQMgNenGxMSYmnZVFfQzcHZ2xuzZ\ns9G2bVtkZWWhXbt26NWrF0JDQ03HxMfH49y5czh79iwSExMxZcoU7N+/3+rviYiIiCwnL08amGPR\nImDvXmD4cOC774DOndklkYhKY0BmpqeffrparwsMDERgYCAAwMvLC6Ghofj777+LBWQbNmzA+PHj\nAQDR0dG4desWMjIyEBAQUON8ExERkfUIAfz5pxSErVgBRERIw9WvWsU5w4ioYgzIFJCSkoKDBw8i\nOjq62P709HQ0btzY9DgoKAhpaWkMyIiIiGzUlSvA//4HLF4MZGdLQdiBA1LXRCKiqmBAJrOsrCyM\nGDECc+bMgZeXV6nnS45qU1Y3yLi4ONN2TEwMYmJiLJ1NIiIiKkdeHrBpkxSE7dkDDB0KzJsHdO0K\nqHl3PtkZrVYLrVardDYcGoe9l5Fer8fAgQPRr18/xMbGlnp+8uTJiImJwahRowAALVu2xK5du4q1\nkHEoUiIiIvkJASQnS0HYihVAeLjUGjZ8OFDG76tEdot1TfmxhcxMp0+fxsyZM5GSkoKCggIAUsHd\nsWNHha8TQmDChAkICwsrMxgDgMGDB2PevHkYNWoU9u/fD19fX3ZXJCIiUtDly8DSpVIglpsLjB/P\nLolEZFlsITNTeHg4pkyZgqioKDg5OQGQArJ27dpV+Lo9e/agW7duCA8PN3VDnDFjBi5dugQAmDRp\nEgDgpZdewtatW+Hp6YlFixYhKiqq2Hn4qwUREZF15eYC69dLQdj+/cBjj0mBWJcuHCWRaj/WNeXH\ngMxM7dq1Q3JysmLp8yIhIiKyPCGAffuAH34A1qwB2rWTgrBhwwAPD6VzRyQf1jXlx4DMTHFxcahf\nvz6GDx8OV1dX034/Pz9Z0udFQkREZDkpKcCPPwJLlgBOTlIQNnYsUGTQYyKHwrqm/BiQmSk4OLjU\nyIcqlQp//fWXLOnzIiEiIqqZzEypFWzJEuDoUeCJJ6RArEMHdkkkYl1TfgzI7AwvEiIiIvMZDMD2\n7VIQtmkT0L27FIQNGAAU6fBC5PBY15QfAzIz5efnY/78+UhISIBKpUL37t0xefJkODs7y5I+LxIi\nIqKqO35cCsKWLgUaNgSeegoYNQqoX1/pnBHZJtY15ceAzEwTJkxAQUEBxo8fDyEEfvzxR2g0Gnz3\n3XeypM+LhIiIqGL//AMsXy4FYhkZ0j1h48YBrVopnTMi28e6pvwYkJkpPDwcR44cqXSftfAiISIi\nKk2nAzZskAbo2LMHGDxYCsIeeUQarIOIqoZ1TflxYmgzaTQanDt3DiEhIQCA8+fPQ6Phx0hERCQ3\noxHYvVsKwtauBdq3l4KwFSsALy+lc0dEVDWMJMz0+eef45FHHkGzZs0AACkpKVi0aJHCuSIiInIc\np05JQdj//gd4e0v3hR09CjRqpHTOiIjMxy6L1ZCbm4vTp09DpVLhwQcfLDYfmbWxGZmIiBzRP/9I\nLV8//gikpwNjxkitYeHhHKqeyJJY15QfA7Iq2r59O3r27ImffvqpWEEtnJNs+PDhsuSDFwkRETmK\nnJx794X9/jswaJAUhPXsyfvCiKyFdU35sctiFSUkJKBnz57YuHFjqYmhgaoFZM8++yw2b94Mf39/\nHD16tNTzWq0WQ4YMQfPmzQEAjz32GN57772aZ56IiMhOGAzAzp3SMPXr1wPR0dIoiStX8r4wIqqd\n2EJmpr/++ssUMFW0ryy7d++Gl5cXnnrqqXIDsi+++AIbNmwo9xz81YKIiGobIYDDh6V7wpYtAwID\npSBs9Ghpm4jkw7qm/NRKZ8DejBgxotS+xx9/vEqv7dq1K+rWrVvhMbwAiIjIUVy8CHzyCdCmDTB0\nKODsDPz2G5CcDLz6KoMxInIM7LJYRSdPnsSJEydw69YtrF27FkIIqFQq3LlzB7m5uRZJQ6VSYe/e\nvYiIiECjRo0wc+ZMhIWFWeTcREREtuDGDWD1aqk17MQJYMQI4Ouvgc6dATV/JiYiB8SArIrOnDmD\njRs34vbt29i4caNpv7e3N7799luLpBEVFYXU1FR4eHhgy5YtGDp0KM6cOVPquLi4ONN2TEwMYmJi\nLJI+ERGRNeTkABs3St0RtVqgTx/g9deBfv0AFxelc0fk2LRaLbRardLZcGi8h8xMe/fuRefOnav9\n+pSUFAwaNKjMe8hKatasGZKTk+Hn52fax369RERkDwoKgO3bpSBswwagQwdpqPrhw4E6dZTOHRGV\nh3VN+bGFzEyRkZGYN28eTpw4AZ1OZxpxceHChTU+d0ZGBvz9/aFSqZCUlAQhRLFgjIiIyJYJASQm\nSkHYqlVAkybAk08Cn34KNGigdO6IiGwTAzIzjRs3DqGhodi6dSumTZuGpUuXIjQ0tEqvHT16NHbt\n2oVr166hcePGmD59OvR6PQBg0qRJWLNmDebPnw+NRgMPDw+sWLHCmm+FiIjIIo4fB5YvlwIxFxep\nJSwhAXjgAaVzRkRk+9hl0Uxt27bFoUOHEB4ejiNHjkCv16NLly5ITEyUJX02IxMRkS24eBFYsUIK\nwq5fl4aoHz0aiIwEypiuk4jsBOua8mMLmZlc7t597OPjg6NHjyIwMBBXr15VOFdERETWd+WKNELi\n8uXA2bPS/WBz5wJdu3KERCKi6mJAZqbnnnsON27cwEcffYTBgwcjKysLH374odLZIiIisoqbN4G1\na6UgLDkZGDQIeO89oFcvad4wIiKqGXZZtDNsRiYiImvLzJRGRlyxQroXrFcvYNQoYMAAwN1d6dwR\nkTWxrik/BmRmunbtGqZPn449e/ZApVKha9eueP/993HffffJkj4vEiIisoacHGDzZmDlSuC336Ru\niKNGAYMHc5h6IkfCuqb8GJCZ6dFHH0X37t0xduxYCCGwbNkyaLVabNu2TZb0eZEQEZGl5OYCv/wi\nBWHx8UDHjsATTwDDhgGcdYXIMbGuKT8GZGZq3bo1jh07VmxfmzZtqjTRsyXwIiEioprIywN+/VWa\nJ2zTJqBtWykIGz4c8PdXOndEpDTWNeXHMZHM1Lt3byxfvhxGoxFGoxErV65E7969lc4WERFRufLz\npe6ITz8tTdD8+efAQw8BJ08CO3cCkyczGCMiUgpbyMzk5eWFnJwcqO+O72s0GuHp6QlA+kXhzp07\nVk2fv1oQEVFV5OVJ94KtXg1s3AiEhQGPPw6MGAE0aqR07ojIVrGuKT8GZHaGFwkREZUnN/deELZp\nE9CqlRSEPfYYgzAiqhrWNeXHgMxMCQkJZe7v1q2bLOnzIiEioqJycoCtW4E1a4AtW4DwcKkV7LHH\ngIYNlc4dEdkb1jXlx4DMTAMHDoRKpQIA5ObmIikpCe3atcOOHTsqfe2zzz6LzZs3w9/fv9xBQF5+\n+WVs2bIFHh4eWLx4MSIjI4s9z4uEiIgyM6V7wn76SRqgo2NHKQAbOhQIDFQ6d0Rkz1jXlJ9G6QzY\nm02bNhV7nJqaildeeaVKr33mmWcwdepUPPXUU2U+Hx8fj3PnzuHs2bNITEzElClTsH///hrnmYiI\n7N+1a9JkzT//DOzaBTz8sNQSNn8+UK+e0rkjIqLqYkBWQ0FBQTh58mSVju3atStSUlLKfX7Dhg0Y\nP348ACA6Ohq3bt1CRkYGAgICLJFVIiKyM2lpwLp1wNq1QHIy0KsXMHo0sHQp4OOjdO6IiMgSGJCZ\naerUqaZto9GIQ4cOoV27dhY5d3p6Oho3bmx6HBQUhLS0NAZkREQOQghpKPp166Tl/Hlg4EDglVeA\n3r0Bd3elc0hERJbGgMxM7dq1M91DptFoMGbMGDz88MMWO3/JPruFaRUVFxdn2o6JiUFMTIzF0ici\nInkZjUBi4r0gTKeT7gX79FOga1fA2VnpHBJRbabVaqHVapXOhkPjoB5mysrKgru7O5ycnAAABoMB\neXl58PDwqNLrU1JSMGjQoDIH9Zg8eTJiYmIwatQoAEDLli2xa9euYi1kvNGSiMj+5eQA27dL94Rt\n2gTUry8FYUOHApGRQBm/xRERyYJ1Tfmplc6AvXn00Ueh0+lMj3NycvDoo49a5NyDBw/GkiVLAAD7\n9++Hr68vuysSEdUSGRnA998DQ4ZIIyHOni3NE7ZnD3DkCPDBB0BUFIMxIiJHwy6LZsrNzYWXl5fp\nsbe3N3Jycqr02tGjR2PXrl24du0aGjdujOnTp0Ov1wMAJk2ahP79+yM+Ph4hISHw9PTEokWLrPIe\niIjI+oQADh+WWsA2bQJOnQL69AGeeAJYvBioW1fpHBIRkS1gQGYmT09PJCcnmwbyOHDgANyreJf1\n8uXLKz1m3rx5NcofEREpJycH2LHjXhDm5gYMGgR8/LF0P5iLi9I5JCIiW8OAzEz/+c9/MHLkSDRo\n0AAAcPnyZaxcuVLhXBERkVL++guIj5eWPXuAdu2kkRG3bwceeIBdEImIqGIc1KMa8vPzcfr0aQDA\ngw8+CBcZf/LkjZZERMrKywMSEoAtW6Qg7NYtoF8/oH9/aZ4wX1+lc0hEVH2sa8qPAZmZ5s2bhyef\nfBJ173b+v3nzJpYvX44XXnhBlvR5kRARyUsI4Nw54JdfgK1bpWCsdWspAOvfH2jbFlBziCwiqiVY\n15QfAzIzRURE4PDhw8X2tW3bFocOHZIlfV4kRETWl5kJ7NwpBWC//ALk5koDcvTtCzz6KODnp3QO\niYisg3VN+fEeMjMZjUYYjUao7/4cajAYTCMlEhGRfSooAP74A/jtN2k5dAiIjpaCsHXrpBYx3gtG\nRETWwIDMTH369MGoUaMwadIkCCGwYMEC9O3bV+lsERGRGYQAzpyRBt747TdAqwWaNJHuAXvvPWlE\nRA8PpXNJRESOgF0WzWQwGPDNN99g+/btAIBevXph4sSJcHJykiV9NiMTEVVPaqo0JP327dJapQIe\neQTo3Rvo2VOarJmIyNGxrik/BmRmys3NxdmzZwEAISEhVZ6DzFJ4kRARVc3ly8CuXVLr144dwM2b\nQI8eUvD1yCNASAi7IRIRlcS6pvwYkFWRXq/Hu+++i4ULF6JJkyYAgEuXLuGZZ57BjBkz4OzsLEs+\neJEQEZXt77/vBWC7dgH//AN06wZ07y4FYG3acDREIqLKsK4pPwZkVRQbG4usrCzMnj0b3t7eAIA7\nd+7g9ddfh4eHB+bMmSNLPniREBFJ94D99Rewe7e0JCQA169LwVf37kBMjBSAydSbnIio1mBdU34M\nyKooJCQEZ86cMY2uWMhgMODBBx/EuXPnKj3H1q1bERsbC4PBgIkTJ+Ktt94q9rxWq8WQIUPQvHlz\nAMBjjz2G9957r9gxvEiIyBEZDMDRo8Dvv98LwFQqafCNwqV1a7aAERHVFOua8uMoi1WkVqtLBWMA\n4OTkVOb+kgwGA1566SVs27YNjRo1QocOHTB48GCEhoYWO6579+7YsGGDxfJNRGSPbt8GEhOlAGzv\nXiApCWjYEHj4YaBfP2DGDKBZM94DRkRE9o8BWRWFhobihx9+wPjx44vt//HHH9GyZctKX5+UlISQ\nkBAEBwcDAEaNGoX169eXCsj4iwQRORqjETh5UgrA9u+Xlr/+Atq3Bzp3Bl55BejUCbjvPqVzSkRE\nZHkMyKrov//9L4YPH46FCxeiXbt2AIDk5GTk5OTg559/rvT16enpaNy4selxUFAQEhMTix2jUqmw\nd+9eREREoFGjRpg5cybCwsIs+0aIiBR2+TJw4IAUgCUmSq1f/v7SRMwPPQQ89xwQEQG4uCidUyIi\nIutjQFZFhQHUjh07cPz4cahUKgwYMAA9e/as0utVVehXExUVhdTUVHh4eGDLli0YOnQozpw5U+q4\nuLg403ZMTAxiYmKq+jaIiGR14waQnAz88ce9RacDOnSQlthYKRCrV0/pnBIROSatVgutVqt0Nhwa\nB/WQyf79+xEXF4etW7cCAD755BOo1epSA3sU1axZMyQnJ8PPz8+0jzdaEpGtunoV+PPPe0tysrQv\nKupeANahA+/9IiJ5CCEgIGAURhiFEULc2zbtQ/F9RY8p77Vl7S/cV53H5W0XHldyu+TxlthXdB3b\nKZZ1TZmxhUwm7du3x9mzZ5GSkoKGDRti5cqVWL58ebFjMjIy4O/vD5VKhaSkJAghigVjRES2wGgE\nLlwADh8GDh2S1n/+CWRmSsFXVBQwbBjw4YdAixYcep6oJCEECowFZi0GYbi3bTQU21fWY4MwFNtf\nuK/k8wZRYvvu2iiMxfYZhbHS7aKvKwxYytpXdL/pcSXPV3UpGTipoIJapYZKdXcNFZzUTqZttUpt\nWgqPKfmcSqUyva6s/SVfX1aaJR+X9VzR/WUdVzS9osebc1x5ry26JvkxIJOJRqPBvHnz0KdPHxgM\nBkyYMAGhoaFYsGABAGDSpElYs2YN5s+fD41GAw8PD6xYsULhXBORo7tzBzh2TFqOHJECsCNHAF9f\n6T6viAhg7Fjgiy+A5s3Z8kXyEEIg35CPPEOetC6Q1kX3VbToDfp720b9vX3Ge88X3a836stdFxgL\nSm0XGAtKPS4ZXGnUGmjUGjirnU3bTmqne9sqJzg7OcNJdW9f0WMK9xd9XNF20eOL7itcuzq5ltqn\nVqmL7VOr1GZvFz42bZezv+Rzhc+rVKpSxxUNgIo+V1ZAVZVbRqi4L/Gl0llwOOyyaGfYZZGIrCE3\nFzh9Gjh+XJrv69gxaX31KhAWJk2y3KYN0LYtEB7OEQ8dmRACuQW50BXooNPrTNu5BbnStv7edsnn\nii55hjxpXZBX6nGeIa/Y/sJ9hcGX3qiHs9oZrhpXuDi5wNXp7vru48J9zk7OpudcnFzg7OR8b1vt\nXGq/s9rZtL/YPifnCtcatabUdtFgq/Bx4T4GCmTLWNeUHwMyO8OLhIhqIisLOHMGOHHi3nL8OJCa\nCtx//73gq3Vrad28Obsc2gshBHQFOmTnZyNHn4Ns/d11icclF12Brvhjvc60v7qS87QAABC7SURB\nVOS2rkCHvII8uDi5wN3ZHe4ad7g7u8NN4wY3jRvcNdK2u7M7XJ1ciz1nWpzubbtqXKW1k6vpsauT\nq2ld1r7CIIoBDZF1sK4pPwZkdoYXCRFVxmgE0tKkFq/Tp4FTp+6tr18HQkKkwKtwadVK2ufsrHTO\nHYNRGJGdn42s/KwKl2x9drHtwtcUbpdc5+hz4KpxhYezBzydPeHp4mna9nD2MD0utmjubbs7u0tr\njXupxyWDL7VKrfTHSERWwrqm/BiQ2RleJEQESEFXejpw/jxw9mzx5a+/gLp1gQceAFq2BB58UFq3\nbAk0aQKoWZc2S2EAlZmficy8TNzJu2PaLra+u52Vn1VqOys/y/RYV6CDu8YdXi5epsXb1Ruezp7F\n9nm5eJn2ebp4mh6X3C4adDmp2ZxJRDXDuqb8GJDZGV4kRI4jOxtISZFGNPzrLyn4KlxSUqSBNe6/\nXxrJsHB54AGptcvTU+ncK6vwPqc7eXdKLZn5meXuKwy4iu7L0efAXeMOb1dv1HGtA28Xb3i7epe5\n9nLxKv24xLaHswdbmIjIZrGuKT8GZHaGFwlR7XHnDnDpkrRcvCgtFy5IS0qKNIx806bSvF3Nm0vB\n1/33S9vNm9fOoKvwPqg7eXdwO/d2saDpdt7tMgOs8p53UjlJAZSrN3xcfVDHtY7psWnb5d52ycdF\nAym2PBGRo2BdU34MyOwMLxIi+5CTI3UpTE2V7ucqXFJT7wVh+flSwNWkyb11s2bSEhwMBATYT/fC\nooGUKUCqJKAq+rjosRq1Bj5uPsWCqDqudeDj5gNvF2/4uPmgjov0uOjzdVzrmF7j7eoNFycXpT8W\nIiK7w7qm/BiQ2RleJETKys8HMjKAK1eAv/+WlvT00tvZ2UCjRkDjxkBQkLQUbhcGYHXrKj9vl1EY\nTfc3VdT6dCe/gueKBFIlg6OirVOFgVTJIKvk8QykiIiUw7qm/BiQ2RleJESWp9dL8239848UbJVc\nrlyRlsuXgdu3AX9/IDAQaNBACroaNQIaNpSWwu169awXbJUcZKLo/U/F7oXKv1NsEArTvVFFgq9s\nfTY8nD1MXfVKdu8r2Z2vrFapwv0MpIiI7B/rmvJjQGZneJEQVUwIaa6ta9ekId6vXbu3ffVq8eWf\nf6R1ZqY00XFAgBRsBQTcW/z9pcCrQQMpCKtXz/xuhHqDHtn6bNMoe4VL4eh7RUfgK2+0vqLrwkEm\nit7nVHLAiaL3QxUNtkreJ8X7o4iIqCjWNeXHgMzO8CIhR6HXAzdvArduSeuylhs3pOX69XvbN25I\n82nVqyct991XfO3vD9SvX3zx85OCrHxDfrlzPZU1F1SpuaLKmVtKb9SbBofwdPE0BU2FI/IVHfq8\nspH6Cl/HUfqIiMgaWNeUHwMyGW3duhWxsbEwGAyYOHEi3nrrrVLHvPzyy9iyZQs8PDywePFiREZG\nFnueFwnZKq1Wi5iYGBiN0v1Td+5ILU+ZmdJ24XL7dun17dtS4FW4vnVLulfL11e6z8q3roCPXx7q\n+Ong6ZsDT19p7eadAzdvHVw8cqDxyIHGLQdqVx3yhTRJbk5BjmnC3Gz93XUFj1VQwdPFs9T8TiXn\ngSo5H1TJeaMKg67CfW4aN6iUvlnMgRWWTSJbwnJJtop1TflplM6AozAYDHjppZewbds2NGrUCB06\ndMDgwYMRGhpqOiY+Ph7nzp3D2bNnkZiYiClTpmD//v0K5ppqs4ICaSTA7Ozy11lZJdbZAplZBbid\nk4s7ObnI1OUiKzcXWbpcXE1dBvg6IbcgF66euXDz1sHNKxcuHoWLDhp3HTRuOqhdc6H20QH1dIBG\nB+Gkg0Gtg4tKh7rQwUvokGvQIUefg78LdDiv18HZyRnuGnd4OHvA3Vlaezh7wMPgAY/ce2t3jbsp\nmKrjUgcNvBrcO7bIBLqFgVfRbWcnZ6W/FrICVnzJFrFcElEhBmQySUpKQkhICIKDgwEAo0aNwvr1\n64sFZBs2bMD48eMBANHR0bh16xYyMjIQEBCgRJbJyoSQgqK8vHtLfr601ukEsnP1yMzJR06eHtm6\nfGTn5SM7Nx85ufnIybu75OdDl5+PnLw85OrzodNL61x9HvIK8pFXkI98Qx7yjXnIN+RBb8yHXuSh\nQORBOOXByTUPTi7SonbJg8o5D9DkQqWRnhdOuRDqPBhUuTC45qLANQ8qPxVcVO5wcXKDq5MrXJ3c\n4O7shjq/3UCzoSfg5eoON2c3uGmkxV3jDleNK9w17nB3doe7pq5pv7uzu2m7MNC6d5y7KfBy17jz\nPiciIiKqlRiQySQ9PR2NGzc2PQ4KCkJiYmKlx6SlpTlsQCYEoC8wQl9gRL7egPwCadEXWefppbW+\nwAC9wYB8vbQuPEZaCu49f3c7v6BA2jaUXpe1FBjvbhv1KDAWoMBQgAJxd1voUWDUwyCkbUPhAmkx\n3l0M0EOo9DCqpLVQ6wGnfKicpDWc9IBaD+GUD6gLoDI6QyWcoTa6QA0XqIUznOACjcoVGpULNCoX\nOKtc4KxxgbOLC1ycXOGqcYGrxgV1Na5wc3aBu7O09nR1hYerK7zcvODl7govN1e4u7jAVeMKN83d\nwErjClenu49LbBc9RqMu+89G3K04xD0XJ28hISIiIrJzDMhkUtX7R0r22S3rdbwXpXYpr5e2gB4C\nehiRI2t+amL69On/v717i4nq+uI4/j2WVkVAyovXioq3QXBmCIVWvMdUJYI01iYQNF6DRsWmjdqm\nT03UxCZNoxIMakJCNJF6SzRe4oOAFiSYdjRm8IYyOt5jvGtSmHL6YP4T+DMIWJ0zld/naYaz2WcN\n2VmwXMe9rQ5BJCCtTQlFWpciAirIgmbAgAF4vV7/e6/Xy8CBA1875ubNmwwYMKDFGP0nSxERERGR\n94f2TQ6S5ORkrly5gsfjoaGhgdLSUjIzM1uMyczMpKSkBIDq6mqio6O77OOKIiIiIiJdgTpkQRIW\nFkZBQQHTpk3j77//ZtGiRdhsNoqKigDIy8sjPT2dI0eOMGzYMHr16kVxcbHFUYuIiIiIyLukDlkQ\nzZgxg0uXLlFXV8cPP/wAvCrE8vLy/GMKCgqoq6vj3Llz3L9/n1GjRjF8+HA2btwYcM78/HyGDx+O\n3W7H5XIF5XNI13bs2LHXrsvy8nJ69+6N0+nE6XSybt06C6KUrmbhwoX06dOHxMTENscoX4oV2lub\nypliBa/Xy+TJkxk9ejQJCQls3rw54DjlzSAxJST5fD4zLi7OrK+vNxsaGky73W7W1ta2GHP48GFz\nxowZpmmaZnV1tZmammpFqNKFdGRdlpWVmRkZGRZFKF3VyZMnzT///NNMSEgIeF35UqzS3tpUzhQr\n3Llzx3S5XKZpmuazZ8/MESNG6O9MC6lDFqKan1v24Ycf+s8ta66tc8tE3pWOrEvQ5jMSfOPHj+fj\njz9u87rypVilvbUJypkSfH379sXhcAAQERGBzWbj9u3bLcYobwaPCrIQFehMslu3brU75ubNm0GL\nUbqejqxLwzCoqqrCbreTnp5ObW1tsMMUaUX5UkKVcqZYzePx4HK5SE1NbfF15c3g0aYeIeptnlsm\n8rZ0ZH0lJSXh9XoJDw/n6NGjZGVlcfny5SBEJ/J6ypcSipQzxUrPnz/nq6++YtOmTURERLS6rrwZ\nHOqQhai3dW6ZyNvUkXUZGRlJeHg48Gojm8bGRh4+fBjUOEX+n/KlhCrlTLFKY2Mjs2fPJjc3l6ys\nrFbXlTeDRwVZiNK5ZRKKOrIu79275/8XtZqaGkzTJCYmxopwRfyULyVUKWeKFUzTZNGiRcTHx/PN\nN98EHKO8GTx6ZDFE6dwyCUUdWZd79+5l69athIWFER4ezu7duy2OWrqC7OxsKioqePDgAZ988gk/\n/fQTjY2NgPKlWKu9tamcKVaorKxk586djBkzBqfTCcCGDRu4ceMGoLwZbIaprX1EREREREQsoUcW\nRURERERELKKCTERERERExCIqyERERERERCyigkxERERERMQiKshERCQkDR482H8eU1pa2ju7z5Mn\nT9i6des7m7+5iooKTp8+7X8/f/589u3bF5R7i4hIaFJBJiIiIckwDP/rysrKd3afR48eUVhYGPCa\nz+d7q/cqKyujqqrK/775ZxQRka5JBZmIiLyRkpIS7HY7DoeDefPmAeDxeJgyZQp2u52pU6fi9XqB\n1p2giIgIAMrLy5kwYQIzZ85k1KhRLFu2jECnsTQfP2nSJObMmYPNZiM3N9c/5siRI9hsNpKTk8nP\nzycjI6PVPG63m9TUVJxOJw6Hg7q6Or7//nuuXr2K0+lkzZo1VFRUMH78eGbNmkVCQgJNTU2sXr2a\nlJQU7HY727Zte6NYrl+/TlFREb/++itJSUn8/vvvAJw8eZK0tDTi4uLULRMR6YJ0MLSIiHSa2+1m\n/fr1nD59mpiYGB4/fgzAypUrWbBgAXPnzqW4uJj8/HwOHDjQqhPU/P2ZM2e4cOECgwYNYvr06ezf\nv5/Zs2e3Of7s2bPU1tbSr18/0tLSqKqqIikpiaVLl3Lq1CliY2PJyckJ2H0qKipi1apV5OTk4PP5\n8Pl8bNy4EbfbjcvlAl4VWi6XC7fbTWxsLNu2bSM6Opqamhr++usvxo0bxxdffNHpWGJjY1m6dCmR\nkZF8++23AOzYsYO7d+9SWVnJhQsXyMzMbPXZRUTk/aYOmYiIdNqJEyf4+uuviYmJASA6OhqA6upq\ncnJyAMjNzfV3gV4nJSWFwYMH061bN7Kzs9v9npSUFPr3749hGDgcDurr67l48SJDhw4lNjYWgOzs\n7ICdts8//5wNGzbw888/4/F46NGjR8BxKSkp/rmOHz9OSUkJTqeTzz77jIcPH1JXV4dhGG8US/PX\nhmGQlZUFgM1m4969e+3+vERE5P2igkxERDrNMIyAhQwQ8OthYWE0NTUB0NTURENDQ4u5mn9vt26v\n/9XUvXt3/+sPPvgAn8/XqhvWVmzZ2dkcOnSInj17kp6eTllZWcBxvXr1avG+oKAAl8uFy+Xi6tWr\nTJ06FdM0/1Us//PRRx91eKyIiLx/VJCJiEinTZkyhT179vh3QXz06BEAY8eOZffu3QDs2rWLCRMm\nAK92TPzjjz8AOHjwII2Njf65ampq8Hg8NDU1UVpayrhx4zoVi2EYjBw5kmvXrnH9+nUASktLAz6y\nWF9fz5AhQ1i5ciWzZs3i/PnzREVF8ezZszbnnzZtGoWFhf4NPi5fvszLly/fKJbIyMjX3ktERLoe\nFWQiItJp8fHx/Pjjj0ycOBGHw8F3330HwJYtWyguLsZut7Nr1y42bdoEwJIlS6ioqMDhcFBdXe3f\npAPg008/ZcWKFcTHxxMXF8eXX37Z6n7Ni6tAhVaPHj0oLCxk+vTpJCcnExUVRVRUVKtxv/32GwkJ\nCTidTtxuN/PmzSMmJoa0tDQSExNZu3YthmG0uMfixYuJj48nKSmJxMREli1b5u+EdTaWjIwMDhw4\n0GJTj/Y+m4iIvN8MU89HiIiIRcrLy/nll184dOjQv57rxYsX/kcNly9fzogRI1i1atW/nve/HouI\niIQ2dchERMQybXWZ3sT27dtxOp2MHj2ap0+fkpeX91bm/a/HIiIioU0dMhEREREREYuoQyYiIiIi\nImIRFWQiIiIiIiIWUUEmIiIiIiJiERVkIiIiIiIiFlFBJiIiIiIiYhEVZCIiIiIiIhZRQSYiIiIi\nImKRfwCmTM5owv7jyAAAAABJRU5ErkJggg==\n" } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Entropy of atom/cavity as a measure of entanglement" ] }, { "cell_type": "code", "collapsed": false, "input": [ "entropy_cavity = zeros(shape(g_vec))\n", "entropy_atom = zeros(shape(g_vec))\n", "\n", "for idx, psi in enumerate(psi_list):\n", " \n", " rho_cavity = ptrace(psi, 0)\n", " entropy_cavity[idx] = entropy_vn(rho_cavity, 2)\n", "\n", " rho_atom = ptrace(psi, 1)\n", " entropy_atom[idx] = entropy_vn(rho_atom, 2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 1, figsize=(12,6))\n", "axes.plot(g_vec/(2*pi), entropy_cavity, 'b', label=\"cavity\", linewidth=2)\n", "axes.plot(g_vec/(2*pi), entropy_atom, 'r--', label=\"atom\", linewidth=2)\n", "axes.set_ylim(0,1)\n", "axes.set_ylabel(\"entropy\", fontsize=16)\n", "axes.set_xlabel(\"coupling strength\", fontsize=16)\n", "axes.legend(loc=0)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 10, "text": [ "" ] }, { "output_type": "display_data", "png": 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LREQMpi38RERyaf58GDIELlvLsurFrSrYIiKSJ1SyRaTYmjMHhg0DqxUmTYI3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\n0XQguV6sa9euxWKxcOLECQdEJSLNldO28BMRacq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} ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dynamics of an initially excited cavity" ] }, { "cell_type": "code", "collapsed": false, "input": [ "H = H0 + 1.0 * 2 * pi * H1\n", "\n", "psi0 = tensor(basis(N,1), basis(2,0))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = linspace(0, 20, 1000)\n", "output = mesolve(H, psi0, tlist, [], [a.dag() * a, sm.dag() * sm])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 1, sharex=True, figsize=(8,4))\n", "\n", "axes.plot(tlist, real(output.expect[0]), 'r', linewidth=2, label=\"cavity\")\n", "axes.plot(tlist, real(output.expect[1]), 'b', linewidth=2, label=\"atom\")\n", "axes.legend(loc=0)\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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n9+7aReMAfwSOkfAUoJxXJ+6xWPk3APWVyck0qDY3x3YMnMaIwAkEaKzYu5fG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\na1POf2Zm+M+RcJ9w+ul0dEvg8D2Vm6u42loC55//pLyR0aPdaQujnlx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4pAtvvcU7vMZG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XasKl5qIiWFy/lPn0704ov6/yIRtojaAk8lcnP1dtjWelAXFZHbcp+TQ/TTn7rnAOYrAv9da0WW\no0A6eiLratw4JjleZMRmwfEau5EjE7d04PkRZBzPRQXYalARxcauuWIcXRg9WpfLrqDpeOgQhf6A\nPn3cEeXxEJTgHDrEr65ocSLewU2YwIvYx8Hqznshpds1yKmpnD326KPq4EAvjB/P5biDmkaDQBIc\nWVDNTz/IMfRDcO6/n5Xxv/7FghEEx2tsTJ+uH+KVCCC8ENflx4IDS5SX2+z227k+iVkA0fa7CXwv\nKgu77mUecJqIhUASmjPPtG8GgsTgENkPOvQLeaAkMi5cwPpDfaig9/KLSEQnW2aMhYnXXuN1sXo1\nH03hp89aA1gzsI7jBcQ+9hjPYVcJDCK24rz8sr/1bYM8LoTITnBgxdy7V5HAZMk89D024l6kBW4q\nhB0kQnD8QBIcPy661sCce34ITkqK91yXeiDemjDRqZN+BpbXXPRChyj0dzSASQcG7iI4yG4CvNwg\n/frxTmXGjMTa5JfgELGAvOuuYFkuyQQm5/r18c2RJqZMYQV+662x1TRtyMlhgZqTw/dCdL6XBcd0\nGSaL4Jjf68eCAwRVqFJ4eQXlyRoRXgQH16HicSKC+Nxz1U76ppvs1wRxUcl2EQVXkBddxBaQSy7R\nj22xwYzrSNTK5wewvA4dGpslY6KgQLkm5s/3l2rcGsBNBUtykIyfZAIZXjk5dsWdmqr6BBvXtlLw\nHY3g+LVgJQrz+V2y1ywU6KXPYU1KT3cHUnvh6adZJ77+emIGBiIiSxm15CCei6q1wACB6bqEWWoq\nm66RChgkCykoMBlRZC2oma49UVDAC2zHDs6wIHKbI0107coumCDIy+OYGGSmZWV5W3DMWCCvjI3W\nQAaAE3kLM7MNQQmO/G4vgdC3L7uLsKtNS7O3y0znjpfubEOvXpyxtHq120yMdHK0JzXVnoECyHEN\nSnC6dtUPlfWCOXbJJDg33sgugpISfwkSF17I1yHmoVcve1HLowFzXibDFZYI7ryTya4r8JeI5cLu\n3WrjmixyhgrhKNXhh+Ag8SBZpEMW+mtLgoOq/TYUFrJr/d132eXnhbvuYlkwbFhiG/cRI9ir0Rp0\nmBic1sJkoF7CTMaIJJPgmIsxmfc62khJUXFH+/ZxVlm8nWlrIS0EF13kLfDN8U6W0DaVpJeAKSzU\nXThBSZcM4PVy1aam6uSlb1+7ADEJTaIEOy/P2weOU+HjtQeQgdWJujj8wLTgxMvoaw1SUjiWzq98\n69JFt4ia8+xowiTLrrorbY2cHD5X0Gvt4n+wQiZLwUcier94bQbayoIjA5qTTXDk2hg40H4cBvDK\nKxwHGi+cIjWVSY6rrlVb4LgkONK9kUzSYQqtoMUL2xsy+Pk//zN46n5Q9O3L2SvTphGVlsa//qvD\n7X2l8iYKUyl6CbPUVJ08ByWEhYUsNLKy4rv2pBXERaSGDtUzGZI516W1Kt59rr+e6KGH2E3jZelp\nLeT669s3ufdKBLI2k5+zpRKFmSDRUQiOH5gu4mTFKRHp/eJlQcU8QlxpsgiOPEIh2QRHxrh4Wc6J\n+Hn9hB50BBwzBMecZF4ER8Y3+El7ThTmkQTJDApOBm66SdVMkMdHJBMXXsjFzPxYPx56iE2lTzyR\nvPZ06aJnZcTzJSOz7eyz3dl5XnjpJXb1xLNISfLkCsBLTdUzerzqK7UWcr3FIzgpKUT33ssuimRC\nKsPGxuTeKxHIc3m8Mq9ai7599UJ6HSUGxw8kwcnJsZ8Dd7QQlOAAyZLrbUlwJKlJJGO4o6LNCI48\nByUZCGLBmTaNFcjjjycvOJVIF/RBKzl2BAwZwr7vykp36e/2RCTCu+BkC2xJDLwOqyQimj2ba/Ms\nWJDYvdLS/KUmy3goL0vRvffybgtnvCUL0qXWUSwEKSmq3tONN7ZvW2wYN44tlSUlRJdemtx7IVFi\n+vTEAzbbA1JuJpph6xff/ja/duvmvcEyCU6yXJ+QNTt28DlTXsU/W4tIhGMg+/dXZ0QdC4hEo/Bu\nJvEmkQgRRSk1lXdSyVhgTU26Ob6+PvkuFT847zzODFq4UN+xhfj64MEHueDbKadwyfuOgP37WUEO\nH87nuASpbpsMLFyoMok+/lgvZtieaGzkIPnJk5OXwfl1wKFDXMhwxIivF8FZulRVR77qKo7/SCa2\nbGEy4WXB+fWv9WrBIB9HGzt36hv1/v25NEQyEY123PkRiUQoKF1psywqIt5pJ6vzzIDUjkBuiIgW\nLWJfbTJ9xyGSi3vvZUufV+n5tkZ2tjoYryPgggv4Z9iwjkNuiHjTg5358YwuXbyPteiokCEEyYxT\nAvxkGso4u379kre5MAsWtkWIQ0clN4mizQlOMnHRRXx2ha2cfHuhc2f+CfH1RWpqx3RxdCR07sxl\n8kOEOJro3Ztrau3fz68dATJJJZHSC34B3XH4MP/9dYqd6ihoU4KT7CyGF14gevhhPggzRIgQIUJ8\n/RG0playIQtVehWKPRro0UMRnGSWOThW0aZ1c5PNQHv35sPUzAJnIUKECBEixNFASgqfl5if7z68\n82hBZgcns1bSsYo2JTgdrQ5FiPbD0qVL27sJIToQwvkQQqKjz4dnn+Wg7WRbcGS8T0hwgiMuwVm8\neDENGzaMiouL6bHHHrNec/vtt1NxcTGVlJRQGY4utiAkOCGAji7AQrQtwvkQQuLrMB/aIiBXEpzQ\nMxEcngSnubmZbr31Vlq8eDGtWbOGXnnlFVq7dq12zaJFi2jjxo20YcMG+s1vfkM3y/w5A3KwQoQI\nESJEiBBuSKtNsq1FxyI8Cc7y5cupqKiI8vPzKT09na666ip68803tWv+/Oc/08yZM4mIaNy4cVRd\nXU07d+60ft+xVCExRIgQIUKESCZQciE3t2OVX/i6wDOLavv27TRI0MaBAwfSP//5z7jXbNu2jfJi\nSgRHwkJ3ITQ8gKPDQ4SgcD6E0BHOB4Vdu5J32vyxDM8ui/h0MprVBc3PtUGx5BAhQoQIESJEiCPw\ndFENGDCAtm7deuTvrVu30kAj0sm8Ztu2bTQgDPcOESJEiBAhQrQjPAnO2LFjacOGDVRRUUENDQ20\nYMECmooDZ77C1KlT6fnnnyciomXLllHPnj0t7qkQIUKECBEiRIi2g6eLKi0tjZ566imaNGkSNTc3\n06xZs2j48OE0b948IiKaPXs2XXzxxbRo0SIqKiqibt260e9+97s2aXiIECFChAgRIoQLST9NfPHi\nxTRnzhxqbm6mG264ge66665k3i7E1wD5+fmUlZVFqamplJ6eTsuXL2/vJoVoQ1x//fX0l7/8hXJz\nc2nVqlVERLRv3z6aNm0abdmyhfLz8+nVV1+lnj17tnNLQ7QVbHOitLSUnnnmGcr56qTiRx55hCZP\nntyezQzRRti6dSt95zvfoV27dlEkEqEbb7yRbr/99sByIqmVjP3U0Qlx/CESidDSpUuprKwsJDfH\nIa677jpavHix9t6jjz5KF1xwAa1fv54mTpxIjz76aDu1LkR7wDYnIpEIff/736eysjIqKysLyc1x\nhPT0dHr88cdp9erVtGzZMpo7dy6tXbs2sJxIKsHxU0cnxPGJMLPu+MU555xD2UZZc1lPa+bMmfSn\nP/2pPZoWop1gmxNEoZw4XtG3b186+eSTiYioe/fuNHz4cNq+fXtgOZFUgmOrkbN9+/Zk3jLE1wCR\nSITOP/98Gjt2LD399NPt3ZwQHQA7d+48kpyQl5fnLBYa4vjCk08+SSUlJTRr1iyqrq5u7+aEaAdU\nVFRQWVkZjRs3LrCcSCrB8VtHJ8TxhX/84x9UVlZGb7/9Ns2dO5fef//99m5SiA6ESCQSyo4QdPPN\nN1N5eTmtXLmS+vXrRz/4wQ/au0kh2hg1NTV0xRVX0K9+9SvKzMzU/udHTiSV4PipoxPi+EO/fv2I\niCgnJ4cuu+yyMA4nBOXl5dEXX3xBRERVVVWUm5vbzi0K0d7Izc09osRuuOGGUE4cZ2hsbKQrrriC\nrrnmGrr00kuJKLicSCrB8VNHJ8Txhbq6Ojp48CAREdXW1tJf//pXOumkk9q5VSHaG1OnTqX58+cT\nEdH8+fOPCLQQxy+qqqqO/P7GG2+EcuI4QjQapVmzZtGIESNozpw5R94PKieSnib+9ttvH0kTnzVr\nFt1zzz3JvF2IDo7y8nK67LLLiIioqamJZsyYEc6J4wzTp0+n9957j/bs2UN5eXn005/+lC655BK6\n8sorqbKyMkwTPw5hzokHHniAli5dSitXrqRIJEIFBQU0b968sIjscYIPPviAxo8fT6NHjz7ihnrk\nkUfotNNOCyQnkk5wQoQIESJEiBAh2hpJdVGFCBEiRIgQIUK0B0KCEyJEiBAhQoQ45hASnBAhQoQI\nESLEMYeQ4IQIESJEiBAhjjmEBCdEiBAhQoQIccwhJDghQoQIESJEiGMO/w+pBzxb9mZxYwAAAABJ\nRU5ErkJggg==\n" } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fock-state distribution and Wigner function for the cavity as a function of time" ] }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = linspace(0, 0.35, 8)\n", "output = mesolve(H, psi0, tlist, [], [])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "rho_ss_sublist = output.states #[::4]\n", "\n", "xvec = linspace(-5,5,200)\n", "\n", "fig, axes = subplots(2, len(rho_ss_sublist), figsize=(2*len(rho_ss_sublist), 4))\n", "\n", "for idx, rho_ss in enumerate(rho_ss_sublist):\n", "\n", " # trace out the cavity density matrix\n", " rho_ss_cavity = ptrace(rho_ss, 0)\n", " \n", " # calculate its wigner function\n", " W = wigner(rho_ss_cavity, xvec, xvec)\n", " \n", " # plot its wigner function\n", " axes[0,idx].contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-.25,.25), \n", " cmap=get_cmap('RdBu'))\n", "\n", " # plot its fock-state distribution\n", " axes[1,idx].bar(arange(0, N), real(rho_ss_cavity.diag()), color=\"blue\", alpha=0.6)\n", " axes[1,idx].set_ylim(0, 1)\n", " axes[1,idx].set_xlim(0, N)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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KixmK8ymY4OBxBDa4gMlnYIPKOraI/JiUdlfcRaXBmYDhwXN1dZ1dr2WbLtOu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GdRx3aWH4SO3WiS5Doq0hp9mM1K2+pm+bmi4/79BxoaiaT2E9d+W7Vh6hhPkm0lyXvw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\nAElFTkSuQmCC\n" } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Same thing with a little bit of dissipation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "kappa = 0.25" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = linspace(0, 20, 1000)\n", "output = mesolve(H, psi0, tlist, [sqrt(kappa) * a], [a.dag() * a, sm.dag() * sm])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 1, sharex=True, figsize=(8,4))\n", "axes.plot(tlist, output.expect[0], 'r', linewidth=2, label=\"cavity\")\n", "axes.plot(tlist, output.expect[1], 'b', linewidth=2, label=\"atom\")\n", "axes.legend(loc=0)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 18, "text": [ "" ] }, { "output_type": "display_data", "png": 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r8yDXhWNfExERVbL4THnv3r1Yu3Yt+vbti9jYWADASy+9hHPnzgEAEhMTsXHjRrz11ltw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\nn35SFB8fWd+1S3vfzJmybeV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} ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = linspace(0, 10, 8)\n", "output = mesolve(H, psi0, tlist, [sqrt(kappa) * a], [])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "xvec = linspace(-5,5,200)\n", "\n", "fig, axes = subplots(2, len(output.states), figsize=(2*len(output.states), 4))\n", "\n", "for idx, rho_ss in enumerate(output.states):\n", "\n", " # trace out the cavity density matrix\n", " rho_ss_cavity = ptrace(rho_ss, 0)\n", " \n", " # calculate its wigner function\n", " W = wigner(rho_ss_cavity, xvec, xvec)\n", " \n", " # plot its wigner function\n", " axes[0,idx].contourf(xvec, xvec, W, 100, \n", " norm=mpl.colors.Normalize(-.25,.25), cmap=get_cmap('RdBu'))\n", "\n", " # plot its fock-state distribution\n", " axes[1,idx].bar(arange(0, N), real(rho_ss_cavity.diag()), color=\"blue\", alpha=0.6)\n", " axes[1,idx].set_ylim(0, 1)\n", " axes[1,idx].set_xlim(0, N)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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eLKUATMgk4LZDoQ7HExXZBBZswhnCCSbTmcNBg9mG9aCrs6HmtA2HFHYxOG37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\n9z585CMf6aWs++67D1LqS7znnnvw5JNPdv7tl7/8ZbzmNa/Bbbfdhjz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} ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Entropy as a function of time in presence of dissipation and starting in the ideal ground state" ] }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = linspace(0, 30, 50)\n", "\n", "psi0 = H.groundstate()[1]\n", "\n", "output = mesolve(H, psi0, tlist, [sqrt(kappa) * a], [])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 }, { "cell_type": "code", "collapsed": false, "input": [ "entropy_tot = zeros(shape(tlist))\n", "entropy_cavity = zeros(shape(tlist))\n", "entropy_atom = zeros(shape(tlist))\n", "\n", "for idx, rho in enumerate(output.states):\n", " \n", " entropy_tot[idx] = entropy_vn(rho, 2) \n", " \n", " rho_cavity = ptrace(rho, 0)\n", " entropy_cavity[idx] = entropy_vn(rho_cavity, 2)\n", "\n", " rho_atom = ptrace(rho, 1)\n", " entropy_atom[idx] = entropy_vn(rho_atom, 2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = subplots(1, 1, figsize=(12,6))\n", "axes.plot(tlist, entropy_tot, 'k', label=\"total\", linewidth=2)\n", "axes.plot(tlist, entropy_cavity, 'b', label=\"cavity\", linewidth=2)\n", "axes.plot(tlist, entropy_atom, 'r--', label=\"atom\", linewidth=2)\n", "axes.set_ylabel(\"entropy\", fontsize=16)\n", "axes.set_xlabel(\"coupling strength\", fontsize=16)\n", "axes.set_ylim(0, 1.5)\n", "axes.legend(loc=0)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 23, "text": [ "" ] }, { "output_type": "display_data", "png": 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KMkKyLTA7Wk6fvrR97pxr6/Lzkxo2vLQ0aGCsQ0Kk4GAj+AYFVW1d2aVePeP6AADUZYRr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\n+OOPUVBQoJknlFyLioqQn5+Pd999Fx0dHXC5XDA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