{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP Example: Quantum System Subject to to Coherent Feedback with Discrete Time-Delay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Arne L. Grimsmo](http://arnegrimsmo.weebly.com/)
\n", "Université de Sherbrooke
\n", "[arne.grimsmo@gmail.com](email:arne.grimsmo@gmail.com)\n", "$\\newcommand{\\ket}[1]{\\left|#1\\right\\rangle}$\n", "$\\newcommand{\\bra}[1]{\\left\\langle#1\\right|}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook shows how to use the `memorycascade` module, one of the modules for non-Markovian systems in qutip. This module is an implementation of the method introduced in [Phys. Rev. Lett 115, 060402 (2015)](http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.060402) ([arXiv link](http://arxiv.org/abs/1502.06959)) to integrate the dynamics of open quantum systems coupled to a coherent feedback loop with a time-delay.\n", "\n", "At the end of the notebook we also show how the `memorycascade` module can be used in conjunction with the `transfertensormethod` module.\n", "\n", "In this notebook we consider a paradigmatic quantum optics example of a system subject to coherent feedback, namely a two-level atom in front of a mirror. The setup is illustrated in the figure below:\n", "\n", "![Atom in front of a mirror](images/atommirror.png)\n", "\n", "An atom is placed a distance $l$ in front of a mirror. The incomming field on the left side, $b_{\\text{in}}(t)$, we take to be a vacuum field. The field on the right side of the atom, i.e., the field between the atom and the mirror, creates a coherent feedback loop with time-delay $\\tau = l/c$, where $c$ is the speed of light. The atom couples to the input field via a system operator $L_1$, and to the returning feedback field via a system operator $L_2$. We assume that an arbitrary phase shift, $\\phi$, can be applied to the feedback field (e.g., there could be a phase-shifter placed in the loop [not shown]). In addition, there can be Markovian non-radiative decay, described by a rate $\\gamma_{\\rm nr}$. The red arrow denotes a classical drive field, assumed to couple to the atom via a side-channel." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Preamble" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "\n", "import qutip as qt\n", "from qutip.ipynbtools import version_table\n", "\n", "import qutip.nonmarkov.memorycascade as mc\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem setup" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tau= 1.0\n" ] } ], "source": [ "gamma = 1.0 # coupling strength to feedback reservoir\n", "gamma_nr = 0.2*gamma # non-radiative decay\n", "eps = 1.0*np.pi*gamma # classical drive strength, eps/2 = Rabi frequency\n", "delta = 0. # detuning from the drive frequency\n", "\n", "tau = np.pi/(eps) # time-delay, chosen to exactly match the Rabi period due to the drive\n", "print('tau=', tau)\n", "phi = 1.0*np.pi # phase shift in feedback loop\n", "\n", "# Hamiltonian and jump operators\n", "H_S = delta*qt.sigmap()*qt.sigmam() + 1j*eps*(qt.sigmam()-qt.sigmap())\n", "# coupling at first port of feedback loop (into the loop)\n", "L1 = sp.sqrt(gamma)*qt.sigmam()\n", "# coupling at second port of feedback loop (out of the loop)\n", "L2 = sp.exp(1j*phi)*L1\n", "\n", "# Markovian decay channels\n", "c_ops_markov = [sp.sqrt(gamma_nr)*qt.sigmam()]\n", "\n", "# initial state\n", "rho0 = qt.ket2dm(qt.basis(2,0)) # atom start in the excited state\n", "\n", "# integration times\n", "times = np.arange(0.0, 3.0*tau, 0.01*tau)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Memory cascade simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The memory cascade method works by mapping the non-Markovian feedback problem onto a problem of $k$ identical cascaded quantum systems, where $(k-1)\\tau < t < k\\tau$ for a time $t$.\n", "\n", "To use the memory cascade method in qutip, first create a `MemoryCascade` object. The syntax is\n", "\n", "````\n", "sim = MemoryCascade(H_S, L1, L2, S_matrix=None, c_ops_markov=None, integrator='propagator', paralell=False, options=None)\n", "````\n", "\n", "where\n", "\n", "`H_S` is a system Hamiltonian (or a Liouvillian).\n", "\n", "`L1` and `L2` are either single system operators, or lists of system operators. `L1` couples the system into the feedback loop, and `L2` couples out of the loop. If `L1` and `L2` are lists, the optional argument `S_matrix` can be used to specify an $S$-matrix that determines which operator in `L1` couples to which operator in `L2` (note that `L1` and `L2` must have the same number of elements). By default `S_matrix` will be set to an $n \\times n$ identity matrix, where n is the number of elements in `L1`/`L2`. Having multiple coupling operators into and out of the feedback loop can for example be used to describe composite systems emitting at multiple frequencies. The $S$-matrix can then be used to include, e.g., beam splitters mixing the different signals in the feedback loop.\n", "\n", "`c_ops_markov` is an optional list of additional Lindblad operators describing conventional Markovian noise channels, e.g., non-radiative decay.\n", "\n", "`integrator` is a string which can be either 'propagator' or 'mesolve', referring to which method will be used to integrate the dynamics. \"propagator\" tends to be faster for larger systems (longer times)\n", "\n", "`parallel` if set to True means the time-integration is parallelized. This is only implemented for `integrator='propagator'`\n", "\n", "`options` an instance of the `qutip.Options` class for genereic solver options, used in internal calls to `qutip.propagator()`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "sim = mc.MemoryCascade(H_S, L1, L2, c_ops_markov=c_ops_markov, integrator='mesolve')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reduced atom dynamics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute the reduced density matrix of the atom at time $t$ with time-delay $\\tau$, simply call the method `rhot` of the `MemoryCascade` object." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 27.9 s, sys: 316 ms, total: 28.2 s\n", "Wall time: 16.8 s\n" ] } ], "source": [ "%time rho = [sim.rhot(rho0, t, tau) for t in times]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now lets plot the atomic inversion as a function of time:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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5NhxlNU2w2hWKqhrd1ukRERERHcdhIINJ5+YLIiIiageGPIPRTtly8wURERGdDEOewbid\nYcuRPCIiIjoJhjyDSWNDZCIiImoHhjyDSedIHhEREbUDQ57BpCW4N0RWSulYDREREfkrhjyDSYoJ\nQ1SYGQBQ02hFVYNF54qIiIjIHzHkGYyIcIctERERnRJDngH1Za88IiIiOgWGPANiQ2QiIiI6FYY8\nA3LrlcfpWiIiImoFQ54Bua3JY688IiIiagVDngFpQ97higYdKyEiIiJ/xZBnQKndoyDieHykqgFN\nVpu+BREREZHfYcgzoLAQE3rHRwIAlAIKKjmaR0RERO4Y8gwqjTtsiYiIqA0MeQaVzh22RERE1AaG\nPINiQ2QiIiJqC0OeQWlH8ni0GREREZ2IIc+g3NuoMOQRERGRO4Y8g0pPiHY9zq+oh1JKx2qIiIjI\n3zDkGVR8VCjiIkIAAA0WG8pqm3SuiIiIiPwJQ56BpSdqRvO4Lo+IiIg0GPIMjL3yiIiI6GRCOvMi\nETEDOAvATAAzAFQDmA/gC6XUeo9VR21K4w5bIiIiOol2j+SJSKyIXC0i7wAoA7AYwN0ACpy3/BHA\nGhEpEJHnReR8EQn1fMl0HHfYEhER0cmcciRPRO6CY8TuLABhABoALAHwOYCvlFJlzvsyAVzqvHc2\ngDkAakXkGwDvKaU+98YfIJila0LeIYY8IiIi0mjPdO3zcIzcvQNHsFuilGo48Sal1EEA/wbwbxFJ\nAHAxHIHvIgADnK8lD+J0LREREZ1Me0LeZAArVQcasSmlKgC8CeBNEQkHMLKT9VEbesVHItQssNgU\njtY2ob7ZiqiwTi2zJCIiogBzyjV5SqmfOhLwWnl9k1JqbWdfTydnNglSu3OHLREREf2cx1qoiMij\nItLPU5+P2qevto0Kp2yJiIjIyZN98v4EYLmI9Nc+KSLhInK2B9+HNNLZK4+IiIha4elmyO8C+F5E\nsjTPdQPwrYffh5zYEJmIiIha48mQpwA8CeA5OIJepuZj4ok3EJELRWS3iOwTkQdb+fgNIrJVRLaJ\nyEoRCfgNH9xhS0RERK3x+FZMpdTjImIC8KOITIGjr16nN24c5zxl43kA58HRgHmdiHyhlNqpue0g\ngDOVUpUiMg3APADju/re/owNkYmIiKg1ngx5rtE6pdQ/naHsBwDXeujzjwOwTyl1AABE5H04+vC5\nQp5SaqXm/tUAUj303n7LLeRV1sNmVzCbPDJwSkRERAbmyenaBwDUHb9QSv0NwKsAvvTQ5+8D4LDm\nusD53MnMAvCNh97bb0WHhyApJgwAYLEpFFc36lwRERER+YMOj+SJSPLxo8y0lFJPtvLcX0TEDuB3\nnayvU5y7eWcBOKONe2bDcfwa0tLSfFSZd6QlROFobTMA4FB5Hfp0i9S5IvK2XUXVWLKzBBsOVWJ/\nWS3Ka5thUwpRYWb07R6FgT1jcUb/JJw5IBndo8P0LpeIiHTQmenaEhFZpZSa1J6bnSN6f+vE+5yo\nEEBfzXWq8zk3IjICwCsApimlytuoax4ca/aQk5PT5TWDekpPjMbG/GMAnOvysk7xAjIkm13hq61H\nMPfHA9hVVN3qPc1WO47VV2FbYRU+3lCAULPggqE9cdukDIxJT/BxxUREpKfOrslLdp5PexocU777\nlFJ5HquqdesAZDt37RbCsdbveu0NIpIG4FMANyml9ni5Hr+hbYjMHbaBaWN+JR7+dBtyi2s69DqL\nTeGrrUX4amsRzhqYjIemDcbAnrFeqpKIiPxJZ0NeGoAi7etF5ACAlwA8q5Rq9kBtbpRSVhG5F8Ai\nAGYAryqldojIHOfH58LRkDkRwAsiAgBWpVSOp2vxN9qGyIe4wzagWG12PLl4N+YtOwDt4YLhISac\nP7QnzhmUjOF9uiElLhyhZhOqGy3YX1qHDYcqsGRnCbYUVLle88PuMqzYexR3TO6H+6dmIyLUrMOf\niIiIfEU6eiytc42dAtAMYDmAKjimTsfCscN2F4DpSql8z5bqPTk5OWr9+vV6l9Fp6/IqcNXcVQCA\nEanx+OLeky5FJAOprGvGve9txE/7WlYdRIWZMeuMTMw6IxPdok691m7nkWq8svwAPttc6BYSB/WM\nxX+uG4XsFI7qEREZjYhsaM8gVmd31xYDyFZKna+UukopNQFAbwBPAxgEYJGIRLX5Gchj0jldG3CK\nqxpx1Uur3ALe5OwkLP71FPz2/IHtCngAMKR3HP51zWlYeN8UjMtoWZOXW1yDS55bga+3Fnm8diIi\n8g+dDXkfKaUKtE8opUqVUr+FY63cQAC/7Gpx1D7JseGICHX8p6xqsKCq3qJzRdQVR4414KqXVmJf\naa3ruV9PHYA3bhuH1O6d+91pYM9YvD/7dPz10mEID3F8rTRa7Ljn3Y145tu96OiIPhER+b/OhLxa\nAE0n+6BS6mM4zqq9prNFUceIiFtT5EMVdW3cTf6ssq4ZN/13DQ5XNAAAQkyC/1w3CvdNzYapi02u\nTSbBTaen44t7z0BmUrTr+X9/uwd//WoXgx4RUYDpTMjbB+D8U9yzDsCATnxu6qT0xJYf2nmcsjWk\nRosNt7+xDvvLHCE91Cx46aYxuGRkb4++z8CesZh/9yRMzk5yPffqTwfx4CfbYLMr1DVZkV9ej93F\nNSiorEejxebR9yciIt/ozO7a+QD+LCL/UEo9fJJ7+sID59VS+2lHZg4d5Uie0Sil8IfPtmOTs9+h\nCPDva07DuYNTvPJ+8VGh+O8tY3H/B5uwYFsxAOCD9YexNLcUR2vdB+rNJkH/5BhMyErEtGE9MTYj\nocujikRE5H2dGcl7CsAeAA+IyA8icqmIuI5YEJHr4Jiq3eKhGqkd0hNbpmsPljPkGc2bqw7hk40t\ny1wfuWgILh7h2RG8E4WFmPDstaNw5ZiWI55PDHiAownz7pIavL4yD9fMW40Lnl6GjzcUwGbn73FE\nRP6swyFPKVUHYAqA753//gRAtYgUikg1gLfhGCF83JOFUtsytdO1HMkzlB1HqvD3r3e5rq8ck4rb\nJmX45L1DzCY8ccUI3Dqx5f1CTILe8RHo3yMGPeMiICcM2u0trcXvPtqCS/6zAhsOVfikTiIi6rhO\nNUN2nl07VUTOA3AjHGfEpjs/vBnAX5RSX3qmRGqPdO10LdfkGUZDsw2/em8Tmm12AMCwPnH426XD\nICcmKy8ymQSPzhiKy0b1gdWuMLR3nFuj5NomKzblV+Kb7cX4fFMh6poda/R2FlXjyrmrMOfMLPx6\n6gCEhXR2sz4REXlDZ0+8AAAopZYAWAIAImJSStk9UhV1WK+4CISFmNBstaO8rhnVjRbERYTqXRad\nwhOLcl0bLSJDzXj22lG6nUQxsm+3Vp+PCQ/B5OxkTM5OxgMXDsJrPx3E3B/3o9Fih1LAiz/sx5oD\n5Zh70xj0iI3wcdVERHQyp/zVW0Ti2vOJ2gp47f0c1Hkmk7g3RT7K0Tx/t+FQJV5fmee6fnTGEPRL\njtGvoHaIjwzF/VMH4NvfnOm2O3dj/jFc+txPyC2u1rE6IiLSas/8ylERWSQid4tI3/Z+YhEZKiIP\ni8gaAN91vkRqrwzNlC03X/i3ZqsdD3yy1XXU2JQBybg6p93/e+kutXsU3rhtHB6ePgjHN9oeqWrE\n1XNXYWN+pb7FERERgPaFvDcBjATwHIA8EdkgIo+IyEjtTeIwRUSeEpF9ALYC+BuABAAfebpw+jlt\nGxVuvvBv/11x0HWiRVSYGf+4zLfr8DzBZBLMnpKF124bh9hwx8qP6kYrbnxlDTdkEBH5gVOGPKXU\nHQB6wbG54ikA0QD+F8BGETkoIs+KyOsASuHYcXs/gAoAfwIwXCmVrZTiTlsf0LZRyeNInt8qrmrE\nf77b67r+7fkDO31cmT84c0Ay3pt9OhKiHefp1jfbcOur67CtoErnyoiIglu7tsMph5VKqd8rpQYB\nGALgjwCKAdwD4DoAGwHcCyBNKTVOKfV3pdQObxVOP8c2Ksbwz292od65Q3VgSixumZB+ilf4v2F9\n4vHhnacjKcYR9GqarLjltbU4XMG1oUREeulUzwOlVK5S6p9KqQkAegNIVkpdoJR6USlV6NkSqb3Y\nRsX/bS+swuebj7iuH50xFCHmwGg90r9HLN6aNR7xkY5d3RV1zbj99XWobrToXBkRUXDq8k8XpVSJ\nUopb6vxAr7gIhDt7lR1vo0L+5anFu12Pzx+SgglZiTpW43mDe8Xh1VtzEOYMrntLa/HLdzfBamN3\nJSIiX+tSnzzyLyaTID0xCntKHAv6847WYURq673PyPfW5VXg+91lABxn0/7ugoE6V+QdY9IT8MSV\nI3D/B5sBAD/uKcPfvt6FR2cM1bky8gcVdc3YV1qLoqoG1DXZYFMKdruCySRIiQ1Hn+6R6NMtEvGR\noYbbjETkbxjyAkx6YnRLyCuvZ8jzE0opPLmwZRTvstP6YEBKrI4Vedelo/pgX2ktnvt+HwDg9ZV5\nGNo7DlcZqE0MecaRYw1YuL0YG/IrsbXgGA5XNLTrdSlx4RiXmYhxmQmY0C8B/XsE7v8vRN7CkBdg\n2EbFP/24pwxr8xxtRULNgl+fN0DnirzvN+cNwIGjtViwrRgA8KfPd2BUWjf+sA4ClXXN+HxzIb7c\nWoQNhzrXN7GkuglfbjmCL7c41rAO6hmLS0f1wczTeqNXfKQnyyUKWAx5AcatjQpDnl+w2xWeXNQy\ninft2DT0TTBuy5T2MpkE/3fVSOwursH+sjo0WGy4991NmH/PJN2ObiPvKqpqwCvLD+K9tfmuHeQn\nCgsxYVDPWKR2j0RcRChMJoFZBBabHUVVjThyrAEFlQ1osLi/Pre4Bo99k4vHF+bi7IE9MOfMLIzN\n6M4pXaI2MOQFGLc2KuyV5xeW7CrBjiOOvUkRoSb88pz+OlfkO1FhIXju+tGY+fxPaLbakVtcg79+\ntRN/v2y43qWRB5XVNOFfS3bj4w0FsNiU28fMJsGk/kk4b3APnNa3Owb2jEVYSNt7/mx2hV1F1Vhz\nsAJrDpTjxz1laLI6Nu8oBXyXW4rvcksxOq0b7jqrP6YO7sGwR9QKhrwAoz3aLI9tVPzCvGUHXI9v\nmZCBHnEROlbje4N7xeHPlwzBHz7bDgB4Z00+JmYl4aIRvXSujLrKarPj7dWH8NSSPahptLp9bFDP\nWNx4ejqmDeuJxJjwDn1es0kwrE88hvWJx6wzMlHTaMGiHSWYv6kQP+0/6joOcGP+MfzizfXISe+O\nP1w0GKPSunvqj0YUEBjyAkxPZxuVJqsdFXXNqGqwuPqWke+tz6twrUkKM5tw+xmZOlekj+vHpWHl\nvnJ8va0IAPDwZ9swNqN70AXeQLK14Bh+//FW5BbXuD0/NqM77j6rP84amOyx0bXYiFBcOSYVV45J\nxf6yWry87AA+3ViIZmdrnvWHKnHZCytx8YheeGj6YPTpxjV7RIAH+uSRfzneRuW4Q5yy1dVLmlG8\nS0f1RkqQhhoRwT+vGO764VvVYMFDn26DUuoUryR/Y7crzP1xPy5/YaVbwOuXFI03bh+Hj+ZMxNmD\nvDd9mpUcg8euGIEVD5yNWWdkItTc8j5fbS3C+f/6Ea//dBA2O7+2iBjyAlC6Zl3eQW6+0M2+0los\n2Vniup49pZ+O1egvLiIUT141wnW9NLcUn2zkATlGUlzViBv/uwaPfZMLqzNERYaa8T8XDMQ390/G\nmQOSfVZLj7gIPHLxEHz7mzMxfXhP1/N1zTY8+uVOXPHiSuw+YZSRKNgw5AWgTB5v5hdeWd4yijd1\ncA+2DgEwMSvJ7aze//1yB4qq2tc3jfS1Lq8CFz27HCv3l7ueO61vNyy6fwruObs/wkP02TGdnhiN\nF24Yg4/mTED/HjGu5zcfPoZL/rMCryw/ADtH9ShIMeQFILZR0V9pTSM+1YxS3Xlmlo7V+JcHpg1C\nhvNrtKbRigc+4bStv/to/WFc//JqlNc1A3Cc2PLLc/rjozkTkJboH+2AxmYk4OtfnYH7p2a7pnCb\nbXb87etduPX1dSitadS5QiLfY8gLQGyjor83Vua5FoWPSuuGnHTu+jsuKiwET141EseXbC3bU+YW\niMl/2OwK/1iwC//z8VZXa5TE6DC8e8fp+O35AxFq9q8fIeEhZtw/dQAW/GoyhvWJcz2/bE8ZLnx6\nOZbtKdMcj6QDAAAgAElEQVSxOiLf86//Q8kj2EZFX01WG95be9h1feeUfuzhdYKxGQm4fVLLTuO/\nfb0TFc5RIvIPzVY7fvX+JrcWQIN6xmL+PZMwIStRx8pOLTslFp/eNQl3ntnP9ctERV0zbnltLZ5d\nupfTtxQ0GPIC0PE2KgBcbVTIdxZuL3YFlj7dInHekJ6neEVw+u35A1y7bSvrLfjHgl06V0THNTTb\n8Is31+PrrUWu56YOTsHHd000zGktYSEmPDRtMN6ZNR49Yh19+pQC/rVkD+54cz2q6vl9kTrGarOj\nqt6Cgsp6FB5rQGl1IyrqmtFoaf10F3/APnkB6HgblT0ltQAcbVRGpHbTuarg8fbqQ67H143rC7OJ\no3itiQoLwV8vHYrbX18PAPh4QwEuH90HE7OSdK4suFU1WDDr9XVYrzlz9pYJ6fjzJUNhMuDX8sT+\nSfj6V5Nx77sbseag4/zo73JLMfP5FfjvrWORlRxzis9AwaTJasOuohpsOXwMB8pqkV9Rj0MV9Siu\najzpUX0AEBsRguTYcPSIDUdybAT+MmMoukeH+bDy1jHkBaj0xGhXyDt4lCHPV3KLq7Euz/HDMcQk\nuHpsX50r8m/nDErBRcN7uZok/+Gz7fjmvsk821YnVQ0W3PjKGmwrrHI996tzs/HrqdmGXnKQHBuO\nd+4YjycX7Xb1rswrr8dlz/+EF28cg0n9+YtFsLLa7Nh8+Bi+312KFfvKsetItWs9dUfUNFpR02jF\ngTLHOvjHLvePoxsZ8gKUto1K3lGuy/OVd1bnux5fMKwnesQGZ/PjjvjTJUOwbE8ZapqsOHi0Di98\nvw+/OX+g3mUFnZpGC255da1bwHvk4iGYFSCntISYTXho+mCM7NsNv/lwMxotdlQ3WnHLq2vxl5nD\ncP34NL1LJB+x2RVW7DuK+ZsK8V1uabuXNIkAMWEhiIlwRCeLTcFqt6O20erqGwkA0WFmRIf7R7zy\njyrI4zIStb3yuMPWF2qbrPh0Y4Hr+sbx6W3cTcelxEXg99MG4ZH5jrNtX/xxP2ac1pt9BX2orsmK\n215bh82Hj7me++flw3HduMALPtOH90Lf7lG44811KKlugtWu8PBn27C/rBYPTx/M5RUB7ODROry7\n5hDmbz6Cspqmk96XnhiFkandMKR3HNITopCWGIXU7lGIDQ9pdcmC3a5wrMGC0ppGlNU0oa7J2spn\n1YehQp6IXAjgGQBmAK8opR474ePi/Ph0APUAblVKbfR5oX4gQ9O76iBDnk/M31SIOueajf49YnB6\nvwSdKzKOG8al4dONBdiUfwwWm8LDn27H+7NPN+QaMKNptNhw+wlr8P566bCADHjHDU+Nx+f3nIE7\n3lyH7YXVAID/rjiIvKN1eO760YgM43KBQKGUY9TutZ/y8P3uUrTWkjMlLhxnD+yBswYmY1xmIhI6\nuJbOZBIkRIchIToMg/xsn51hQp6ImAE8D+A8AAUA1onIF0qpnZrbpgHIdv4zHsCLzn8HnQyeeuFT\nSim3DRc3jE8z9BomXzOZBP+8fDgufnYFrHaFtXkV+GjDYVwzNnCDhj+w2uy4991Nrg0JAPDnS4bg\nptMDfxS6Z3wEPrxzAn79wWYs2uE4fnBpbimuf2U1Xr1lrF8smqfOs9sVFu0oxjNL97qdsXxcUkw4\nZozsjUtH9cbwPvEB+/3aSC1UxgHYp5Q6oJRqBvA+gJkn3DMTwJvKYTWAbiLSy9eF+gO2UfGtrQVV\nrm8kkaFmXD46VeeKjGdQzzj8QnO+7z+/yWXvPC9SSuGRz3fg210t5ys/NG0QbpsUGGvw2iMqLAQv\n3jAGczQn0mzKP4Yr5q5EQSV/OTYipRS+2VaE6c8ux13vbPxZwDtnUA+8dutYrH7oHPzpkiEYkdot\nYAMeYKyQ1wfAYc11gfO5jt4DABCR2SKyXkTWl5UFXhf0421UjuPxZt718YaWtXjTh/dCfGSojtUY\n16/OyXb1zjtWb8Fj37B3nrc8s3Qv3lvbslHozjP7BeXxeyaT4MFpg/DoJUNcjZMPlNXhihdXIre4\nWt/iqEPW5VXgshdW/izcRYaacevEDHz/u7Pw6q1jcfagHgjxs9NavCU4/pStUErNU0rlKKVykpOT\n9S7HK7SbLw4y5HlNo8WGL7YccV1fOYajeJ0VGWbGX2YOdV1/uL4A6/Mq2ngFdca7a/Lx9Ld7XdeX\nj+qDBy4YpGNF+rt1Uib+c90ohDl/+JdUN+Gquauw5kC5zpXRqeSX12POWxtw1dxVbpuHosLMmHNm\nFlY8cDYenTHUretEsDBSyCsEoG06lup8rqP3BI1+miafB8pqdawksC3d1bIFP7V7JMZncsNFV5w7\nOAXnD0lxXf/hs+2wdKJvFbVu8Y5i/HH+Ntf1lAHJePzKEdzkAuDiEb3x+u1jEeNsf1HTaMVNr67F\nwu1Fp3gl6aHJasNz3+3Fef/+EQt3FLueDzObMHtKP6x44Bw8OG0QEmPCdaxSX0YKeesAZItIpoiE\nAbgWwBcn3PMFgJvF4XQAVUqpoP2/s19yy28t+zmS5zUfb2hZIXDF6FT+sPSAP88YikhnQ+TdJTV4\n7aeDOlcUGDbmV+KX723C8ZZeI1Lj8eINoxEaJFNX7TExKwkf3Hk6kp1HoTVb7bjrnY14S7OxivS3\n+kA5pj+zHP+3eA+arC2/BM4Y2RtLf3smHp4+uMO7ZAORYf7PVkpZAdwLYBGAXQA+VErtEJE5IjLH\nedsCAAcA7APwMoC7dSnWT2RpQ14pR/K8obS6ET/uaVnTeQU3XHhEn26RuH9qtuv66W/34sixBh0r\nMr7CYw2Y/eYG1w/E9MQovHrrWL9p2upPhvaOx6d3TXRN7ykFPDJ/O/69ZA9Uaz04yGfKa5vw2w+3\n4Np5q7G/rGXwYmjvOHx690Q8e90ow5yv7AuGCXkAoJRaoJQaoJTKUkr93fncXKXUXOdjpZS6x/nx\n4Uqp9fpWrK9+SS3TtXnldbDb+c3J0z7bVOgaFRmfmYC0RH5z8ZTbz8jEwBRHQ+T6Zhv+98sdOldk\nXHVNVtzxxnocrXU0gO0eFYo3bhuHpCCexjqVvglR+HjOBIxMjXc998zSvfjj/O2w8XupLpbuKsEF\nTy/DJ5qm8zHhIfjzJUPw+T2TMDqtu47V+SdDhTzqmO7O5owA0Gix40gVR0I8SSnltquWGy48K9Rs\nwt8uG+a6XrSjBEs17T6ofex2hfs/2IxdRY6doqFmwdwbx7j10qTWJcaE491fnI4pA1o2572zJh/3\nvrsRjZaTH1ZPnlXfbMXDn23DrDfW42htS1uli4b3wre/ORO3TcoMmt2yHcW/lQDXT/ON/EAZ1+V5\n0taCKux1ToNHhZkxfXhQtmT0qrEZCbg6pyU8//mLHWho5g/Xjnhy8W4s2dkSjv9+6XCM75eoY0XG\nEh0eglduzsHM03q7nvtmezFufW0tqhvZf9Tbthw+houeXYF317S0++kRG45Xb83B8zeMRs94ng/e\nFoa8AKfdfMEdtp712aaWjdvThvXi2iYveXDaYHSLcvQdLKhswH++23uKV9Bxn2wowIs/7Hddz57S\nD1eP7dvGK6g1YSEm/Pvq03C7plH06gMVuPal1SitadSxssBltdnx7NK9uPzFlW4twKYN64lF90/B\nOYNS2ng1HceQF+C0bVT2cyTPY6w2O77a2rJx+7JRrfbcJg9IiA7DQ9Naeri9vPwA9pX+/Jgicrc+\nrwIPfdrSKuXcQT3wwIXB3QuvK0wmwSMXD3b7O9xZVI0rX1zFZvMedqi8Dle/tAr/WrLHtf4xJjwE\n/3fVSLxww2geOdcBDHkBLkvbK+8oR/I8ZdWBctci9uTYcEzI4vSXN101pi/GpDsWVVtsCn+cv527\nHNtwuKIed761Ac3O/oIDU2LxzHWjYGZ7ny4REdx1VhaeuHKE6+8yv6IeV85die2FVTpXZ3xKKXy4\n7jCmP7McG/NbmhrnpHfHN/dNxpVjUgP6CDJvYMgLcO7Ttfxt01O+2NxywsVFw3vxh6eXmUyCv182\nzPX3vPpAhdt0ObWode6kLXee+5sYHYZXbslxNfilrrs6py9eunGM63zwo7XNuHbeaqzcd1Tnyoyr\noq4Zd761Ab//ZCvqnOtuQ0yC/7lgID64cwLbonQSQ16AS0uIQojzB2NRVSPqm606V2R8TVabW3f1\nGZoF2eQ9g3rGYdYZLWui/v71Lhyrb27jFcHHble4//3N2F3imM4OM5vw0k1j+APSC6YOScE7d4xH\nXIQjPNc2WXHra+vw9dag7b/fad/vLsUFTy/DYs0GoX7J0fjs7km45+z+/CW6CxjyAlyo2YQ0zTd4\njuZ13Q+7y1DT6AjLfRMiMapvN50rCh73nZuN3s7ddOV1zXhi0W6dK/Iv/7d4N77VtJn5x+XDkZPB\nY/a8JScjAR/NmYiUOOfpGDY77n1vI95aladrXUbR0GzDnz7fjtteW4eymibX8zdPSMfXv5yM4Zoe\nhdQ5DHlBwO14M+6w7bIvtrRM1c4Y2ZtrRHwoOjwEf7pkqOv6vbX52JRfqWNF/uPzzYV44YSdtOzd\n6H0De8bik7smur7PKgU88vkOPLEwlw3o27C9sAoX/2c53lzVclxcUkw4Xrt1LP4ycxgiw8w6Vhc4\nGPKCgNvmC47kdUltkxXfaqYUZozkrlpfu2BoCs4d1AOA4wfqHz7bDqvNfopXBbYth4/h9x9vdV2f\nPTCZO2l9KLV7FD6eMxEjNaP6L/ywH3e/s5FLZE5gsys8//0+XPr8T24dH84bkoJF90/G2c7/t8kz\nGPKCgNvmC27175IlO4tdZ38OTInFwJ6xOlcUfEQEj84YiohQx7evnUXVbqMBwaakuhGz31rv+rrM\nSo7mTlodJESH4b1fjMfZA1tOx1i4oxhXv7QKxVXspQc4dn1fO28Vnly0G1bnKGdUmBmPXzEc824a\ng0Qes+dxDHlBoJ/bSB6na7tCu6uWGy700zchCr88J9t1/a8le1B4LPiO7Wu02DD7rQ0oqXasZ4qP\nDMUrt4xFXESozpUFp6iwELx8c45b0+TthdWY+fwKbCsI3hYrx4+AnPbMcqzLa1leMSqtGxb8ajKu\nGZvGZS9ewpAXBE482ozrRDqnqt6CFZoWCZeMYMjT0y8m90P/Ho5fYGqbrHjo021B1TtPKYWHPt2G\nLYcd/cTMJsHz149GJs+k1VWI2YQ/XTLEreVPSXUTrnppJb7aeuQUrw48ZTVNmPP2Bvzuoy2obXJM\nXZtNgl9PHYCP7pzAM5S9jCEvCCREhyE+0vGbfYPFhuJqTh10xpJdJbDYHCFiRGo80hLZlkJPYSEm\nPHb5cBwfAFi2pwwfrj+sb1E+9NKyA269Ah+5aDDOyE7SsSLSumF8Ot68fZyrxUqjxY57392Ev361\nE5YgWUO6YFsRLnh6GRbtaFnHnJEYhY/nTMB9U7MRYmYE8Tb+DQcBEUEWmyJ32TfbWvpfTR/eS8dK\n6LicjATM0kyN/e2rXTgSBNO2S3eV4PGFua7r68b1xS0TM/QriFo1qX8SPrtnktvo6n9XHMT1L69G\naQD/sl1Z14xfvrcJd7+zERV1Lb0srx+fhq9/NRmj0rrrWF1wYcgLEv14vFmXVDdasHxvy1TttGE9\ndayGtH53wUDXkoSaJiseDPBp270lNbjv/c04/kccl5GA/50xjGua/FRWcgzm3zMJUwenuJ5bl1eJ\n6c8ux/e5pTpW5nlKKSzcXoTzn16GLzWtpnrFR+DN28fhH5cNRzRPXvEphrwgwePNumbprhLXOaBD\ne8chPZHrSPxFRKgZT1w5wm3a9r21gTltW1rTiFtfW+da29SnWyRevHE0wkL4rdyfxUeGYt5NY/D7\nCwfi+Kbno7XNuO31dXj0ix1otNj0LdADDlfUY9Yb6zHn7Y1ujY2vGJ2KhfdPwZQByW28mryF3xmC\nhLZX3t7SGh0rMaYF21qOMeNUrf85cdr2r1/txL7SwBqxrm+2Ytbr6127iKPCzHjllhy2nTAIk0lw\n91n98fas8UiObflv9vrKPMx4bgW2FhzTsbrOs9jsePGH/Tjv3z/iO83IZFJMOF6+OQdPXT3StSac\nfI8hL0hk92gJeYH2w8/bahot+HFPmeuaIc8//e6CgRiQ4vg6b7DY8Kv3NqHJavwREgCw2uz45bub\nsK3Q0Ybj+E7awb3idK6MOmpi/yQsun8KzhvSMn27p6QWlz7/E/761U5DNU9eue8oLnp2OR5fmItG\ni2OmQwS4YXwalv7mTLc/I+mDIS9IpCVEIcy5k6mkuglVDRadKzKO73JL0exsNDu4VxxbVPipiFAz\nnr1ulGvqcmdRNZ5YaPyzbZVSePTLHViqGSX5y8yhPBnAwBKiwzDvpjH4x2XDERnqOL7LrhybMs77\n1zJ8u7PEr9eV7i6uwa2vrcX1r6zBnpKWQYPBveLwyV0T8ffLhiM+iqN3/oAhL0iEmE1u6/L2ccq2\n3b7RTtVyw4VfG9QzDn+YPth1/d8VB/HDbmMvbp+37ADeXp3vup5zZhZuGJ+uY0XkCSKC68enYeH9\nk3FG/5bWN4XHGnDHm+tx/ctrsL3Qvxoo5x2tw/98tAXTnlmGH3a3zG5EhZnxx4sG48t7J2E0d876\nFYa8IJKd0nIE194STtm2R12TFd9rQsI0TtX6vZsnpOMczSjXbz7cgoLKeh0r6rwvtxzBP79paZVy\nycje+P0FA3WsiDwtPTEab80ah6euGonumtGvVQfKcfF/VuC+9zdhT4m+v5TvKanB/e9vwjlP/YCP\nNhTgeD99EeDKMalY+tszccfkfux754e4lzmIaNfl7eW6vHb5cU+Z21m1/TV/h+SfRARPXjkCFz6z\nHGU1Taioa8actzfg4zkTEeGcGjOC73NL8esPNruux2Uk4P+uGgETz6QNOCKCK8ak4qyByXhm6V68\nsyYfNmeS+nzzEXy++QjOHdQDd56ZhbEZ3X3SLsdis2PprhK8vTrf7aSf46YMSMZD0wZxXaifY8gL\nIgx5Hbd4R8tU7QWcqjWMxJhwPH/9aFz/8mpY7QrbC6vx0Kfb8K+rRxqin9yq/eWY8/YG1yHuWcnR\nmHfzGISHGCekUsclxoTjLzOH4ZaJGXj8m1ws3tlyUsTS3FIszS1Fdo8YXD46FZeO6o1e8ZEefX+l\nFLYUVOGbbUWYv7nQdSay1uTsJNxzdn+c3i/Ro+9N3sGQF0SyUzQhT+fhfyOw2OxuLQHO504xQxmX\nmYA/zxiKR+ZvBwB8tqkQw/rEY9YZmad4pb425VfijjfWuUaQU7tH4u07xqNbVJjOlZGvZCXHYN7N\nOdiUX4m5P+7H4p0lrubXe0tr8fjCXDyxKBej07rjjP5JmJydhJF9uyG0E9OlJdWNWJdXgbUHK7B0\nV6mrRY+WSYBzB6fgnrP747S+3br6xyMfYsgLIumJ0Qg1Cyw2haKqRtQ0WhAbwR1QJ7PuYAWqGx3t\nDHrHR2Bob05LGM2N49OwvaAKHzjPtP3Hgl3ITIrCOYP8M7BvPnwMt7y6FnXNjtYvKXHhePeO0z0+\nYkPGMCqtO166KQf7y2rx8rID+GLLEdQ7vzaUAjYcqsSGQ5V4ZulehIeYkJUcg+yUGPRPjkFCTBji\nIkIRd/zc8mYbGixWVNZZcKi8Dnnl9dhXWttqqDsuKSYc147ti+vGp6FPN34NGhFDXhAJNZuQmRTt\n2vK+r7SWZwi2QTtVct6QFENM85E7EcFfLh2K3SU12Hz4GGx2hbve3oi37xiPsRkJepfnZu3BCtz+\nestpFgnRYXh71nikJUbpXBnpLSs5Bo9dMQKPXDwEi3YU49ONhfhp/1Fou6w0We3YWVSNnUXVXXqv\n+MhQnDckBdOG9cTk7GSepmJwDHlBJrtHrCvk7WXIOymlFJa4hTyuxzOq8BAz5t00Bpe/uBIFlQ1o\nstpx++vr8OGdE/xm0fjyvWX4xZvrXQ1lu0eF4s3bx7ntiCeKDg/B5aNTcfnoVJTXNuGn/eX4ae9R\nrNh3tM0RubaEh5gwKq0bxmYkYHxmIsb3S+jUtC/5J4a8IKPdHcp1eSe340i165tmbEQIxvfzr1Ef\n6pgecRF4e9Z4XDl3JY7WNqOm0YqbX12Lj+dM0P0c4q+3FuHXH2x2nY2cHBuOd+4YjwEMeNSGxJhw\nzBjZGzNG9gYAVNY1Y19ZLfaW1CKvvA5V9RbUNFlQ3WCFiKNZeFSYGTHhIUhLiEJ6YjQykqLQLymG\no3UBjCEvyGh/cHCH7clpR/HOGdSDv9kGgIykaLxx+zhc+9Jq1DRZUVbThGteWo13fjHe7WxnX1FK\n4bnv9uGpJXtcz/WOj8A7vzidp6pQh3WPDsPY6AS/W4ZA+uJPriDjvsOWIe9klpywHo8Cw9De8Xjl\nlhyEO0cuiqsbcc1Lq3x+OHyjxYZff7DZLeBlJkXjgzsnMOARkccw5AWZjMRohDibqRYea0Bdk3EO\nw/aVwxX1rsXLYWYTzhyQrHNF5Enj+yXi1VvHIirM0XPuaG0zrnlpNRZpeiJ60/6yWlw1dxXmbz7i\nem5iViI+u3si+iZwkwUReQ5DXpAJCzEhI0l7hi1H80707a6WUbwJWYlsMxOAJvVPwluzxiH+eHsJ\niw13vrUBTyzMhdW5Ns7TlFJ4e/UhXPTscmzTnEl63bg0vHH7OPbBIyKPM0zIE5EEEVkiInud//7Z\ntlAR6Ssi34vIThHZISL36VGrv+PJF23jVG1wGJOegE/vnog0zejZCz/sx1UvrfL4Lz+HK+px++vr\n8Mf52107aMPMJvz5kiH4x2XDuOaTiLzCSN9ZHgSwVCmVDWCp8/pEVgC/VUoNAXA6gHtEZIgPazQE\n95DHHbZax+qbseZgheuaIS+wZSXHYP49kzBFMyW/Kf8Ypj+7HE8szHX1rOusY/XNeGJhLqb+60d8\nv7vM9fyAFMf73jYpk/0XichrjLS7diaAs5yP3wDwA4AHtDcopYoAFDkf14jILgB9AOz0WZUG0F+z\nw3YfN1+4+X53qetg8JF9uyElLkLnisjbEqLD8PqtY/Hij/vx9Ld7YLEpNFvteOGH/XhvbT5unpCB\nG8anoUcHvhb2l9XindX5+HD94Z8FxdsmZeCBCwchIpTn0BKRdxkp5KU4QxwAFANoc4hFRDIAjAKw\nxrtlGc8AzQ7bPRzJc6OdquVZtcHDZBLcc3Z/nDu4Bx74ZBu2HHbstq2st+CZpXvxn+/2YkJWIqZk\nJ2N0endkJcegW2QoTCaB1WZHUVUj9pXVYkNeJb7LLW311IHhfeLx6IyhGJPOBuRE5Bt+FfJE5FsA\nrR0t8AfthVJKiYhq5b7jnycGwCcA7ldKtXrGi4jMBjAbANLS0jpdsxFlJkXDJIBdAYcrGlDfbEVU\nmF99Keii0WLDD5opNYa84DOoZxw+u2siPt9SiKcW70FBpaMhtl0BP+0rx0/7yl33ijiOCmy2tr1R\no3+PGNx3bjYuGt4LJhOnZonId/zqJ7tSaurJPiYiJSLSSylVJCK9AJSe5L5QOALeO0qpT9t4r3kA\n5gFATk7OSQNjIAoPMSMzKRr7y+oAAHtKanFa3246V6W/VfvLXYd/ZyRGuZ0OQsHDZBJcNioVl4zo\nja+3FeG9tflYfaDiZ/cphZMGvLAQE84akIwbT0/HGf2TGO6ISBd+FfJO4QsAtwB4zPnvz0+8QRwr\nmP8LYJdS6l++Lc9YBvWKc4W83KJqhjwAi0/YVcsF8cEtxGzCzNP6YOZpfXDkWAOW7y3D6gMV2FNS\ng0Pl9a61diJAYnQY0hOjMbxPPMZlJmBydhJb7xCR7owU8h4D8KGIzAJwCMDVACAivQG8opSaDmAS\ngJsAbBORzc7XPayUWqBHwf5sSK84fL3VscRxVyvrh4KN3a7c+uOdP7S1VQMUrHp3i8Q1Y9NwzdiW\npR02u4LFZkd4iIm/EBCRXzJMyFNKlQM4t5XnjwCY7ny8AgC/27bDoJ4tO2x3FXPzxeaCYyiraQLg\nGJUZncbF8dQ2s0lgNnGHLBH5LyP1ySMPGtQrzvU4t6gaSgXVssSfWbyjZRTvnEE9YOYaKiIiMjiG\nvCDVOz4CcRGOgdzqRiuOVDXqXJG+luxsObeUU7VERBQIGPKClIj8bDQvWO0vq3VtQokINeGM/kk6\nV0RERNR1DHlBbLBmXV5uEK/L0zZAnpydjMgwrrMiIiLjY8gLYoM1I3mtdegPFjzlgoiIAhFDXhDj\ndC1QVtOEjfmVAACTAOcOZsgjIqLAwJAXxAakxOB4e6+DR+vQaLHpW5AOlu4qwfGNxTnpCUiIDtO3\nICIiIg9hyAtiUWEhyEyMBuA4m3NPSfCty3Obqh3KUTwiIgocDHlBblAvzeaLouAKeXVNVizfd9R1\nfR7X4xERUQBhyAtyg3u2rMvbVRxc6/KW7y1zHTA/ICUG6c5RTSIiokDAkBfktJsvgu0M28Vuu2rZ\nAJmIiAILQ16QG3RCr7xgOd7MarPju9xS1zWnaomIKNAw5AW51O6RiA13HG92rN6CkuomnSvyjXV5\nlThWbwEApMSFY3ifeJ0rIiIi8iyGvCDnON6sZTQvWKZstbtqzxuSApNJdKyGiIjI8xjyCIN6BtfJ\nF0opLN5Z7Lo+j+vxiIgoADHkkdtU5baCKh0r8Y3c4hoUVDYAAGLCQ3B6vwSdKyIiIvI8hjzCMG3I\nKwz8kKedqj1rYDLCQ8w6VkNEROQdDHmE7JQYhIc4vhQKjzXgaG1gb75wn6rlrloiIgpMDHmEULMJ\nQ3q3rMsL5NG8I8casL3Qse4wxCQ4a2APnSsiIiLyDoY8AgCMCJJ1edqp2glZiYiPDNWxGiIiIu9h\nyCMAwPDUbq7HWwM45C3a0TJVe/5Q7qolIqLAxZBHAIARqdrNF8d0rMR7jtU3Y83BCtf1eYO5Ho+I\niAIXQx4BALKSYxAZ6thlWlLdhNLqRp0r8rylu0phszuObTutbzf0jI/QuSIiIiLvYcgjAIDZJBjW\nJ2oViKYAABItSURBVLA3X2h31Z4/lKN4REQU2BjyyGV4n8Bdl9fQbMOPe8pc1xdwPR4REQU4hjxy\ncV+XF1ghb9neMjRa7ACA/j1ikJUco3NFRERE3sWQRy7aky+2FlRBKaVjNZ61eEdL65Tz2QCZiIiC\nAEMeufRLikZ0mGPzxdHaJhQHyOYLq82OpbktIY9TtUREFAwY8sjFZJKfjeYFgrV5FThWbwEA9IyL\nwHDNn5GIiChQMeSRG7d1eQES8tymaoemwGQSHashIiLyDYY8cqM9+WJLgfGbIiulsFhzygWnaomI\nKFgw5JGbESdM19rtxt58sb2wGkeqHGsL4yNDMS4zQeeKiIiIfIMhj9ykJ0YhIToMAFDVYMGBo3U6\nV9Q12gbI5w7qgVAzv+SJiCg48CceuRERjE5rmbLdeKhSx2q6btEO7SkXnKolIqLgYZiQJyIJIrJE\nRPY6/929jXvNIrJJRL7yZY2BYlRay1/txnzjhryDR+uwp6QWABAeYsKUAUk6V0REROQ7hgl5AB4E\nsFQplQ1gqfP6ZO4DsMsnVQWgMektIW+DgUfyFmwrcj2eMiAZUWEhOlZDRETkW0YKeTMBvOF8/AaA\nS1u7SURSAVwE4BUf1RVwRqTGw+xsM7K3tBZVDRadK+ocbcibPpxTtUREFFyMFPJSlFLHf2oXAzjZ\n2VRPA/g9AHtbn0xEZovIehFZX1ZW1tatQScqLARDesW5rjcfNl4rlUPlddhxpBoAEBZiwtTBPMqM\niIiCi1+FPBH5VkS2t/LPTO19ynGo6s96e4jIxQBKlVIbTvVeSql5SqkcpVROcnKy5/4QAUK7+WJD\nXoWOlXTO19qp2uxkxEaE6lgNERGR7/nVIiWl1NSTfUxESkSkl1KqSER6ASht5bZJAGaIyHQAEQDi\nRORtpdSNXio5YI3JSMAbqw4BANblGW9dnnaq9qIRnKolIqLg41cjeafwBYBbnI9vAfD5iTcopR5S\nSqUqpTIAXAvgOwa8zhmX0dI0eGN+JZqtbc5++5VD5XXYXuicqjWbcC6naomIKAgZKeQ9BuA8EdkL\nYKrzGiLSW0QW6FpZAOoZH4H0xCgAQJPVjm2FxlmX5zZVOyAJcZyqJSKiIGSYkKeUKldKnauUylZK\nTVVKVTifP6KUmt7K/T8opS72faWBQzuat+agcdblue+q7aVjJURERPoxTMgj39Oe87rWICEvv7ze\nbap26hBO1RIRUXBiyKOTGp+Z6Hq8Ia8SNvvPNjT7He1U7eRsTtUSEVHwYsijk+qbEImecREAgJom\nK3Y6+875sy+2HHE95lQtEREFM4Y8OikRwfh+LVO2K/cf1bGaU9tdXINdRY4gGh5iwvlDOVVLRETB\niyGP2jQpK8n1+Kf95TpWcmrzNxe6Hk8dksIGyEREFNQY8qhNE/u3rMtbe7AcTVabjtWcnN2u8MXm\nlqnaS0/ro2M1RERE+mPIozaldo9ChrNfXuP/t3fnwXWV5x3Hv49lCa8gvGCMF2wTszg2YEcYDIFA\nS6eAaR3SpJCUJQmZtGlKmzYzJc3QpPmn00ka0jLJ0LrshbI0BOw0hMQQlgLB2GAbvIJZvLFY2MgL\n3mT77R/3WpJVCd0rXd0rHX0/M3fuObov9zx+eW395rznvKfxIEvW98z18ha9tZVNDbsBqB1UzadO\n9FF1kqS+zZCnDp39sRZTtmt75nV5D7c4izd72mhq+ju0JUl9m78J1aGW1+U90wND3t79Bw5bAPnT\n052qlSTJkKcOzTphOBG57WUbGti2q7GyBbXy5Jp6tu3O1TT26IF8YvzRFa5IkqTKM+SpQ8MG13Dq\n2FoADiZ4+rX6Cld0uHkt7qqdc/px9OsXFaxGkqSewZCnglxwUvONDE+s2VzBSg7XsGsfj61qrse7\naiVJyjHkqSAXnHRM0/ZTa+o52EMecfbQkk3s238QgKljjmTyqKEVrkiSpJ7BkKeCTBtzFMMH1wCw\n5cN9LH97W4UrgpQS972woWn/ijPGV7AaSZJ6FkOeCtKvXxy29txvVld+ynbJhgbWvLcDgIHVVcw5\n/bgKVyRJUs9hyFPBzj+5ecp2wcr3KlhJzn0vrG/avvTU0T7GTJKkFgx5KtgFJ42kpio3ZFa8vZ0N\nW3dVrJYdexr5+bLmtfGumOlUrSRJLRnyVLChA6o5p8WzbH+14t2K1TJ/2dvsbsw9R/fEUUOYMb62\nYrVIktQTGfJUlIumHtu0/ejyyoW8e1tM1V5xxngiXBtPkqSWDHkqyoWnjOLQWsMvrv+Azdv3lL2G\n5Zu2sXzTdgBq+vfjMzNcG0+SpNYMeSrK8CFHMHPiMABSgl+0eGZsudz53FtN2xdPPZbaQTVlr0GS\npJ7OkKeiXXpq81IlDy99u6zHfn/nXuYtaz7m1bMmlPX4kiT1FoY8FW32tNFUV+XmbJdtaOCN+p1l\nO/Z/LVzf9ISL08bVesOFJEntMOSpaEcPrjnsMWflOpu3d/8B/vP5dU37Xz5ngjdcSJLUDkOeOuWy\n6c03Ozy8ZFNZnmX7s5c2Ub9jLwCjjjyCS6aN7vZjSpLUWxny1CkXnHwMQwf0B2D91l089/qWbj3e\ngYOJf3/q9ab9az85keoqh68kSe3xt6Q6ZUB1FX80Y2zT/t0tplG7wyOvvMNbW3JP2DhqYDVfOPP4\nbj2eJEm9nSFPnfYnZzY/SmzBqvd4r5vWzDt4MPGTJ9Y27V8z63iGHNG/W44lSVJWGPLUaZNHDW1a\nM+/AwXTYUyhK6ecvv83qd3cAMKimii+eM7FbjiNJUpYY8tQlV57VPG1612/XsXvfgZJ+f+OBg9y4\n4NWm/Ws/OZFhg138WJKkjhjy1CUXTz2WMbUDAdj64T7uW1Tas3n3LdrAuhbX4n3l3Ekl/X5JkrLK\nkKcuqa7qx1fPaw5ec59+o2mx4q5q2LWPH/56TdP+n35qEkcNrC7Jd0uSlHWGPHXZ5WeMY8SQ3BTq\nO9v2cH+Jzub98Nev0rCrEYCxRw/ky16LJ0lSwXpNyIuIYRGxICJey78f3U672oj4aUSsjohVETGr\n3LX2NQOqqw6bRv3RY6+xbXdjl75z6YYG7lnYvCzLDbOnMKC6qkvfKUlSX9JrQh7wLeDxlNJk4PH8\nflv+FXg0pXQycBqwqkz19WlfPHvCYdfmtVzypFh7Gg/wzQeWcughGudOHsHvf3xUKcqUJKnP6E0h\nbw5wZ377TuDTrRtExFHAecCtACmlfSmlhrJV2IcNqK7i+otPbtq//dk3Wb5pW6e+6/uPruH1+g+B\n3JIp/3jZNJ9RK0lSkXpTyBuVUnonv/0u0NapnYlAPXB7RCyJiFsiYnDZKuzj/uDU0dQdn5tFbzyQ\n+Mb9S9nTWNySKvOWbuK2Z99s2r9h9hTGDRtU0jolSeoLelTIi4jHImJ5G685LdullBKQ2viK/sAM\n4OaU0nTgQ9qZ1o2Ir0bE4ohYXF9fX+o/Sp8UEfzgc6cxMH/t3NrNO/nOvOXk/nd1bOmGBq5/8OWm\n/QtPOYbPzxzXLbVKkpR1PSrkpZQuTClNbeM1D3gvIkYD5N83t/EVG4GNKaWF+f2fkgt9bR1rbkqp\nLqVUN3LkyO744/RJE0cM5u8vndK0/8DijfyoxWLG7Vmy/gOuunUhexpzy69MGjmYGy8/3WlaSZI6\nqUeFvA7MB67Jb18DzGvdIKX0LrAhIk7K/+h3gZXlKU+HfH7mOC6bPqZp/6bfrOUf5q9od/28h5Zs\n5MpbFrJjz34AagdV8x9X13HkANfEkySps3rTU97/CXggIq4F1gF/DBARxwG3pJQuybe7DrgnImqA\nN4AvVaLYviwi+P5nT+WDXft4ck1uKvyO597i+Te28LXzT+CsScOprurHso0N3P7sWzz9avN0+bDB\nNdx97ZmcMHJIpcqXJCkTotDrpbKsrq4uLV68uNJlZM6uffv5m/uX8eiKdwtqP2H4IOZeXceJo4Z2\nc2WSJPVeEfFiSqmuo3a9abpWvcygmv7cfOUMbph9CgOq2x9qEXB53Th+8ZfnGvAkSSqR3jRdq14o\nIvjKuZP4zIyx3P38Oh5fvZk363ey/2Bi4ojBzJw4jGtmTWDCCFe6kSSplJyuxelaSZLUezhdK0mS\n1IcZ8iRJkjLIkCdJkpRBhjxJkqQMMuRJkiRlkCFPkiQpgwx5kiRJGWTIkyRJyiBDniRJUgYZ8iRJ\nkjLIkCdJkpRBhjxJkqQMMuRJkiRlkCFPkiQpgwx5kiRJGRQppUrXUHERUQ+s6+bDjADe7+Zj9DX2\naenZp6Vnn5aefVpa9mfpdXefHp9SGtlRI0NemUTE4pRSXaXryBL7tPTs09KzT0vPPi0t+7P0ekqf\nOl0rSZKUQYY8SZKkDDLklc/cSheQQfZp6dmnpWeflp59Wlr2Z+n1iD71mjxJkqQM8kyeJElSBhny\nSiwiLoqINRGxNiK+1cbnERE35T9/OSJmVKLO3qSAPj0/IrZFxNL86zuVqLO3iIjbImJzRCxv53PH\naJEK6FPHaBEiYlxEPBERKyNiRUT8VRttHKdFKLBPHadFiIgBEfFCRCzL9+n32mhT0XHav5wHy7qI\nqAJ+AvwesBFYFBHzU0orWzS7GJicf50J3Jx/VxsK7FOA/00pXVr2AnunO4AfA3e187ljtHh38NF9\nCo7RYuwHvplSeikihgIvRsQC/y3tkkL6FBynxdgL/E5KaWdEVAPPRMQvU0rPt2hT0XHqmbzSmgms\nTSm9kVLaB9wHzGnVZg5wV8p5HqiNiNHlLrQXKaRPVYSU0tPA1o9o4hgtUgF9qiKklN5JKb2U394B\nrALGtGrmOC1CgX2qIuTH3s78bnX+1fpGh4qOU0NeaY0BNrTY38j//0tUSBs1K7S/zs6fCv9lRHy8\nPKVllmO0ezhGOyEiJgDTgYWtPnKcdtJH9Ck4TosSEVURsRTYDCxIKfWocep0rbLgJWB8/pT5JcDD\n5E6NSz2FY7QTImII8CDwjZTS9krXkwUd9KnjtEgppQPA6RFRCzwUEVNTSm1em1sJnskrrU3AuBb7\nY/M/K7aNmnXYXyml7YdOmaeUHgGqI2JE+UrMHMdoiTlGi5e/xulB4J6U0s/aaOI4LVJHfeo47byU\nUgPwBHBRq48qOk4NeaW1CJgcERMjoga4Apjfqs184Or8HTdnAdtSSu+Uu9BepMM+jYhjIyLy2zPJ\njestZa80OxyjJeYYLU6+r24FVqWUbmynmeO0CIX0qeO0OBExMn8Gj4gYSO4GwdWtmlV0nDpdW0Ip\npf0R8RfAr4Aq4LaU0oqI+LP85/8GPAJcAqwFdgFfqlS9vUGBffpZ4GsRsR/YDVyRXOW7XRFxL3A+\nMCIiNgLfJXfBsGO0kwroU8docc4BrgJeyV/vBPBtYDw4TjupkD51nBZnNHBnfhWIfsADKaX/6Um/\n833ihSRJUgY5XStJkpRBhjxJkqQMMuRJkiRlkCFPkiQpgwx5kiRJGWTIkyRJyiBDniRJUgYZ8iSp\nTCLiryMiRcQXKl2LpOwz5ElS+Xwi//5iRauQ1Cf4xAtJKpOIWEXuAeVH+rgoSd3NM3mS1AkRcVlE\nNEbEwog4vp0238tPz26NiAScDAwBDuZ/niLiqrIWLqnP6F/pAiSpl9oMLAAuBv4W+HrLDyNiUv7n\ni4B/JveQ8muA5/L/3SFPlqFWSX2QIU+SOiGl9GxEXAZsAeraaHITUAP8eUppcUTUkgt5d6aU5pax\nVEl9lNO1ktRJKaW9wEpy07BNIuIPgdnA3JTS4vyPZ+TfXypfhZL6MkOeJHXNauDIiBgLEBEDgX8B\n3ge+3aLdDKAReKXsFUrqkwx5ktQ1q/PvU/LvfwdMBK5PKX0AEBH9gWnAyvzZP0nqdoY8SeqappAX\nESeQu9nit8DtLdpMAQbgVK2kMvLGC0nqmpZn8i4k9+/q11utg3d6/n1JOQuT1LcZ8iSpa9YCB4DP\nAbXAj1NKrcPc8Pz79nIWJqlv84kXktRFEfEa8DFya+edmFLa1urz84CngE3AvcCHwIqU0n+Xu1ZJ\nfYfX5ElS1x2asr2+dcADSCk9DVxHLtxdB3yX5ilcSeoWnsmTpC6KiGeAWcDQlNKuStcjSWDIk6Qu\niYggd63dhpTSlI7aS1K5OF0rSV0zGRiCd85K6mEMeZLUNdPz74Y8ST2K07WSJEkZ5Jk8SZKkDDLk\nSZIkZZAhT5IkKYMMeZIkSRlkyJMkScogQ54kSVIGGfIkSZIyyJAnSZKUQf8Hxp4lMBgrSSwAAAAA\nSUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10, 7))\n", "ax.plot(times, qt.expect(qt.sigmaz(), rho), linewidth=3.0)\n", "ax.set_xlabel(r'$\\gamma t$', fontsize=20)\n", "ax.set_ylabel(r'$\\langle \\sigma_z \\rangle$', fontsize=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Output field dynamics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `MemoryCascade` class also has a convenient method called `outfieldcorr` that allows you to compute any ouput field correlation function of the type\n", "\n", "$$\n", "\\langle c_1(t_1) c_{2}(t_{2}) \\dots c_n(t_n) \\rangle\n", "$$\n", "\n", "where each $c_i(t_i)$ is one of $b_{\\rm out}(t_i)$ or $b_{\\rm out}^\\dagger (t_i)$ (see the figure at the top). Below we use `outfieldcorr` to compute the photon number and the $g^{(2)}(0,t)$ correlation function of the output field.\n", "\n", "The syntax of `outfieldcorr` is\n", "\n", "````\n", "outfieldcorr(rho0, blist, tlist, tau)\n", "````\n", "\n", "where\n", "\n", "`rho0` is the atom's initial state\n", "\n", "`blist` is a list of integers specifying the operators $c_i$, where an entry of `1` means $b_{\\rm out}$ and an entry of `2` means $b_{\\rm out}^\\dagger$. So, for example `blist = [1, 2, 2, 1]` means that we want to compute $\\langle b_{\\rm out}(t_1) b_{\\rm out}^\\dagger(t_2) b_{\\rm out}^\\dagger(t_3) b_{\\rm out}(t_4)\\rangle$.\n", "\n", "`tlist` is the corresponding list of times, $t_1, t_2, \\dots, t_n$.\n", "\n", "`tau` is as usual the time-delay." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Output field photon number" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 28.2 s, sys: 338 ms, total: 28.5 s\n", "Wall time: 17.2 s\n" ] } ], "source": [ "%time bdb = [sim.outfieldcorr(rho0, [2, 1], [t, t], tau) for t in times]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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cOjFok+aYMAteuH02Lp3qGoXz2vYy/OSNPbDZ9bOxnb5t/ZE6LH50PV7e7Erk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\nzwpqYO+rsc7IikN6XLjGEREREXkHk7kgoC6zHqp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2MLNRkq6V9FGLtxin7XSRPpUYp1kx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\nQIQR5gAAACKMMAcAABBhhDkAAIAI+3/jhzTQeCgO4wAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10, 7))\n", "ax.plot(times, bdb, linewidth=3.0)\n", "ax.set_xlabel(r'$\\gamma t$', fontsize=20)\n", "ax.set_ylabel(r'$\\langle b^\\dagger b \\rangle$', fontsize=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Output field second order correlation function" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 26.1 s, sys: 283 ms, total: 26.4 s\n", "Wall time: 15.9 s\n" ] } ], "source": [ "%time g2 = [sim.outfieldcorr(rho0, [2, 1, 2, 1], [times[i], times[i], 0., 0.], tau)/(bdb[0]*bdb[i]) for i in range(len(times))]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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sCPlCxc5oEOQmR9mvT3A5loiIyD8SOxGJAfAWgPuVUk29vrwDQI5S6iwAjwP4Tz/fY5mI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\nU2t3HE583uXSpr1NHzp4/XReqPlAH505RpNHD+m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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10,7))\n", "ax.plot(times, g2, linewidth=3.0)\n", "ax.set_xlabel(r'$\\gamma t$', fontsize=20)\n", "ax.set_ylabel(r'$g^{(2)}(0,t)$', fontsize=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Extrapolate to large times using the Transfer Tensor Method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the memory cascade method maps the non-Markovian problem onto a chain of $k$ cascaded systems, where $(k-1)\\tau < t < k\\tau$, it is intractable for large times due to the exponential growth of the Hilbert space with $k$.\n", "\n", "A useful approach is therefore to use the memory cascade method in conjunction with the Transfer Tensor Method (TTM), implemented in qutip in the `transfertensormethod` module in the `nonmarkov` subpackage.\n", "\n", "The usage of the `transfertensormethod` module is discussed in more detail in the [example-transfer-tensor-method](example-transfer-tensor-method.ipynb) notebook." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "import qutip.nonmarkov.transfertensor as ttm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Construct a list of exact timepropagators to learn from" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `MemoryCascade` class also has a method `propagator` that returns the time-propagator for the atom at a time $t$, i.e., the superoperator $\\mathcal{E}(t)$ such that\n", "\n", "$$\n", "\\rho(t) = \\mathcal{E}(t)\\rho(0),\n", "$$\n", "\n", "where $\\rho(t)$ is the state of the atom. We compute a list of exact propagators $\\mathcal{E}(t_k)$ for a set of \"learning times\" $t_k$, which we then use as input to the TTM." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 2.71 s, sys: 48 ms, total: 2.76 s\n", "Wall time: 1.74 s\n" ] } ], "source": [ "learningtimes = np.arange(0, 3*tau, 0.1*tau) # short times to learn from\n", "%time learningmaps = [sim.propagator(t, tau) for t in learningtimes] # generate exact dynamical maps to learn from" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute approximate solution for long times using the TTM" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 1.26 s, sys: 14.3 ms, total: 1.27 s\n", "Wall time: 1.23 s\n" ] } ], "source": [ "longtimes = np.arange(0, 10*tau, 0.1*tau) # long times for extrapolation\n", "%time ttmsol = ttm.ttmsolve(learningmaps, rho0, longtimes) # extrapolate using TTM" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot and compare" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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QERFRKOKOFxoxJ7SAW2eAMESgrMKhdTlEREQUYhjyNDLonx9gy9EiAEBcs2SNqyEiIqJQ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\n17oOBnW0tjHp/QEAgOxAyAuZyikh79ix5M/kdR3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10, 7))\n", "ax.plot(times, qt.expect(qt.sigmaz(), rho), linewidth=3.0)\n", "ax.plot(longtimes, qt.expect(qt.sigmaz(), ttmsol.states), '--k', linewidth=3.0)\n", "ax.set_xlabel(r'$\\gamma t$', fontsize=20)\n", "ax.set_ylabel(r'$\\langle \\sigma_z \\rangle$', fontsize=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above example shows how the memory cascade method can work well in conjunction with the TTM. The list of learning times necessary to get good result with the TTM will wary from problem to problem and from parameter set to parameter set. There is also no guarantee for the result being correct, but one can check convergence with increasing learning times." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.2.0
Numpy1.13.1
SciPy0.19.1
matplotlib2.0.2
Cython0.25.2
Number of CPUs2
BLAS InfoINTEL MKL
IPython6.1.0
Python3.6.1 |Anaconda custom (x86_64)| (default, May 11 2017, 13:04:09) \n", "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
OSposix [darwin]
Wed Jul 19 22:19:57 2017 MDT
" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version_table()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }