{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Optimization of a Dissipative State-to-State Transfer in a Lambda System" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:51.297636Z", "start_time": "2019-11-10T17:36:49.706568Z" }, "attributes": { "classes": [], "id": "", "n": "1" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:51.989457Z", "iopub.status.busy": "2024-06-03T14:27:51.989274Z", "iopub.status.idle": "2024-06-03T14:27:52.490207Z", "shell.execute_reply": "2024-06-03T14:27:52.489897Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python implementation: CPython\n", "Python version : 3.12.0\n", "IPython version : 8.25.0\n", "\n", "numpy : 1.26.4\n", "matplotlib: 3.7.5\n", "qutip : 4.7.6\n", "scipy : 1.12.0\n", "krotov : 1.3.0+dev\n", "\n" ] } ], "source": [ "# NBVAL_IGNORE_OUTPUT\n", "%load_ext watermark\n", "import os\n", "import qutip\n", "import numpy as np\n", "import scipy\n", "import matplotlib\n", "import matplotlib.pylab as plt\n", "import krotov\n", "import qutip\n", "from qutip import Qobj\n", "import pickle\n", "from functools import partial\n", "%watermark -v --iversions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\newcommand{tr}[0]{\\operatorname{tr}}\n", "\\newcommand{diag}[0]{\\operatorname{diag}}\n", "\\newcommand{abs}[0]{\\operatorname{abs}}\n", "\\newcommand{pop}[0]{\\operatorname{pop}}\n", "\\newcommand{aux}[0]{\\text{aux}}\n", "\\newcommand{opt}[0]{\\text{opt}}\n", "\\newcommand{tgt}[0]{\\text{tgt}}\n", "\\newcommand{init}[0]{\\text{init}}\n", "\\newcommand{lab}[0]{\\text{lab}}\n", "\\newcommand{rwa}[0]{\\text{rwa}}\n", "\\newcommand{bra}[1]{\\langle#1\\vert}\n", "\\newcommand{ket}[1]{\\vert#1\\rangle}\n", "\\newcommand{Bra}[1]{\\left\\langle#1\\right\\vert}\n", "\\newcommand{Ket}[1]{\\left\\vert#1\\right\\rangle}\n", "\\newcommand{Braket}[2]{\\left\\langle #1\\vphantom{#2}\\mid{#2}\\vphantom{#1}\\right\\rangle}\n", "\\newcommand{ketbra}[2]{\\vert#1\\rangle\\!\\langle#2\\vert}\n", "\\newcommand{op}[1]{\\hat{#1}}\n", "\\newcommand{Op}[1]{\\hat{#1}}\n", "\\newcommand{dd}[0]{\\,\\text{d}}\n", "\\newcommand{Liouville}[0]{\\mathcal{L}}\n", "\\newcommand{DynMap}[0]{\\mathcal{E}}\n", "\\newcommand{identity}[0]{\\mathbf{1}}\n", "\\newcommand{Norm}[1]{\\lVert#1\\rVert}\n", "\\newcommand{Abs}[1]{\\left\\vert#1\\right\\vert}\n", "\\newcommand{avg}[1]{\\langle#1\\rangle}\n", "\\newcommand{Avg}[1]{\\left\\langle#1\\right\\rangle}\n", "\\newcommand{AbsSq}[1]{\\left\\vert#1\\right\\vert^2}\n", "\\newcommand{Re}[0]{\\operatorname{Re}}\n", "\\newcommand{Im}[0]{\\operatorname{Im}}\n", "\\newcommand{toP}[0]{\\omega_{12}}\n", "\\newcommand{toS}[0]{\\omega_{23}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example illustrates the use of Krotov's method with a non-Hermitian\n", "Hamiltonian. It considers the same system as the [previous\n", "example](02_example_lambda_system_rwa_complex_pulse.ipynb), a transition\n", "$\\ket{1} \\rightarrow \\ket{3}$ in a three-level system in a\n", "$\\Lambda$-configuration. However, here we add a non-Hermitian decay term to\n", "model loss from the intermediary level $\\ket{2}$. At a technical level, this\n", "examples also illustrates how to use `args` in time-dependent control fields\n", "(\"QuTiP style\"), as opposed to hard-coding parameters or setting them through\n", "a closure, as was done in the previous examples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The effective Hamiltonian\n", "\n", "We consider the system as in the following diagram:\n", "\n", "![Lambda system considered in this notebook](energylevels.png)\n", "\n", "with the Hamiltonian\n", "\n", "$$\n", "\\Op{H}_{\\text{lab}} = \\begin{pmatrix}\n", " E_1 & -\\mu_{12} \\epsilon_P(t) & 0 \\\\\n", " -\\mu_{12} \\epsilon_P(t) & E_2 & - \\mu_{23} \\epsilon_S(t) \\\\\n", " 0 & -\\mu_{23} \\epsilon_S(t) & E_2\n", "\\end{pmatrix}\n", "$$\n", "\n", "in the lab frame.\n", "\n", "However, we now also include that the level $\\ket{2}$ decays incoherently. This\n", "is the primary motivation of the STIRAP scheme: through destructive\n", "interference it can keep the dynamics in a \"dark state\" where the population is\n", "transferred from $\\ket{1}$ to $\\ket{3}$ without ever populating the $\\ket{2}$\n", "state. A rigorous treatment would be to include the dissipation as a Lindblad\n", "operator, and to simulate the dynamics and perform the optimization in\n", "Liouville space. The Lindblad operator for spontaneous decay from level\n", "$\\ket{2}$ with decay rate $2\\gamma$ is $\\Op{L} = \\sqrt{2\\gamma} \\ketbra{1}{2}$.\n", "However, this is numerically expensive. For the optimization,\n", "it is sufficient to find a way to penalize population in the $\\ket{2}$ state.\n", "\n", "Motivated by the [Monte-Carlo Wave Function\n", "(MCWF)](https://en.wikipedia.org/wiki/Quantum_jump_method) method, we define\n", "the non-Hermitian *effective Hamiltonian*\n", "\n", "$$\n", "\\Op{H}_{\\text{eff}} = \\Op{H}_{\\text{lab}} - \\frac{i}{2} \\Op{L}^{\\dagger} \\Op{L}\n", "$$\n", "\n", "In explicit form, this is\n", "\n", "$$\n", "\\Op{H}_{\\text{eff}} = \\begin{pmatrix}\n", " E_1 & -\\mu_{12} \\epsilon_P(t) & 0 \\\\\n", " -\\mu_{12} \\epsilon_P(t) & E_2 - i \\gamma & - \\mu_{23} \\epsilon_S(t) \\\\\n", " 0 & -\\mu_{23} \\epsilon_S(t) & E_2\n", "\\end{pmatrix}\n", "$$\n", "\n", "The only change is that the energy of level $\\ket{2}$ now has an imaginary part\n", "$-\\gamma$, which causes an exponential decay of any population amplitude in\n", "$\\ket{2}$, and thus a decay in the norm of the state. In the MCWF, this decay\n", "of the norm is used to track the probability that quantum jump occurs\n", "(otherwise, the state is re-normalized). Here, we do not perform quantum jumps\n", "or renormalize the state. Instead, we use the decay in the norm to steer the\n", "optimization. Using the functional\n", "\n", "$$\n", "J_{T, \\text{re}} = 1 - \\Re{\\Braket{\\Psi(T)}{\\Psi^{\\tgt}}}\n", "$$\n", "\n", "to be minimized, we find that the value of\n", "the functional increases if $\\Norm{\\ket{\\Psi(T)}} < 1$. Thus, population in\n", "$\\ket{2}$ is penalized, without any significant numerical overhead.\n", "\n", "The decay rate $2\\gamma$ does not necessarily need to correspond to the actual\n", "physical lifetime of the $\\ket{2}$ state: we can choose an artificially high\n", "decay rate to put a stronger penalty on the $\\ket{2}$ level. Or, if the\n", "physical decay is so strong that the norm of the state reaches effectively\n", "zero, we could decrease $\\gamma$ to avoid numerical instability. The use of a\n", "non-Hermitian Hamiltonian with artificial decay is generally a useful trick to\n", "penalize population in a subspace.\n", "\n", "The new non-Hermitian decay term remains unchanged when we make the rotating\n", "wave approximation. The RWA Hamiltonian now reads\n", "\n", "$$\n", "\\Op{H}_{\\text{RWA}} = \\begin{pmatrix}\n", " \\Delta_P & -\\frac{1}{2} \\Omega_P(t) & 0 \\\\\n", " -\\frac{1}{2} \\Omega_P^*(t) & -i \\gamma & -\\frac{1}{2} \\Omega_S(t) \\\\\n", " 0 & -\\frac{1}{2} \\Omega_S^*(t) & \\Delta_S\n", "\\end{pmatrix}\\,,\n", "$$\n", "\n", "with complex control fields $\\Omega_P(t)$ and $\\Omega_S(t)$, see the [previous\n", "example](02_example_lambda_system_rwa_complex_pulse.ipynb). Again, we split\n", "these complex pulses into an independent real and imaginary part for the\n", "purpose of optimization.\n", "\n", "The guess controls are" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:51.316137Z", "start_time": "2019-11-10T17:36:51.300148Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:52.511590Z", "iopub.status.busy": "2024-06-03T14:27:52.511407Z", "iopub.status.idle": "2024-06-03T14:27:52.514485Z", "shell.execute_reply": "2024-06-03T14:27:52.514201Z" } }, "outputs": [], "source": [ "def Omega_P1(t, args):\n", " \"\"\"Guess for the real part of the pump pulse.\n", "\n", " Blackman shape with amplitude `Ω0` from `t0P` to `t0P` + `ΔTP`, with\n", " parameters from `args`.\n", " \"\"\"\n", " t0 = args['t0P']\n", " T = t0 + args['ΔTP']\n", " return args['Ω0'] * krotov.shapes.blackman(t, t_start=t0, t_stop=T)\n", "\n", "\n", "def Omega_P2(t, args):\n", " \"\"\"Guess for the imaginary part of the pump pulse (zero).\"\"\"\n", " return 0.0\n", "\n", "\n", "def Omega_S1(t, args):\n", " \"\"\"Guess for the real part of the Stokes pulse.\n", "\n", " Blackman shape with amplitude `Ω0` from `t0S` to `t0S` + `ΔTS`, with\n", " parameters from `args`.\n", " \"\"\"\n", " t0 = args['t0S']\n", " T = t0 + args['ΔTS']\n", " return args['Ω0'] * krotov.shapes.blackman(t, t_start=t0, t_stop=T)\n", "\n", "\n", "def Omega_S2(t, args):\n", " \"\"\"Guess for the imaginary part of the Stokes pulse (zero).\"\"\"\n", " return 0.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "with the Hamiltonian defined as" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:51.334402Z", "start_time": "2019-11-10T17:36:51.319722Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:52.515988Z", "iopub.status.busy": "2024-06-03T14:27:52.515900Z", "iopub.status.idle": "2024-06-03T14:27:52.518841Z", "shell.execute_reply": "2024-06-03T14:27:52.518614Z" } }, "outputs": [], "source": [ "def hamiltonian(args):\n", " \"\"\"Lambda-system Hamiltonian in the RWA\"\"\"\n", " E1, E2, E3, ΩP, ΩS, γ = (args[key] for key in 'E1 E2 E3 ΩP ΩS γ'.split())\n", "\n", " # detunings\n", " ΔP = E1 + ΩP - E2\n", " ΔS = E3 + ΩS - E2\n", "\n", " H0 = Qobj([[ΔP, 0.0, 0.0], [0.0, -1j * γ, 0.0], [0.0, 0.0, ΔS]])\n", "\n", " HP_re = -0.5 * Qobj([[0.0, 1.0, 0.0], [1.0, 0.0, 0.0], [0.0, 0.0, 0.0]])\n", " HP_im = -0.5 * Qobj([[0.0, 1.0j, 0.0], [-1.0j, 0.0, 0.0], [0.0, 0.0, 0.0]])\n", "\n", " HS_re = -0.5 * Qobj([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0], [0.0, 1.0, 0.0]])\n", " HS_im = -0.5 * Qobj([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0j], [0.0, -1.0j, 0.0]])\n", "\n", " return [\n", " H0,\n", " [HP_re, Omega_P1],\n", " [HP_im, Omega_P2],\n", " [HS_re, Omega_S1],\n", " [HS_im, Omega_S2],\n", " ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and using the following physical parameters:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:51.343719Z", "start_time": "2019-11-10T17:36:51.337196Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:52.520217Z", "iopub.status.busy": "2024-06-03T14:27:52.520134Z", "iopub.status.idle": "2024-06-03T14:27:52.522134Z", "shell.execute_reply": "2024-06-03T14:27:52.521849Z" } }, "outputs": [], "source": [ "ARGS = dict(\n", " Ω0=5.0, # amplitude of both the Pump and the Stokes laser\n", " ΔTP=3.0, # duration of the Pump laser\n", " ΔTS=3.0, # duration of the Stokes laser\n", " t0P=2.0, # starting time for the Pump laser\n", " t0S=0.0, # starting time for the Stokes laser\n", " t_rise=0.3, # switch-on/-off time in update shape\n", " E1=0.0, # energy of level |1⟩\n", " E2=10.0, # energy of intermediary level |2⟩\n", " E3=5.0, # energy of target level |3⟩\n", " ΩP=9.5, # frequency of the Pump laser\n", " ΩS=4.5, # frequency of the Stokes laser\n", " γ=0.5, # decay rate on intermediary level |2⟩\n", " T=5.0, # total process time\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(cf. the [previous example](02_example_lambda_system_rwa_complex_pulse.ipynb),\n", "where these values were hard-coded).\n", "\n", "The Hamiltonian is now instantiated as" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:51.354864Z", "start_time": "2019-11-10T17:36:51.346901Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:52.523434Z", "iopub.status.busy": "2024-06-03T14:27:52.523352Z", "iopub.status.idle": "2024-06-03T14:27:52.525901Z", "shell.execute_reply": "2024-06-03T14:27:52.525628Z" }, "lines_to_next_cell": 2 }, "outputs": [], "source": [ "H = hamiltonian(ARGS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check the hermiticity of the Hamiltonian:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:51.364285Z", "start_time": "2019-11-10T17:36:51.357446Z" }, "attributes": { "classes": [], "id": "", "n": "3" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:52.527187Z", "iopub.status.busy": "2024-06-03T14:27:52.527108Z", "iopub.status.idle": "2024-06-03T14:27:52.529146Z", "shell.execute_reply": "2024-06-03T14:27:52.528908Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "H0 is Hermitian: False\n", "H1 is Hermitian: True\n" ] } ], "source": [ "print(\"H0 is Hermitian: \" + str(H[0].isherm))\n", "print(\"H1 is Hermitian: \"+ str(\n", " H[1][0].isherm\n", " and H[2][0].isherm\n", " and H[3][0].isherm\n", " and H[4][0].isherm))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define the optimization target\n", "\n", "We optimize for the phase-sensitive transition $\\ket{1} \\rightarrow \\ket{3}$.\n", "As we are working in the rotating frame, the target state must be adjusted with\n", "an appropriate phase factor:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:51.375198Z", "start_time": "2019-11-10T17:36:51.366724Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:52.530531Z", "iopub.status.busy": "2024-06-03T14:27:52.530448Z", "iopub.status.idle": "2024-06-03T14:27:52.533144Z", "shell.execute_reply": "2024-06-03T14:27:52.532910Z" } }, "outputs": [], "source": [ "ket1 = qutip.Qobj(np.array([1.0, 0.0, 0.0]))\n", "ket2 = qutip.Qobj(np.array([0.0, 1.0, 0.0]))\n", "ket3 = qutip.Qobj(np.array([0.0, 0.0, 1.0]))\n", "\n", "def rwa_target_state(ket3, *, E2, ΩS, T):\n", " return np.exp(1j * (E2 - ΩS) * T) * ket3\n", "\n", "psi_target = rwa_target_state(ket3, **{k: ARGS[k] for k in 'E2 ΩS T'.split()})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The objective is now instantiated as" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:51.388371Z", "start_time": "2019-11-10T17:36:51.381216Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:52.534402Z", "iopub.status.busy": "2024-06-03T14:27:52.534325Z", "iopub.status.idle": "2024-06-03T14:27:52.537683Z", "shell.execute_reply": "2024-06-03T14:27:52.537387Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "text/plain": [ "[Objective[|Ψ₀(3)⟩ to |Ψ₁(3)⟩ via [A₀[3,3], [H₁[3,3], u₁(t)], [H₂[3,3], u₂(t)], [H₃[3,3], u₃(t)], [H₄[3,3], u₄(t)]]]]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "objectives = [krotov.Objective(initial_state=ket1, target=psi_target, H=H)]\n", "objectives" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate dynamics under the guess field\n", "\n", "We use a time grid with 500 steps between $t=0$ and $T=5$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:51.398777Z", "start_time": "2019-11-10T17:36:51.393811Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:52.538935Z", "iopub.status.busy": "2024-06-03T14:27:52.538849Z", "iopub.status.idle": "2024-06-03T14:27:52.540403Z", "shell.execute_reply": "2024-06-03T14:27:52.540172Z" } }, "outputs": [], "source": [ "tlist = np.linspace(0, ARGS['T'], 500)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We propagate once for the population dynamics, and once to obtain the\n", "propagated states for each point on the time grid:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:54.720111Z", "start_time": "2019-11-10T17:36:51.401596Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:52.541671Z", "iopub.status.busy": "2024-06-03T14:27:52.541593Z", "iopub.status.idle": "2024-06-03T14:27:54.211487Z", "shell.execute_reply": "2024-06-03T14:27:54.211213Z" } }, "outputs": [], "source": [ "proj1 = qutip.ket2dm(ket1)\n", "proj2 = qutip.ket2dm(ket2)\n", "proj3 = qutip.ket2dm(ket3)\n", "\n", "guess_dynamics = objectives[0].propagate(\n", " tlist,\n", " propagator=krotov.propagators.expm,\n", " e_ops=[proj1, proj2, proj3],\n", " args=ARGS,\n", ")\n", "guess_states = objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm, args=ARGS,\n", ")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:54.741953Z", "start_time": "2019-11-10T17:36:54.723039Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:54.213177Z", "iopub.status.busy": "2024-06-03T14:27:54.213083Z", "iopub.status.idle": "2024-06-03T14:27:54.216103Z", "shell.execute_reply": "2024-06-03T14:27:54.215851Z" } }, "outputs": [], "source": [ "def plot_population(result):\n", " fig, ax = plt.subplots()\n", " ax.axhline(y=1.0, color='black', lw=0.5, ls='dashed')\n", " ax.axhline(y=0.0, color='black', lw=0.5, ls='dashed')\n", " ax.plot(result.times, result.expect[0], label='1')\n", " ax.plot(result.times, result.expect[1], label='2')\n", " ax.plot(result.times, result.expect[2], label='3')\n", " ax.legend()\n", " ax.set_xlabel('time')\n", " ax.set_ylabel('population')\n", " plt.show(fig)\n", "\n", "\n", "def plot_norm(result):\n", "\n", " state_norm = lambda i: result.states[i].norm()\n", " states_norm=np.vectorize(state_norm)\n", "\n", " fig, ax = plt.subplots()\n", " ax.plot(result.times, states_norm(np.arange(len(result.states))))\n", " ax.set_xlabel('time')\n", " ax.set_ylabel('state norm')\n", " plt.show(fig)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:55.325200Z", "start_time": "2019-11-10T17:36:54.746616Z" }, "attributes": { "classes": [], "id": "", "n": "15" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:54.217420Z", "iopub.status.busy": "2024-06-03T14:27:54.217337Z", "iopub.status.idle": "2024-06-03T14:27:54.347849Z", "shell.execute_reply": "2024-06-03T14:27:54.347559Z" }, "lines_to_end_of_cell_marker": 2 }, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_population(guess_dynamics)\n", "plot_norm(guess_states)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The population dynamics and the norm-plot show the effect the non-Hermitian\n", "term in the Hamiltonian, resulting in a 30% loss.\n", "\n", "## Optimize\n", "\n", "For each control, we define the update shape and the $\\lambda_a$ parameter that\n", "determines the magnitude of the update:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:55.332957Z", "start_time": "2019-11-10T17:36:55.327833Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:54.349456Z", "iopub.status.busy": "2024-06-03T14:27:54.349350Z", "iopub.status.idle": "2024-06-03T14:27:54.351109Z", "shell.execute_reply": "2024-06-03T14:27:54.350866Z" } }, "outputs": [], "source": [ "S = partial( # Scale the *update* of the pulse value at time t\n", " krotov.shapes.flattop,\n", " t_start=0.0,\n", " t_stop=ARGS['T'],\n", " t_rise=ARGS['t_rise'],\n", " func='sinsq',\n", ")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:55.347468Z", "start_time": "2019-11-10T17:36:55.336694Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:54.352356Z", "iopub.status.busy": "2024-06-03T14:27:54.352263Z", "iopub.status.idle": "2024-06-03T14:27:54.354219Z", "shell.execute_reply": "2024-06-03T14:27:54.354014Z" } }, "outputs": [], "source": [ "pulse_options = {\n", " H[1][1]: dict(lambda_a=2.0, update_shape=S, args=ARGS),\n", " H[2][1]: dict(lambda_a=2.0, update_shape=S, args=ARGS),\n", " H[3][1]: dict(lambda_a=2.0, update_shape=S, args=ARGS),\n", " H[4][1]: dict(lambda_a=2.0, update_shape=S, args=ARGS)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `args` here are required to plug in in the parameters in the guess\n", "`Omega_P1` and `Omega_S1`. Compare this to the [previous\n", "example](02_example_lambda_system_rwa_complex_pulse.ipynb), where the\n", "parameters were hardcoded in the definition of the guess controls." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now run the optimization for 40 iterations, printing out the fidelity\n", "\n", "$$\n", "F_{\\text{re}} = \\Re{\\Braket{\\Psi(T)}{\\Psi^{\\tgt}}}\n", "$$\n", "\n", "after each iteration." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:36:55.357820Z", "start_time": "2019-11-10T17:36:55.351667Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:54.355606Z", "iopub.status.busy": "2024-06-03T14:27:54.355510Z", "iopub.status.idle": "2024-06-03T14:27:54.357240Z", "shell.execute_reply": "2024-06-03T14:27:54.357006Z" } }, "outputs": [], "source": [ "def print_fidelity(**kwargs):\n", " F_re = np.average(np.array(kwargs['tau_vals']).real)\n", " print(\" F = %f\" % F_re)\n", " return F_re" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:07.238734Z", "start_time": "2019-11-10T17:36:55.360831Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:27:54.358559Z", "iopub.status.busy": "2024-06-03T14:27:54.358481Z", "iopub.status.idle": "2024-06-03T14:29:00.830132Z", "shell.execute_reply": "2024-06-03T14:29:00.829877Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " F = -0.007819\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.055166\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.117611\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.178915\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.238526\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.295951\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.350777\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.402680\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.451424\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.496859\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.538920\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.577612\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.613000\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.645200\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.674362\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.700665\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.724303\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.745478\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.764395\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.781255\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.796250\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.809566\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.821372\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.831829\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.841083\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.849267\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.856501\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.862895\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.868544\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.873538\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.877952\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.881855\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.885310\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.888369\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.891080\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.893485\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.895622\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.897522\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.899214\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.900724\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " F = 0.902073\n" ] } ], "source": [ "opt_result = krotov.optimize_pulses(\n", " objectives, pulse_options, tlist,\n", " propagator=krotov.propagators.expm,\n", " chi_constructor=krotov.functionals.chis_re,\n", " info_hook=print_fidelity,\n", " iter_stop=40\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We look at the optimized controls and the population dynamics they induce:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:07.796565Z", "start_time": "2019-11-10T17:39:07.240910Z" }, "attributes": { "classes": [], "id": "", "n": "17" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:00.831745Z", "iopub.status.busy": "2024-06-03T14:29:00.831640Z", "iopub.status.idle": "2024-06-03T14:29:01.012675Z", "shell.execute_reply": "2024-06-03T14:29:01.012396Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pump pulse amplitude and phase:\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Stokes pulse amplitude and phase:\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_pulse_amplitude_and_phase(pulse_real, pulse_imaginary,tlist):\n", " ax1 = plt.subplot(211)\n", " ax2 = plt.subplot(212)\n", " amplitudes = [np.sqrt(x*x + y*y) for x,y in zip(pulse_real,pulse_imaginary)]\n", " phases = [np.arctan2(y,x)/np.pi for x,y in zip(pulse_real,pulse_imaginary)]\n", " ax1.plot(tlist,amplitudes)\n", " ax1.set_xlabel('time')\n", " ax1.set_ylabel('pulse amplitude')\n", " ax2.plot(tlist,phases)\n", " ax2.set_xlabel('time')\n", " ax2.set_ylabel('pulse phase (π)')\n", " plt.show()\n", "\n", "print(\"pump pulse amplitude and phase:\")\n", "plot_pulse_amplitude_and_phase(\n", " opt_result.optimized_controls[0], opt_result.optimized_controls[1], tlist)\n", "print(\"Stokes pulse amplitude and phase:\")\n", "plot_pulse_amplitude_and_phase(\n", " opt_result.optimized_controls[2], opt_result.optimized_controls[3], tlist)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check the evolution of the population due to our optimized pulses." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:09.965861Z", "start_time": "2019-11-10T17:39:07.799328Z" }, "attributes": { "classes": [], "id": "", "n": "18" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:01.014157Z", "iopub.status.busy": "2024-06-03T14:29:01.014047Z", "iopub.status.idle": "2024-06-03T14:29:02.589048Z", "shell.execute_reply": "2024-06-03T14:29:02.588654Z" } }, "outputs": [], "source": [ "opt_dynamics = opt_result.optimized_objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm, e_ops=[proj1, proj2, proj3])\n", "opt_states = opt_result.optimized_objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:10.403930Z", "start_time": "2019-11-10T17:39:09.968140Z" }, "attributes": { "classes": [], "id": "", "n": "19" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:02.590858Z", "iopub.status.busy": "2024-06-03T14:29:02.590739Z", "iopub.status.idle": "2024-06-03T14:29:02.743541Z", "shell.execute_reply": "2024-06-03T14:29:02.743222Z" } }, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_population(opt_dynamics)\n", "plot_norm(opt_states)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These dynamics show that the non-Hermitian Hamiltonian has the desired effect:\n", "The population is steered out of the decaying $\\ket{2}$ state, with the\n", "resulting loss in norm down to 10% from the 30% loss of the guess pulses.\n", "Indeed, these 10% are exactly the value of the error $1 - F_{\\text{re}}$,\n", "indicating that avoiding population in the $\\ket{2}$ part is the difficult part\n", "of the optimization. Convergence towards this goal is slow, so we continue the\n", "optimization up to iteration 2000." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:10.423760Z", "start_time": "2019-11-10T17:39:10.406834Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:02.745086Z", "iopub.status.busy": "2024-06-03T14:29:02.744975Z", "iopub.status.idle": "2024-06-03T14:29:02.750856Z", "shell.execute_reply": "2024-06-03T14:29:02.750594Z" } }, "outputs": [], "source": [ "dumpfile = \"./non_herm_opt_result.dump\"\n", "if os.path.isfile(dumpfile):\n", " opt_result = krotov.result.Result.load(dumpfile, objectives)\n", "else:\n", " opt_result = krotov.optimize_pulses(\n", " objectives, pulse_options, tlist,\n", " propagator=krotov.propagators.expm,\n", " chi_constructor=krotov.functionals.chis_re,\n", " info_hook=krotov.info_hooks.chain(print_fidelity),\n", " iter_stop=2000,\n", " continue_from=opt_result\n", " )\n", " opt_result.dump(dumpfile)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:10.432245Z", "start_time": "2019-11-10T17:39:10.426406Z" }, "attributes": { "classes": [], "id": "", "n": "21" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:02.752257Z", "iopub.status.busy": "2024-06-03T14:29:02.752150Z", "iopub.status.idle": "2024-06-03T14:29:02.754116Z", "shell.execute_reply": "2024-06-03T14:29:02.753861Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final fidelity: 0.966\n" ] } ], "source": [ "print(\"Final fidelity: %.3f\" % opt_result.info_vals[-1])" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:10.444000Z", "start_time": "2019-11-10T17:39:10.437302Z" }, "attributes": { "classes": [], "id": "", "n": "22" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:02.755654Z", "iopub.status.busy": "2024-06-03T14:29:02.755549Z", "iopub.status.idle": "2024-06-03T14:29:02.757552Z", "shell.execute_reply": "2024-06-03T14:29:02.757286Z" } }, "outputs": [], "source": [ "def plot_convergence(result):\n", " fig, ax = plt.subplots()\n", " ax.semilogy(result.iters, 1-np.array(result.info_vals))\n", " ax.set_xlabel('OCT iteration')\n", " ax.set_ylabel('error')\n", " plt.show(fig)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get a feel for the convergence, we can plot the optimization error over the iteration number:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:11.043915Z", "start_time": "2019-11-10T17:39:10.451812Z" }, "attributes": { "classes": [], "id": "", "n": "23" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:02.758894Z", "iopub.status.busy": "2024-06-03T14:29:02.758806Z", "iopub.status.idle": "2024-06-03T14:29:02.903500Z", "shell.execute_reply": "2024-06-03T14:29:02.903193Z" }, "lines_to_next_cell": 0 }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_convergence(opt_result)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have used here that the return value of the routine `print_fidelity` that was passed to the `optimize_pulses` routine as an `info_hook` is automatically accumulated in `result.info_vals`.\n", "\n", "We also look at optimized controls and the dynamics they induce:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:11.630393Z", "start_time": "2019-11-10T17:39:11.048493Z" }, "attributes": { "classes": [], "id": "", "n": "25" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:02.905100Z", "iopub.status.busy": "2024-06-03T14:29:02.904982Z", "iopub.status.idle": "2024-06-03T14:29:03.086960Z", "shell.execute_reply": "2024-06-03T14:29:03.086642Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pump pulse amplitude and phase:\n" ] }, { 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Stokes pulse amplitude and phase:\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(\"pump pulse amplitude and phase:\")\n", "plot_pulse_amplitude_and_phase(\n", " opt_result.optimized_controls[0], opt_result.optimized_controls[1], tlist)\n", "print(\"Stokes pulse amplitude and phase:\")\n", "plot_pulse_amplitude_and_phase(\n", " opt_result.optimized_controls[2], opt_result.optimized_controls[3], tlist)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:14.461895Z", "start_time": "2019-11-10T17:39:11.633126Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:03.088715Z", "iopub.status.busy": "2024-06-03T14:29:03.088575Z", "iopub.status.idle": "2024-06-03T14:29:04.638557Z", "shell.execute_reply": "2024-06-03T14:29:04.638201Z" }, "lines_to_next_cell": 2 }, "outputs": [], "source": [ "opt_dynamics = opt_result.optimized_objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm, e_ops=[proj1, proj2, proj3])\n", "opt_states = opt_result.optimized_objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:14.988468Z", "start_time": "2019-11-10T17:39:14.463937Z" }, "attributes": { "classes": [], "id": "", "n": "26" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:04.640300Z", "iopub.status.busy": "2024-06-03T14:29:04.640188Z", "iopub.status.idle": "2024-06-03T14:29:04.776702Z", "shell.execute_reply": "2024-06-03T14:29:04.776442Z" } }, "outputs": [ { "data": { "image/png": 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", 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77qBTp04MHjyYZcuWsXnzZlatWnXJYycmJpKXl+daMjMza/JUpR66qrEXv78pEoBpK/djVy+SiIjbMiwgBQQEYLFYyMnJqbA+JyeHkJCQi24TGBjI0qVLKSwsJD09nT179uDr60tkZKSrTVRUFKtXr+bMmTNkZmayadMmSktLK7Q5X2RkJAEBARw4cOCSbby9vfH396+wiFTVyL6tadLIk9TjhSxTL5KIiNsyLCB5eXnRvXt3UlJSXOscDgcpKSn07t37Z7e1Wq2EhYVRVlbGokWLGDRo0AVtGjduTPPmzTl16hTLly+/aJsfHD58mBMnTtC8efPLPyGRSvD19uCR68sfZPv6/w6oF0lExE0ZeoktISGB2bNnk5SUxO7duxk1ahSFhYXEx8cDMHz4cBITE13tN27cyOLFi0lNTWXNmjX0798fh8PB+PHjXW2WL19OcnIyhw4dYsWKFfTr14/o6GjXPs+cOcNTTz3Fhg0bSEtLIyUlhUGDBtGmTRvi4uJq9wuQBml4nwj8rR4cyD3DpzuzfnkDERGpdR5GHnzYsGEcO3aMZ599luzsbLp27UpycrJr4HZGRkaFsUNFRUVMnDiR1NRUfH19GThwIPPnz6dJkyauNnl5eSQmJnL48GGaNm3K0KFD+ctf/oKnpycAFouFHTt2kJSUxOnTpwkNDeXWW2/lxRdfxNvbu1bPXxomf6snD18fyT9W7uP1/+3ntk7NMZtNRpclIiI/Yeg8SHWZ5kGSK5F3rpTrX/kfBUVlzLr/WgZ00uVdEZHa4PbzIIk0ZDYfT+L7lo9FmpayX/MiiYi4GQUkEYM81DcCX28P9mQXkLLn4o/XERERYyggiRikSSMvHriuFQBvrT5ocDUiIvJTCkgiBnqobwReFjNb0k+xJe2k0eWIiMj3FJBEDBTkb+XOa8MAeHN1qsHViIjIDxSQRAz26I2RmEywcncO+3MKjC5HRERQQBIxXFSgL7deXT7319tfqhdJRMQdKCCJuIHHbooCYOn2I2TnFRlcjYiIKCCJuIFuLa+iV+umlNqd/OurQ0aXIyLS4CkgibiJx26KBOC9jRnknSs1uBoRkYZNAUnETfRrH0T7YD/OFJfx7sZ0o8sREWnQFJBE3ITJZOJ3N5b3Is39Ko2SMofBFYmINFwKSCJu5PYuoQT5eZNbUMynO7OMLkdEpMFSQBJxI14eZob3Ln/8yDtrD+F06iG2IiJGUEAScTP3xbTC28PMziN5bEk/ZXQ5IiINkgKSiJtp2tjL9fiRf63VLf8iIkZQQBJxQ/F9WwOw/LtsMk+eNbgaEZGGRwFJxA21C/bjhrYBOJyQtC7N6HJERBocBSQRN/XQ971ICzdncqa4zOBqREQaFgUkETd1U7tAIgMbU1Bcxn+2ZBpdjohIg6KAJOKmzGaTayzSnHVpOBy65V9EpLYoIIm4saHXhuFv9SD9xFlS9uQaXY6ISIOhgCTixhp5eXBvTEtAt/yLiNQmBSQRNzeidwQWs4n1qSfYdTTf6HJERBoEBSQRNxfaxIf+HUMAmLtOvUgiIrVBAUmkDniobwQAS7cf5WRhibHFiIg0AApIInXAtS2volOYjZIyB+9vyjC6HBGRek8BSaQOMJlMxH/fizR/fTqldoexBYmI1HMKSCJ1xG2dmxPg6012fhHJ32YbXY6ISL2mgCRSR3h7WLj/+1v+53ylwdoiIjVJAUmkDrn/upZ4WkxsyzjNN5mnjS5HRKTeUkASqUOC/Kzc3jkUgLnr0owtRkSkHlNAEqljRn4/WHvZjqPk5hcZW4yISD2lgCRSx3Ru0YTura6i1O7k3Y265V9EpCYoIInUQT/c8v/uxnSKy+zGFiMiUg8pIInUQXHXhBDib+X4mRI+2ZFldDkiIvWOApJIHeRpMfNg71YAzPkqDafTaXBFIiL1iwKSSB11b6+WeHuY2Xkkj63pp4wuR0SkXlFAEqmjmjb2YnDXMADm6JZ/EZFqpYAkUof9cMt/8rfZHD19zthiRETqEcMD0syZM4mIiMBqtRITE8OmTZsu2ba0tJRJkyYRFRWF1WqlS5cuJCcnV2hTUFDAuHHjaNWqFT4+PvTp04fNmzdXaON0Onn22Wdp3rw5Pj4+xMbGsn///ho5P5Ga1KG5P9dFNsXucDJ/Q7rR5YiI1BuGBqSFCxeSkJDAc889x7Zt2+jSpQtxcXHk5uZetP3EiRN56623eP3119m1axePPfYYQ4YM4euvv3a1eeSRR1ixYgXz589n586d3HrrrcTGxnLkyBFXm1dffZXp06fz5ptvsnHjRho3bkxcXBxFRZp0T+qe+L6tAXh/UwZFpbrlX0SkOpicBt7+EhMTQ8+ePZkxYwYADoeD8PBwxo4dy4QJEy5oHxoaytNPP83o0aNd64YOHYqPjw8LFizg3Llz+Pn58d///pfbbrvN1aZ79+4MGDCAl156CafTSWhoKH/605948sknAcjLyyM4OJi5c+dyzz33XLTW4uJiiouLXe/z8/MJDw8nLy8Pf3//avk+RC6H3eHkpr99weFT5/jrnZ24p1dLo0sSEXFb+fn52Gy2X/z9NqwHqaSkhK1btxIbG/tjMWYzsbGxrF+//qLbFBcXY7VaK6zz8fFh7dq1AJSVlWG323+2zaFDh8jOzq5wXJvNRkxMzCWPCzB58mRsNptrCQ8Pr9oJi9QQi9nEiN4RQPnz2XTLv4jIlTMsIB0/fhy73U5wcHCF9cHBwWRnZ190m7i4OKZMmcL+/ftxOBysWLGCxYsXk5VVPlGen58fvXv35sUXX+To0aPY7XYWLFjA+vXrXW1+2HdVjguQmJhIXl6ea8nMzLzscxepbnf3DMfH08Ke7ALWp54wuhwRkTrP8EHaVTFt2jTatm1LdHQ0Xl5ejBkzhvj4eMzmH09j/vz5OJ1OwsLC8Pb2Zvr06dx7770V2lwOb29v/P39Kywi7sLm48nQ7t/f8v9VmrHFiIjUA4YFpICAACwWCzk5ORXW5+TkEBISctFtAgMDWbp0KYWFhaSnp7Nnzx58fX2JjIx0tYmKimL16tWcOXOGzMxMNm3aRGlpqavND/uuynFF6oKRfcoHa6/cnUPmybMGVyMiUrcZFpC8vLzo3r07KSkprnUOh4OUlBR69+79s9tarVbCwsIoKytj0aJFDBo06II2jRs3pnnz5pw6dYrly5e72rRu3ZqQkJAKx83Pz2fjxo2/eFwRd9YmyJcb2wXidEKSJo4UEbkihl5iS0hIYPbs2SQlJbF7925GjRpFYWEh8fHxAAwfPpzExERX+40bN7J48WJSU1NZs2YN/fv3x+FwMH78eFeb5cuXk5yczKFDh1ixYgX9+vUjOjratU+TycS4ceN46aWX+Oijj9i5cyfDhw8nNDSUwYMH1+r5i1S3+D4RACzckklhcZmxxYiI1GEeRh582LBhHDt2jGeffZbs7Gy6du1KcnKyawB1RkZGhbFDRUVFTJw4kdTUVHx9fRk4cCDz58+nSZMmrjZ5eXkkJiZy+PBhmjZtytChQ/nLX/6Cp6enq8348eMpLCzkd7/7HadPn+b6668nOTn5grvfROqam9oFEhnQmNTjhSzedpgHv7+7TUREqsbQeZDqssrOoyBS25LWpfHcR98RGdiYlU/chNlsMrokERG34fbzIIlIzRjavQV+3h6kHitkzYHjRpcjIlInKSCJ1DO+3h78tkf5RKb/WnvI4GpEROomBSSRemhknwjMJli97xh7svONLkdEpM5RQBKph1o2a8SAjs0BeHt1qsHViIjUPQpIIvXUYzdFAfDRN0c5cvqcwdWIiNQtCkgi9VSnFjb6tmlGmcPJP9eoF0lEpCoUkETqsR96kT7YlMmpwhKDqxERqTsUkETqsevbBHBNqD/nSu3MW59udDkiInWGApJIPWYymfj9971ISevTOFdiN7giEZG6QQFJpJ4b2DGE8KY+nCws4cMtmUaXIyJSJyggidRzHhYzv7shEoDZa1IpszsMrkhExP0pIIk0AL/tEU6zxl4cPnWOj3ccNbocERG3p4Ak0gBYPS08dH1rAF7/3wHsDj2jWkTk5yggiTQQw3u3okkjT1KPFbJMvUgiIj9LAUmkgfCzevLI971I01L2qxdJRORnKCCJNCAj+kRg81EvkojIL1FAEmlA/KyePHpDeS/SdPUiiYhckgKSSAPzQy/SQfUiiYhckgKSSAPz07FI01P2a14kEZGLUEASaYBG9o2gSaPyXqRF2w4bXY6IiNtRQBJpgPysnozp1waAKSv26RltIiLnUUASaaAe7N2KsCY+5OQXM2fdIaPLERFxKwpIIg2Ut4eFJ+PaATBr1UFOFZYYXJGIiPtQQBJpwAZ1CaNDc38KisqY8cUBo8sREXEbCkgiDZjZbGLCgGgA5q9PJ/PkWYMrEhFxDx5V3cDpdPKf//yHL774gtzcXByOircIL168uNqKE5Gad2PbAPq2acZXB07wSvIeZtx3rdEliYgYrso9SOPGjePBBx/k0KFD+Pr6YrPZKiwiUreYTCb+b2AHTCZYtiOLDaknjC5JRMRwJqfTWaVnDTRt2pQFCxYwcODAmqqpTsjPz8dms5GXl4e/v7/R5YhcsaeX7OTdjRlEh/ixbOz1eFh0BV5E6p/K/n5X+W9Am81GZGTkFRUnIu7nyVvb06SRJ3uyC1iwId3ockREDFXlgPT888/zwgsvcO7cuZqoR0QMclVjL568tT1QPnnk8TPFBlckImKcKgeku+++m1OnThEUFESnTp249tprKywiUnfd26sl14T6k19UxkvLdhldjoiIYap8F9uIESPYunUrDzzwAMHBwZhMppqoS0QMYDGbeHlIJ4a88RVLtx9lULcw+rUPMrosEZFaV+VB2o0bN2b58uVcf/31NVVTnaBB2lKfvbRsF/9ce4hQm5XPE27C17vK/5YSEXFLNTZIOzw8XIFApJ5LuLUd4U19OJpXxGvL9xpdjohIratyQPr73//O+PHjSUtLq4FyRMQdNPLy4OUhnQBIWp/GuoPHDa5IRKR2VfkS21VXXcXZs2cpKyujUaNGeHp6Vvj85MmT1Vqgu9IlNmkIEhfv4P1NmTS3WUn+443YGnn+8kYiIm6ssr/fVR5YMHXq1CupS0TqkGd+czUbUk9y6HghTy/dyev3dtONGSLSIFQpIJWWlrJ69WqeeeYZWrduXVM1iYibaOTlwT+GdWXorHUs25HFr6KDuPPaFkaXJSJS46o0BsnT05NFixbVVC0i4oa6hjdh3C1tAXh6ybfsyykwuCIRkZpX5UHagwcPZunSpdVWwMyZM4mIiMBqtRITE8OmTZsu2ba0tJRJkyYRFRWF1WqlS5cuJCcnV2hjt9tdPVw+Pj5ERUXx4osv8tOhViNHjsRkMlVY+vfvX23nJFLf/KFfG65vE8C5UjuPzd9KQVGp0SWJiNSoKo9Batu2LZMmTeKrr76ie/fuNG7cuMLnjz/+eKX3tXDhQhISEnjzzTeJiYlh6tSpxMXFsXfvXoKCLpycbuLEiSxYsIDZs2cTHR3N8uXLGTJkCOvWraNbt24AvPLKK8yaNYukpCSuueYatmzZQnx8PDabrUJt/fv3Z86cOa733t7eVf0qRBoMi9nEtHu6cvvra0k9XsiT//6GNx/orvFIIlJvVfkutp8be2QymUhNTa30vmJiYujZsyczZswAwOFwEB4eztixY5kwYcIF7UNDQ3n66acZPXq0a93QoUPx8fFhwYIFAPzmN78hODiYd95555JtRo4cyenTp6vUE1ZcXExx8Y/PpsrPzyc8PFx3sUmDsj3zNHe/uZ4Su4MnYtvxx9i2RpckIlIlNTZR5KFDhy65VCUclZSUsHXrVmJjY38sxmwmNjaW9evXX3Sb4uJirFZrhXU+Pj6sXbvW9b5Pnz6kpKSwb98+AL755hvWrl3LgAEDKmy3atUqgoKCaN++PaNGjeLEiRM/W+/kyZOx2WyuJTw8vNLnKlJfdA1vwguDrgHgHyv3sXjbYYMrEhGpGVUOSD/ldDqpYgeUy/Hjx7Hb7QQHB1dYHxwcTHZ29kW3iYuLY8qUKezfvx+Hw8GKFStYvHgxWVlZrjYTJkzgnnvuITo6Gk9PT7p168a4ceO4//77XW369+/PvHnzSElJ4ZVXXmH16tUMGDAAu91+yXoTExPJy8tzLZmZmZd13iJ13b29WvL7GyMB+POiHaw7oEkkRaT+uayANG/ePDp16oSPjw8+Pj507tyZ+fPnV3dtF5g2bRpt27YlOjoaLy8vxowZQ3x8PGbzj6fx4Ycf8u677/Lee++xbds2kpKSeO2110hKSnK1ueeee7jjjjvo1KkTgwcPZtmyZWzevJlVq1Zd8tje3t74+/tXWEQaqj/3j+a2zs0ptTv5/YKtfHskz+iSRESqVZUD0pQpUxg1ahQDBw7kww8/5MMPP6R///489thj/OMf/6j0fgICArBYLOTk5FRYn5OTQ0hIyEW3CQwMZOnSpRQWFpKens6ePXvw9fUlMjLS1eapp55y9SJ16tSJBx98kCeeeILJkydfspbIyEgCAgI4cOBApesXacjMZhN//20XekU0paCojAfe2ciuo/lGlyUiUm2qHJBef/11Zs2axSuvvMIdd9zBHXfcwauvvsobb7zB9OnTK70fLy8vunfvTkpKimudw+EgJSWF3r17/+y2VquVsLAwysrKWLRoEYMGDXJ9dvbs2Qo9SgAWiwWHw3HJ/R0+fJgTJ07QvHnzStcv0tBZPS28M7IHXcObcPpsKQ+8s5G92ZojSUTqhyoHpKysLPr06XPB+j59+lQYC1QZCQkJzJ49m6SkJHbv3s2oUaMoLCwkPj4egOHDh5OYmOhqv3HjRhYvXkxqaipr1qyhf//+OBwOxo8f72pz++2385e//IVPPvmEtLQ0lixZwpQpUxgyZAgAZ86c4amnnmLDhg2kpaWRkpLCoEGDaNOmDXFxcVX9OkQaND+rJ0kP9aJTmI2ThSXc8/Z6vs44ZXRZIiJXrMoBqU2bNnz44YcXrF+4cCFt21btlt9hw4bx2muv8eyzz9K1a1e2b99OcnKya+B2RkZGhdBVVFTExIkTufrqqxkyZAhhYWGsXbuWJk2auNq8/vrr3HXXXfzhD3+gQ4cOPPnkk/z+97/nxRdfBMp7k3bs2MEdd9xBu3btePjhh+nevTtr1qzRXEgil8Hm48n8h3vRuYWNU2dLuW/2Rr7Ym2t0WSIiV6TK8yAtWrSIYcOGERsbS9++fQH46quvSElJ4cMPP3T11NR3lZ1HQaShKCwuY9S72/hy3zEsZhOTBl3Dfb1aajJJEXErNTYP0tChQ9m4cSMBAQEsXbqUpUuXEhAQwKZNmxpMOBKRCzX29uCfw3twZ7cw7A4nTy/5lj8v2kFR6aWnzxARcVdV7kGScupBErk4p9PJm6tT+dvyPTic0CnMxvR7u9E6oPEvbywiUsMq+/t9WQHJ4XBw4MABcnNzL7g77MYbb6x6tXWQApLIz1uz/xiPv/81p86WYvU0kzigAw9e1wqzWZfcRMQ4NRaQNmzYwH333Ud6evoFs2ibTKafnY26PlFAEvllR0+f46n/fMNXB8of5XNdZFMmDepIu2A/gysTkYaqxgJS165dadeuHS+88ALNmze/YACmzWa7vIrrGAUkkcpxOJzM35DO5M92U1TqwGI2Mbx3K8bd0g5bI0+jyxORBqbGAlLjxo355ptvaNOmzRUXWZcpIIlUTebJs7y4bBef7yqfPd/P6sFDfVvz0PWtsfkoKIlI7aixu9hiYmL0SA4RqbLwpo14e3gP5j/ci/bBfhQUlTEtZT/X//V/vLhsF2nHC40uUUTEpco9SEuWLGHixIk89dRTdOrUCU/Piv/y69y5c7UW6K7UgyRy+RwOJ8nfZTNt5X725vz4eJIb2gYwqGsYt14TjL9VvUoiUv1q7BLb+c85g/LB2U6nU4O0RaRKHA4nq/cfI2ldGqv2HnOt97KYual9IL/uEEyfNs1ocVUjA6sUkfqkxgJSenr6z37eqlWrquyuzlJAEqleaccL+e/2o3y84ygHcs9U+CyiWSN6RwXQpYWNjmE22gb74u1hMahSEanLanQeJFFAEqkpTqeTvTkFfLozm7X7j/HN4Tzsjop/TXlaTLQOaEzLpo1p1awRLZuWL4F+3jRt7EXTxl5YPRWgRORCCkg1TAFJpHYUFJWyMfUkm9NO8t3RfHYeySPvXOkvbtfYy4LNxxMfLwuNvDy+/9OCj6cFs9mExWTCYjZhNpkwmyh//ZP1JhOYf/LaYvq+rfn79t+/NpnKLwk28vKgsbcFX28PGnt74OvtQTNfL5o19sbLo8r3w4hIDans77dHLdYkIlJlflZPYq8OJvbqYKC8h+nwqXOkHi8k4+RZMk4Ukn7iLIdPneNEYTEnC0sotTspLLFTWOIeYyKbNPIk0NebEJuViGblvV6tAxrTPsSPsCY+eqCviBtSD9JlUg+SiHtyOp3kF5VxsrCEgqJSzpbYOVdi52yJnbMlZRSV2rE7nNid5YPE7U4nDqez/LUD7E4nTqcTu8OJw0mF147v27reO8rfl9gdFBbbKSwuo7CkjMLiMgq+r6HM8fN/xTZt7MU1of50adGE3lHN6N7qKl0eFKlBusRWwxSQROSXOBxO8s6VcuxMMccKijly6hxpJwpJO1FI6rFCDuSeuSBAeXmY6RlxFTe3C+K2zs0JbeJjUPUi9VONBqTTp0/zn//8h4MHD/LUU0/RtGlTtm3bRnBwMGFhYVdUeF2hgCQiV6qo1M6+nAJ2Hslja/op1h04QXZ+UYU2PSOu4o4uodzRJUyPZhGpBjUWkHbs2EFsbCw2m420tDT27t1LZGQkEydOJCMjg3nz5l1x8XWBApKIVDen08nBY4Ws3X+MT7/NZnPaSX74G9rqaWZItzBG9IkgOkR/54hcrhoLSLGxsVx77bW8+uqr+Pn58c033xAZGcm6deu47777SEtLu9La6wQFJBGpaVl55/hkRxb/2XqYPdk/zjj+66uDGRfblmtCG8bDwUWqU40FJJvNxrZt24iKiqoQkNLT02nfvj1FRUW/vJN6QAFJRGqL0+lk06GTJK1PI/nbbH4YtjSwUwiJAzoQ3lQzjYtUVo3d5u/t7U1+fv4F6/ft20dgYGBVdyciIr/AZDIRE9mMmMhmHMg9w/SU/Xy84yif7swmZXcuf7i5Db+/KVJ3v4lUoyrPXnbHHXcwadIkSkvLJ2ozmUxkZGTw5z//maFDh1Z7gSIi8qM2Qb5Mv7cbn/3xBnpHNqO4zME/Vu5j4PQ1bM88bXR5IvVGlS+x5eXlcdddd7FlyxYKCgoIDQ0lOzub3r178+mnn9K4ceOaqtWt6BKbiBjN6XTyyc4sXly2i5z8YixmE6NvjmLsLW3xtGj2bpGLqfF5kL766iu++eYbzpw5w7XXXktsbOxlF1sXKSCJiLvIO1vKM//9lo++OQpAr9ZNmXnftQT6eRtcmYj7qbGANG/ePIYNG4a3d8X/45WUlPDBBx8wfPjwy6u4jlFAEhF389E3R/m/xTs5U1xGiL+VWQ9cS7eWVxldlohbqbGAZLFYyMrKIigoqML6EydOEBQUhN3uHs8+qmkKSCLijg7knuH387dw8FghXhYzU+/pysBOzY0uS8RtVPb3u8oXqZ1O50UfrHj48GFsNs3JISJipDZBviwd3ZfYDsGU2B2Mfm8bCzakG12WSJ1T6dv8u3XrhslkwmQyccstt+Dh8eOmdrudQ4cO0b9//xopUkREKs/P6slbD3Zn4tJveX9TBhOXfsuJMyX8Mbat0aWJ1BmVDkiDBw8GYPv27cTFxeHr6+v6zMvLi4iICN3mLyLiJixmEy8P6UignzfTU/bzj5X7MJtg7C0KSSKVUemA9NxzzwEQERHBsGHDsFqtNVaUiIhcOZPJRMKv29HYy8Lkz/bw9xX78PIw8/uboowuTcTtVXkM0ogRIxSORETqkN/fFMWTt7YDYPJne5i/Ps3YgkTqgCoHJLvdzmuvvUavXr0ICQmhadOmFRYREXE/Y37Vlsd/1QaA5z76jpW7cgyuSMS9VTkgvfDCC0yZMoVhw4aRl5dHQkICd955J2azmeeff74GShQRkerwxK/bcU/PcBxOGPv+1+w8nGd0SSJuq8oB6d1332X27Nn86U9/wsPDg3vvvZd//vOfPPvss2zYsKEmahQRkWpgMpl4cXBHbmgbwLlSOw8lbebo6XNGlyXilqockLKzs+nUqRMAvr6+5OWV/wvkN7/5DZ988kn1ViciItXK02LmjfuvJTrEj2MFxfzh3W2UlDmMLkvE7VQ5ILVo0YKsrCwAoqKi+PzzzwHYvHnzBY8fERER9+Nn9eTtB3vgb/Vge+ZpXvpkl9ElibidKgekIUOGkJKSAsDYsWN55plnaNu2LcOHD+ehhx6q9gJFRKT6tWzWiKn3dAVg3vp0ln59xNiCRNxMlZ/Fdr4NGzawbt062rZty+23315ddbk9PYtNROqDKZ/vZfr/DuDjaeGTx68nMtD3lzcSqcNq7FlsX375JWVlZa731113HQkJCQwYMIAvv/zy8qoVERFD/DG2HX2imnGu1M4TC7dTatd4JBG4jIDUr18/Tp48ecH6vLw8+vXrVy1FiYhI7bCYTfz97i74Wz345nAe01P2G12SiFuockByOp2YTKYL1p84cYLGjRtXuYCZM2cSERGB1WolJiaGTZs2XbJtaWkpkyZNIioqCqvVSpcuXUhOTq7Qxm6388wzz9C6dWt8fHyIiorixRdf5KdXEp1OJ88++yzNmzfHx8eH2NhY9u/XXwoi0jA1t/nw8p3ldyfP/OIAW9Iu/EewSENT6Wex3XnnnUD5PBojR46scMea3W5nx44d9OnTp0oHX7hwIQkJCbz55pvExMQwdepU4uLi2Lt3L0FBQRe0nzhxIgsWLGD27NlER0ezfPlyhgwZwrp16+jWrRsAr7zyCrNmzSIpKYlrrrmGLVu2EB8fj81m4/HHHwfg1VdfZfr06SQlJdG6dWueeeYZ4uLi2LVrlx6jIiIN0m86h/K/3bks/voIT/77G5LH3YjV02J0WSKGqfQg7fj4eACSkpK4++678fHxcX3m5eVFREQEjz76KAEBAZU+eExMDD179mTGjBkAOBwOwsPDGTt2LBMmTLigfWhoKE8//TSjR492rRs6dCg+Pj4sWLAAKJ+PKTg4mHfeeeeibZxOJ6GhofzpT3/iySefBMovDwYHBzN37lzuueeeStWuQdoiUt/kF5Xy6ymryckvZtTNUfy5f7TRJYlUu8r+fle6B2nOnDkARERE8OSTT17W5bSfKikpYevWrSQmJrrWmc1mYmNjWb9+/UW3KS4uvqCHx8fHh7Vr17re9+nTh7fffpt9+/bRrl07vvnmG9auXcuUKVMAOHToENnZ2cTGxrq2sdlsxMTEsH79+ksGpOLiYoqLi13v8/Pzq37SIiJuzN/qyYuDOvK7+Vt5+8tUbuvUnI5hNqPLEjFElccgjR8/vsIYpPT0dKZOneqaMLKyjh8/jt1uJzg4uML64OBgsrOzL7pNXFwcU6ZMYf/+/TgcDlasWMHixYtdE1cCTJgwgXvuuYfo6Gg8PT3p1q0b48aN4/777wdw7bsqxwWYPHkyNpvNtYSHh1fpfEVE6oJbrwnhtk7NsTucTFi8gzLd1SYNVJUD0qBBg5g3bx4Ap0+fplevXvz9739n0KBBzJo1q9oL/Klp06bRtm1boqOj8fLyYsyYMcTHx2M2/3gaH374Ie+++y7vvfce27ZtIykpiddee42kpKQrOnZiYiJ5eXmuJTMz80pPR0TELT13x9XYfDz59kg+c9elGV2OiCGqHJC2bdvGDTfcAMB//vMfQkJCSE9PZ968eUyfPr3S+wkICMBisZCTk1NhfU5ODiEhIRfdJjAwkKVLl1JYWEh6ejp79uzB19eXyMhIV5unnnrK1YvUqVMnHnzwQZ544gkmT54M4Np3VY4L4O3tjb+/f4VFRKQ+CvKzkjigfPzR1JX7yS0oMrgikdpX5YB09uxZ/Pz8APj888+58847MZvNXHfddaSnp1d6P15eXnTv3t312BIoH6SdkpJC7969f3Zbq9VKWFgYZWVlLFq0iEGDBlWo76c9SgAWiwWHo7ybuHXr1oSEhFQ4bn5+Phs3bvzF44qINBR39winSwsbZ4rLeOWzvUaXI1LrqhyQ2rRpw9KlS8nMzGT58uXceuutAOTm5la5VyUhIYHZs2eTlJTE7t27GTVqFIWFha475oYPH15hEPfGjRtZvHgxqamprFmzhv79++NwOBg/fryrze23385f/vIXPvnkE9LS0liyZAlTpkxhyJAhQPk0BePGjeOll17io48+YufOnQwfPpzQ0FAGDx5c1a9DRKReMptNvDCoIwCLth1ma7rmRpIGxllF//73v52enp5Os9ns/PWvf+1a//LLLzv79+9f1d05X3/9dWfLli2dXl5ezl69ejk3bNjg+uymm25yjhgxwvV+1apVzg4dOji9vb2dzZo1cz744IPOI0eOVNhffn6+849//KOzZcuWTqvV6oyMjHQ+/fTTzuLiYlcbh8PhfOaZZ5zBwcFOb29v5y233OLcu3dvlerOy8tzAs68vLwqn7OISF3x1L+3O1v9eZlz4LQvnWV2h9HliFyxyv5+X9bDarOzs8nKyqJLly6uy1mbNm3C39+f6OiGMW+G5kESkYbg+Jli+r22ioKiMl77bRfu6t7C6JJErkiNPawWygc6d+vWrcJYn169ejWYcCQi0lAE+Hozpl8bAP7++V6KSu0GVyRSOy4rIImISMMxok8EYU18yMorYs5XaUaXI1IrFJBERORnWT0tJPy6HQBvrDrAqcISgysSqXkKSCIi8osGdwsjOsSPgqIyZnxxwOhyRGqcApKIiPwii9lE4sAOAMxfn07mybMGVyRSsxSQRESkUm5sG0DfNs0osTv4++eaPFLqNwUkERGpFJPJxIT+5b1I//3mKAdyCwyuSKTmKCCJiEildWph49dXB+N0wrQUjUWS+ksBSUREqmRcbFsAlu04yr4c9SJJ/aSAJCIiVXJNqI24a37oRdpvdDkiNUIBSUREqmxcbPm8SJ/uzGJvtnqRpP5RQBIRkSrr0NyfAR1Dvu9F2md0OSLVTgFJREQuyx+/H4v06c5sdmflG1yNSPVSQBIRkcsSHeLPbZ2aAzBr1UGDqxGpXgpIIiJy2UbdHAWU39GWcUKza0v9oYAkIiKXrWOYjRvbBeJwwltfqhdJ6g8FJBERuSJ/+L4X6d9bD5NbUGRwNSLVQwFJRESuSEzrpnRr2YSSMgdzvkozuhyRaqGAJCIiV8RkMvGHm9sAsGB9OvlFpQZXJHLlFJBEROSK3RIdRNsgXwqKy1iwId3ockSumAKSiIhcMbPZ5Lqj7V9r0ygqtRtckciVUUASEZFqcXuXUMKa+HD8TDH/3nrY6HJErogCkoiIVAtPi5lHb2gNwNtfHsTucBpckcjlU0ASEZFqM6xnS65q5EnmyXN8/l220eWIXDYFJBERqTY+XhYeuK4VAP9ce8jgakQunwKSiIhUqwd7t8LLYmZr+im2ZZwyuhyRy6KAJCIi1SrIz8odXUMBeGeNepGkblJAEhGRavfI94O1P/s2i8yTeoit1D0KSCIiUu2iQ/y5oW0ADifMXZdmdDkiVaaAJCIiNeLh68t7kRZuztTjR6TOUUASEZEacVO7QNoG+XKmuIyFmzKNLkekShSQRESkRphMJtdYpDlfHaLM7jC4IpHKU0ASEZEaM6hrGAG+XhzNK+KzbzVxpNQdCkgiIlJjrJ4WHrwuAoB/rknF6dTjR6RuUEASEZEa9cB1LfH2MPPN4Ty2pGviSKkbFJBERKRGNfP15s5rwwBNHCl1hwKSiIjUuIf6lg/WXr4rm4wTmjhS3J8CkoiI1Li2wX7c1C4QpxPmrFMvkrg/BSQREakVP0wc+aEmjpQ6wC0C0syZM4mIiMBqtRITE8OmTZsu2ba0tJRJkyYRFRWF1WqlS5cuJCcnV2gTERGByWS6YBk9erSrzc0333zB54899liNnaOISEN3Q9sA2gX7Ulhi18SR4vYMD0gLFy4kISGB5557jm3bttGlSxfi4uLIzc29aPuJEyfy1ltv8frrr7Nr1y4ee+wxhgwZwtdff+1qs3nzZrKyslzLihUrAPjtb39bYV+PPvpohXavvvpqzZ2oiEgDZzKZXGOR5q5L08SR4tYMD0hTpkzh0UcfJT4+nquvvpo333yTRo0a8a9//eui7efPn8///d//MXDgQCIjIxk1ahQDBw7k73//u6tNYGAgISEhrmXZsmVERUVx0003VdhXo0aNKrTz9/ev0XMVEWnoBncLo1ljL46cPsfy73KMLkfkkgwNSCUlJWzdupXY2FjXOrPZTGxsLOvXr7/oNsXFxVit1grrfHx8WLt27SWPsWDBAh566CFMJlOFz959910CAgLo2LEjiYmJnD176TsriouLyc/Pr7CIiEjVWD0t3H9dKwDeWZtqcDUil2ZoQDp+/Dh2u53g4OAK64ODg8nOvviU9HFxcUyZMoX9+/fjcDhYsWIFixcvJisr66Ltly5dyunTpxk5cmSF9ffddx8LFizgiy++IDExkfnz5/PAAw9cstbJkydjs9lcS3h4eNVOVkREAHjwulZ4WcxsyzjNtgxNHCnuyfBLbFU1bdo02rZtS3R0NF5eXowZM4b4+HjM5oufyjvvvMOAAQMIDQ2tsP53v/sdcXFxdOrUifvvv5958+axZMkSDh48eNH9JCYmkpeX51oyMzXAUETkcgT6eXNH1/K/k99Zq1v+xT0ZGpACAgKwWCzk5FS8Dp2Tk0NISMhFtwkMDGTp0qUUFhaSnp7Onj178PX1JTIy8oK26enprFy5kkceeeQXa4mJiQHgwIEDF/3c29sbf3//CouIiFyeH275T/42myOnzxlcjciFDA1IXl5edO/enZSUFNc6h8NBSkoKvXv3/tltrVYrYWFhlJWVsWjRIgYNGnRBmzlz5hAUFMRtt932i7Vs374dgObNm1ftJEREpMo6NPenb5tm2B1OktalGV2OyAUMv8SWkJDA7NmzSUpKYvfu3YwaNYrCwkLi4+MBGD58OImJia72GzduZPHixaSmprJmzRr69++Pw+Fg/PjxFfbrcDiYM2cOI0aMwMPDo8JnBw8e5MUXX2Tr1q2kpaXx0UcfMXz4cG688UY6d+5c8yctIiKuXqT3N2ZwprjM4GpEKvL45SY1a9iwYRw7doxnn32W7OxsunbtSnJysmvgdkZGRoXxRUVFRUycOJHU1FR8fX0ZOHAg8+fPp0mTJhX2u3LlSjIyMnjooYcuOKaXlxcrV65k6tSpFBYWEh4eztChQ5k4cWKNnquIiPzo5nZBRAY2JvVYIf/ekkn893MkibgDk9PpdBpdRF2Un5+PzWYjLy9P45FERC7Tgg3pTFz6LS2bNuKLJ2/GYjb98kYiV6Cyv9+GX2ITEZGGa+i1LWjSyJOMk2dZuVsTR4r7UEASERHD+HhZuK9XSwDeWaNb/sV9KCCJiIihRvSJwNNiYlPaSXYezjO6HBFAAUlERAwW7G/lN51/mDhSjx8R96CAJCIihvvhlv9lO7LIzisyuBoRBSQREXEDHcNs9GrdlDKHk6T1aUaXI6KAJCIi7uGR73uR3tuYwdkSTRwpxlJAEhERt3BLh2BaNWtE3rlSFm07YnQ50sApIImIiFuwmE3E94kA4F9rD+FwaB5jMY4CkoiIuI3f9gjHz+rBoeOFrNDEkWIgBSQREXEbjb09ePC6VgDMWnUQPQ1LjKKAJCIibiW+b2u8PMxszzzNxkMnjS5HGigFJBERcSuBft7c3aMFUN6LJGIEBSQREXE7v7shCrMJVu87xrdH9PgRqX0KSCIi4nZaNmvE7V3KHz/y5mr1IkntU0ASERG39NhNUQB8ujOLtOOFBlcjDY0CkoiIuKUOzf3p1z4QhxPeXqOH2ErtUkASERG3NermNgD8Z8thcvP1EFupPQpIIiLitnpGXEX3VldRYnfwztpDRpcjDYgCkoiIuC2TycQfbi4fizR/QzonC0sMrkgaCgUkERFxa7+KDqJjmD9nS+zM1lgkqSUKSCIi4tZMJhPjbmkHQNK6NPUiSa1QQBIREbd3Swf1IkntUkASERG3p14kqW0KSCIiUif8tBfpn+pFkhqmgCQiInWCepGkNikgiYhInfFDL1JhiZ1Zqw4YXY7UYwpIIiJSZ5hMJp68tT0ASevSOXL6nMEVSX2lgCQiInXKTe0CuS6yKSV2B/9Ysc/ocqSeUkASEZE6xWQyMWFABwAWbzvMvpwCgyuS+kgBSURE6pyu4U0Y0DEEhxNeTd5rdDlSDykgiYhInfRkXHssZhMrd+ewOe2k0eVIPaOAJCIidVJUoC9392gBwF8/24PT6TS4IqlPFJBERKTO+uMt7fDxtLA1/RQf78gyuhypRxSQRESkzgqxWRl1cxQAkz/dzdmSMoMrkvpCAUlEROq0390YSYurfMjKK+LNVQeNLkfqCQUkERGp06yeFp4eWH7b/1tfppJ58qzBFUl9oIAkIiJ1Xv+OIfSObEZxmYOXP91tdDlSDyggiYhInWcymXjujqsxm+Czb7NZd+C40SVJHecWAWnmzJlERERgtVqJiYlh06ZNl2xbWlrKpEmTiIqKwmq10qVLF5KTkyu0iYiIwGQyXbCMHj3a1aaoqIjRo0fTrFkzfH19GTp0KDk5OTV2jiIiUrOiQ/x54LpWAEz877cUldoNrkjqMsMD0sKFC0lISOC5555j27ZtdOnShbi4OHJzcy/afuLEibz11lu8/vrr7Nq1i8cee4whQ4bw9ddfu9ps3ryZrKws17JixQoAfvvb37raPPHEE3z88cf8+9//ZvXq1Rw9epQ777yzZk9WRERq1J9ubU+gnzepxwp5QwO25QqYnAbPrBUTE0PPnj2ZMWMGAA6Hg/DwcMaOHcuECRMuaB8aGsrTTz9doTdo6NCh+Pj4sGDBgoseY9y4cSxbtoz9+/djMpnIy8sjMDCQ9957j7vuuguAPXv20KFDB9avX8911133i3Xn5+djs9nIy8vD39//ck5dRERqwKc7s/jDu9vwtJj49PEbaBvsZ3RJ4kYq+/ttaA9SSUkJW7duJTY21rXObDYTGxvL+vXrL7pNcXExVqu1wjofHx/Wrl17yWMsWLCAhx56CJPJBMDWrVspLS2tcNzo6Ghatmz5s8fNz8+vsIiIiPsZ0DGE2A5BlNqdJC7eicOhGbal6gwNSMePH8dutxMcHFxhfXBwMNnZ2RfdJi4ujilTprB//34cDgcrVqxg8eLFZGVdfAbVpUuXcvr0aUaOHOlal52djZeXF02aNKn0cSdPnozNZnMt4eHhlT9RERGpNSaTiRcGdaSRl4Ut6adIWp9mdElSBxk+Bqmqpk2bRtu2bYmOjsbLy4sxY8YQHx+P2XzxU3nnnXcYMGAAoaGhV3TcxMRE8vLyXEtmZuYV7U9ERGpOWBMfEgdEA+XPaTt47IzBFUldY2hACggIwGKxXHD3WE5ODiEhIRfdJjAwkKVLl1JYWEh6ejp79uzB19eXyMjIC9qmp6ezcuVKHnnkkQrrQ0JCKCkp4fTp05U+rre3N/7+/hUWERFxXw9c14ob2gZQXOYg4cNvKLM7jC5J6hBDA5KXlxfdu3cnJSXFtc7hcJCSkkLv3r1/dlur1UpYWBhlZWUsWrSIQYMGXdBmzpw5BAUFcdttt1VY3717dzw9PSscd+/evWRkZPzicUVEpG4wmUy8eldn/KwefJN5mjdX6642qTzDL7ElJCQwe/ZskpKS2L17N6NGjaKwsJD4+HgAhg8fTmJioqv9xo0bWbx4MampqaxZs4b+/fvjcDgYP358hf06HA7mzJnDiBEj8PDwqPCZzWbj4YcfJiEhgS+++IKtW7cSHx9P7969K3UHm4iI1A3NbT68cMc1AExduZ9tGacMrkjqCo9fblKzhg0bxrFjx3j22WfJzs6ma9euJCcnuwZuZ2RkVBhfVFRUxMSJE0lNTcXX15eBAwcyf/78CwZcr1y5koyMDB566KGLHvcf//gHZrOZoUOHUlxcTFxcHG+88UaNnaeIiBhjSLcw/rcnl2U7shj73td8+vgN2Bp5Gl2WuDnD50GqqzQPkohI3VFQVMpvXl9L+omz3Hp1MG892N019Ys0LHViHiQREZHa4Gf1ZMa91+JlMfP5rhz+9VWa0SWJm1NAEhGRBqFTCxv/N7D81v+XP92tB9rKz1JAEhGRBmNEnwju7BaG3eHkD+9tI/PkWaNLEjelgCQiIg2GyWTi5Ts70aWFjdNnS3l03hbOFJcZXZa4IQUkERFpUKyeFt56sAeBft7syS7gD+9uo1STSMp5FJBERKTBCbFZmT28Bz6eFr7cd4w/L9qBbuqWn1JAEhGRBqlreBNm3t8Ni9nE4m1HeHX5XqNLEjeigCQiIg3Wr6KDmXxnJwBmrTrI9JT9Blck7kIBSUREGrS7e4S7bv+fsmIfM/6nkCQKSCIiIvzuxij+3L88JL32+T6mp+zXmKQGTgFJREQEGHVzFE/FtQfKe5Je+HgXDodCUkOlgCQiIvK90f3a8OxvrgZg7ro0xn7wNcVldoOrEiMoIImIiPzEQ9e3Zvq93fC0mPhkRxb3vr2B3Pwio8uSWqaAJCIicp47uoQyN74X/lYPtmWc5jevr+XrjFNGlyW1SAFJRETkIvq2CeCjMdfTNsiX3IJihr21gX+uSdW4pAZCAUlEROQSIgIas2R0X/pfE0KJ3cFLn+xmxJxNuuTWACggiYiI/Axfbw9mPXAtLw3uiNXTzJr9x/n1P77kw82ZmgqgHlNAEhER+QUmk4kHrmvFsrHX0zHMn7xzpYxftIN73t7AvpwCo8uTGqCAJCIiUkltgvxY+oe+PD2wAz6eFjYeOkn/qV+SuHgnuQW67FafmJzqH7ws+fn52Gw28vLy8Pf3N7ocERGpZZknz/LSJ7tY/l0OAD6eFu6LackjN7Smuc3H4OrkUir7+62AdJkUkEREBGBz2kn+8slutmeeBsDTYmJw1zAevTGSdsF+xhYnF1BAqmEKSCIi8gOn08mX+48za9UBNqSedK3v1rIJw3qE85suofh6exhYofxAAamGKSCJiMjFbMs4xdurU1mxOwf793Mm+Xha+FV0ELdeE8zN7YOw+XgaXGXDpYBUwxSQRETk5+QWFLF42xE+3JJJ6rFC13oPs4lerZvSJ6oZ10U2o3OLJnh56J6p2qKAVMMUkEREpDKcTic7Dufx+a5sPv8uh/25Zyp8bvU00ynMxjWhNq4O9eeaUH/aBvkpNNUQBaQapoAkIiKXI/XYGdYeOM6G1BNsSD3JycKSC9p4mE2EXeVDq2aNadW0Ea2aNSK0iQ+Bft4E+XkT6OdNIy+NabocCkg1TAFJRESulNPp5EDuGXYeyeO7o/l8d7T8z4Kisl/ctrGXhQA/b/ysHvh5e5b/af3hTw+snha8Pcx4eZjx9jDj7WFxvfbyMGMxm7CYTJjNJswmE2YTmE0mLGYTJhNYXOt//MxkungtJi784FJtL+Vi7Zs08qr2we2V/f1W/BQRETGIyWSibbAfbYP9uPPa8nVOp5OsvCLST5wl42Qh6SfOkn7iLDn5ReQWFJNbUERRqYPCEjuFJ84aewI17OUhnbgvpqUhx1ZAEhERcSMmk4nQJj6ENvGhd1SzCz53Op0UltjJzS/iZGEJBUVl5BeVUlBU9v1SypniMopLHRSX2SmxO75/7aCkrHxdcZkDu8OJw+nE4QSH04nd4cT5k9c/rP/pZxdzsQtRl7o0dcl9XGILi4HDsBSQRERE6hCTyYSvtwe+gb5EBhpdTf2lIfIiIiIi51FAEhERETmPApKIiIjIeRSQRERERM6jgCQiIiJyHgUkERERkfMoIImIiIicRwFJRERE5DwKSCIiIiLnMTwgzZw5k4iICKxWKzExMWzatOmSbUtLS5k0aRJRUVFYrVa6dOlCcnLyBe2OHDnCAw88QLNmzfDx8aFTp05s2bLF9fnIkSMxmUwVlv79+9fI+YmIiEjdY+ijRhYuXEhCQgJvvvkmMTExTJ06lbi4OPbu3UtQUNAF7SdOnMiCBQuYPXs20dHRLF++nCFDhrBu3Tq6desGwKlTp+jbty/9+vXjs88+IzAwkP3793PVVVdV2Ff//v2ZM2eO6723t3fNnqyIiIjUGSbnxZ4yV0tiYmLo2bMnM2bMAMDhcBAeHs7YsWOZMGHCBe1DQ0N5+umnGT16tGvd0KFD8fHxYcGCBQBMmDCBr776ijVr1lzyuCNHjuT06dMsXbr0smvPz8/HZrORl5eHv7//Ze9HREREak9lf78Nu8RWUlLC1q1biY2N/bEYs5nY2FjWr19/0W2Ki4uxWq0V1vn4+LB27VrX+48++ogePXrw29/+lqCgILp168bs2bMv2NeqVasICgqiffv2jBo1ihMnTvxsvcXFxeTn51dYREREpH4yLCAdP34cu91OcHBwhfXBwcFkZ2dfdJu4uDimTJnC/v37cTgcrFixgsWLF5OVleVqk5qayqxZs2jbti3Lly9n1KhRPP744yQlJbna9O/fn3nz5pGSksIrr7zC6tWrGTBgAHa7/ZL1Tp48GZvN5lrCw8Ov8BsQERERd2XYJbajR48SFhbGunXr6N27t2v9+PHjWb16NRs3brxgm2PHjvHoo4/y8ccfYzKZiIqKIjY2ln/961+cO3cOAC8vL3r06MG6detc2z3++ONs3rz5kj1TqampREVFsXLlSm655ZaLtikuLqa4uNj1Pi8vj5YtW5KZmalLbCIiInVEfn4+4eHhnD59GpvNdsl2hg3SDggIwGKxkJOTU2F9Tk4OISEhF90mMDCQpUuXUlRUxIkTJwgNDWXChAlERka62jRv3pyrr766wnYdOnRg0aJFl6wlMjKSgIAADhw4cMmA5O3tXWEg9w+X2NSTJCIiUvcUFBS4Z0Dy8vKie/fupKSkMHjwYKB8kHZKSgpjxoz52W2tVithYWGUlpayaNEi7r77btdnffv2Ze/evRXa79u3j1atWl1yf4cPH+bEiRM0b9680vWHhoaSmZmJn58fJpOp0tv9kh+SrXqmap6+69qh77l26HuuHfqea0dNfs9Op5OCggJCQ0N/tp2ht/knJCQwYsQIevToQa9evZg6dSqFhYXEx8cDMHz4cMLCwpg8eTIAGzdu5MiRI3Tt2pUjR47w/PPP43A4GD9+vGufTzzxBH369OHll1/m7rvvZtOmTbz99tu8/fbbAJw5c4YXXniBoUOHEhISwsGDBxk/fjxt2rQhLi6u0rWbzWZatGhRjd9GRf7+/vo/Xy3Rd1079D3XDn3PtUPfc+2oqe/553qOfmBoQBo2bBjHjh3j2WefJTs7m65du5KcnOwauJ2RkYHZ/OM48qKiIiZOnEhqaiq+vr4MHDiQ+fPn06RJE1ebnj17smTJEhITE5k0aRKtW7dm6tSp3H///QBYLBZ27NhBUlISp0+fJjQ0lFtvvZUXX3xRcyGJiIgIYPA8SHIhza9Ue/Rd1w59z7VD33Pt0PdcO9zhezb8USNSkbe3N88995x6s2qBvuvaoe+5duh7rh36nmuHO3zP6kESEREROY96kERERETOo4AkIiIich4FJBEREZHzKCCJiIiInEcByc3MnDmTiIgIrFYrMTExbNq0yeiS6p0vv/yS22+/ndDQUEwmE0uXLjW6pHpn8uTJ9OzZEz8/P4KCghg8ePAFM9xL9Zg1axadO3d2TajXu3dvPvvsM6PLqtf++te/YjKZGDdunNGl1DvPP/88JpOpwhIdHW1ILQpIbmThwoUkJCTw3HPPsW3bNrp06UJcXBy5ublGl1avFBYW0qVLF2bOnGl0KfXW6tWrGT16NBs2bGDFihWUlpZy6623UlhYaHRp9U6LFi3461//ytatW9myZQu/+tWvGDRoEN99953RpdVLmzdv5q233qJz585Gl1JvXXPNNWRlZbmWtWvXGlKHbvN3IzExMfTs2ZMZM2YA5c+mCw8PZ+zYsUyYMMHg6uonk8nEkiVLXM8DlJpx7NgxgoKCWL16NTfeeKPR5dR7TZs25W9/+xsPP/yw0aXUK2fOnOHaa6/ljTfe4KWXXqJr165MnTrV6LLqleeff56lS5eyfft2o0tRD5K7KCkpYevWrcTGxrrWmc1mYmNjWb9+vYGViVy5vLw8oPyHW2qO3W7ngw8+oLCwkN69extdTr0zevRobrvttgp/T0v1279/P6GhoURGRnL//feTkZFhSB2GPotNfnT8+HHsdrvrOXQ/CA4OZs+ePQZVJXLlHA4H48aNo2/fvnTs2NHocuqlnTt30rt3b4qKivD19WXJkiVcffXVRpdVr3zwwQds27aNzZs3G11KvRYTE8PcuXNp3749WVlZvPDCC9xwww18++23+Pn51WotCkgiUqNGjx7Nt99+a9g4goagffv2bN++nby8PP7zn/8wYsQIVq9erZBUTTIzM/njH//IihUrsFqtRpdTrw0YMMD1unPnzsTExNCqVSs+/PDDWr9krIDkJgICArBYLOTk5FRYn5OTQ0hIiEFViVyZMWPGsGzZMr788ktatGhhdDn1lpeXF23atAGge/fubN68mWnTpvHWW28ZXFn9sHXrVnJzc7n22mtd6+x2O19++SUzZsyguLgYi8ViYIX1V5MmTWjXrh0HDhyo9WNrDJKb8PLyonv37qSkpLjWORwOUlJSNJZA6hyn08mYMWNYsmQJ//vf/2jdurXRJTUoDoeD4uJio8uoN2655RZ27tzJ9u3bXUuPHj24//772b59u8JRDTpz5gwHDx6kefPmtX5s9SC5kYSEBEaMGEGPHj3o1asXU6dOpbCwkPj4eKNLq1fOnDlT4V8jhw4dYvv27TRt2pSWLVsaWFn9MXr0aN577z3++9//4ufnR3Z2NgA2mw0fHx+Dq6tfEhMTGTBgAC1btqSgoID33nuPVatWsXz5cqNLqzf8/PwuGD/XuHFjmjVrpnF11ezJJ5/k9ttvp1WrVhw9epTnnnsOi8XCvffeW+u1KCC5kWHDhnHs2DGeffZZsrOz6dq1K8nJyRcM3JYrs2XLFvr16+d6n5CQAMCIESOYO3euQVXVL7NmzQLg5ptvrrB+zpw5jBw5svYLqsdyc3MZPnw4WVlZ2Gw2OnfuzPLly/n1r39tdGkiVXb48GHuvfdeTpw4QWBgINdffz0bNmwgMDCw1mvRPEgiIiIi59EYJBEREZHzKCCJiIiInEcBSUREROQ8CkgiIiIi51FAEhERETmPApKIiIjIeRSQRERERM6jgCQiIiJyHgUkEWlQVq1ahclk4vTp00aXIiJuTDNpi0i9dvPNN9O1a1emTp0KQElJCSdPniQ4OBiTyWRscSLitvQsNhFpULy8vAgJCTG6DBFxc7rEJiL11siRI1m9ejXTpk3DZDJhMpmYO3duhUtsc+fOpUmTJixbtoz27dvTqFEj7rrrLs6ePUtSUhIRERFcddVVPP7449jtdte+i4uLefLJJwkLC6Nx48bExMSwatUqY05URKqdepBEpN6aNm0a+/bto2PHjkyaNAmA77777oJ2Z8+eZfr06XzwwQcUFBRw5513MmTIEJo0acKnn35KamoqQ4cOpW/fvgwbNgyAMWPGsGvXLj744ANCQ0NZsmQJ/fv3Z+fOnbRt27ZWz1NEqp8CkojUWzabDS8vLxo1auS6rLZnz54L2pWWljJr1iyioqIAuOuuu5g/fz45OTn4+vpy9dVX069fP7744guGDRtGRkYGc+bMISMjg9DQUACefPJJkpOTmTNnDi+//HLtnaSI1AgFJBFp8Bo1auQKRwDBwcFERETg6+tbYV1ubi4AO3fuxG63065duwr7KS4uplmzZrVTtIjUKAUkEWnwPD09K7w3mUwXXedwOAA4c+YMFouFrVu3YrFYKrT7aagSkbpLAUlE6jUvL68Kg6urQ7du3bDb7eTm5nLDDTdU675FxD3oLjYRqdciIiLYuHEjaWlpHD9+3NULdCXatWvH/fffz/Dhw1m8eDGHDh1i06ZNTJ48mU8++aQaqhYRoykgiUi99uSTT2KxWLj66qsJDAwkIyOjWvY7Z84chg8fzp/+9Cfat2/P4MGD2bx5My1btqyW/YuIsTSTtoiIiMh51IMkIiIich4FJBEREZHzKCCJiIiInEcBSUREROQ8CkgiIiIi51FAEhERETmPApKIiIjIeRSQRERERM6jgCQiIiJyHgUkERERkfMoIImIiIic5/8BZ3kY8HRdeEAAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_population(opt_dynamics)\n", "plot_norm(opt_states)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In accordance with the lower optimization error, the population dynamics now show\n", "a reasonably efficient transfer, and a significantly reduced population in\n", "state $\\ket{2}$.\n", "\n", "Finally, we can convert the complex-valued $\\Omega_P$ and $\\Omega_S$ functions to the\n", "physical electric fields $\\epsilon_{P}$ and $\\epsilon_{S}$:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "ExecuteTime": { "end_time": "2019-11-10T17:39:15.431996Z", "start_time": "2019-11-10T17:39:14.994569Z" }, "execution": { "iopub.execute_input": "2024-06-03T14:29:04.778194Z", "iopub.status.busy": "2024-06-03T14:29:04.778081Z", "iopub.status.idle": "2024-06-03T14:29:04.910860Z", "shell.execute_reply": "2024-06-03T14:29:04.910609Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Physical electric pump pulse in the lab frame:\n" ] }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_physical_field(pulse_re, pulse_im, tlist, case=None):\n", "\n", " if case == 'pump':\n", " w = 9.5\n", " elif case == 'stokes':\n", " w = 4.5\n", " else:\n", " print('Error: selected case is not a valid option')\n", " return\n", "\n", " ax = plt.subplot(111)\n", " ax.plot(tlist,pulse_re*np.cos(w*tlist)-pulse_im*np.sin(w*tlist), 'r')\n", " ax.set_xlabel('time', fontsize = 16)\n", " if case == 'pump':\n", " ax.set_ylabel(r'$\\mu_{12}\\,\\epsilon_{P}$')\n", " elif case == 'stokes':\n", " ax.set_ylabel(r'$ \\mu_{23}\\,\\epsilon_{S}$')\n", " plt.show()\n", "\n", "\n", "print('Physical electric pump pulse in the lab frame:')\n", "plot_physical_field(\n", " opt_result.optimized_controls[0], opt_result.optimized_controls[1], tlist, case = 'pump')\n", "\n", "\n", "print('Physical electric Stokes pulse in the lab frame:')\n", "plot_physical_field(\n", " opt_result.optimized_controls[2], opt_result.optimized_controls[3], tlist, case = 'stokes')" ] } ], "metadata": { "hide_input": false, "jupytext": { "formats": "" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.0" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }