{ "cells": [ { "cell_type": "markdown", "id": "f5a06a7d", "metadata": {}, "source": [ "This tutorials reproduces section III.A from:\n", "\n", "- L. Tsunaki, A. Singh, S. Trofimov, & B. Naydenov. (2025). Digital Twin Simulations Toolbox of the Nitrogen-Vacancy Center in Diamond. arXiv:2507.18759 quant-ph. [2507.18759](https://arxiv.org/abs/2507.18759).\n", "\n", "Conditional gates form the building block for quantum information processing applications involving more than one qubit. In case of the NV center, the energy level structure permits to realize them straightforwardly through selective MW and RF pulses.\n", "To begin illustrating the use of the NV software component, we introduce a simple application of a two-qubit conditional gate between the electron spin of the NV and a nuclear spin from a strongly coupled 13C from the diamond lattice, first observed in:\n", "\n", "- F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber,and J. Wrachtrup, Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate, Phys. Rev. Lett. 93, 130501 (2004)." ] }, { "cell_type": "code", "execution_count": 1, "id": "0f62ff49", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from quaccatoo import NV, Rabi, square_pulse, Analysis\n", "from qutip import jmat, tensor, qeye, basis" ] }, { "cell_type": "markdown", "id": "3df8bdf6", "metadata": {}, "source": [ "# 1. System Definition" ] }, { "cell_type": "markdown", "id": "034d0f4f", "metadata": {}, "source": [ "First, the NV system is represented by an instance of the `NV` class for a given external magnetic field $\\mathbf{B}_0$.\n", "This can be obtained simply through the following code:" ] }, { "cell_type": "code", "execution_count": 2, "id": "35176461", "metadata": {}, "outputs": [], "source": [ "sys = NV(B0=200, units_B0='mT', N=0)" ] }, { "cell_type": "markdown", "id": "89504f57", "metadata": {}, "source": [ "where the parameter `N` representing the nitrogen isotope is set to 0.\n", "This way, we neglect the nitrogen nuclear spin, which is not used in this application.\n", "The external magnetic field is assumed to be aligned with the NV axis and to have a magnitude of $B_0 = 200$ mT.\n", "The `NV` class internally calculates the system's observable $\\hat{F}_S$ and Hamiltonian $\\hat{H}_0$, in units of MHz by default. This way, the time units are in microseconds.\n", "\n", "So far, only the electron spin of the NV is defined.\n", "To add the 13C spin to the system, the $\\hat{H}_2$ Hamiltonian needs to be defined.\n", "In this case, the internal Hamiltonian of the 13C spin is simply given by a Zeeman interaction along the $z$-axis, while the hyperfine coupling between the two spins can be expressed in terms of a single component of $a_{zz}^c=-130$ MHz, even though other spatial components might exist.\n", "Hence,\n", "$$\n", "\t\\hat{H}_2 = a_{zz}^c \\hat{S}_z \\hat{I}^c_z - \\gamma^c B_0 \\hat{I}^c_z\n", "$$\n", "with gyromagnetic ratio $\\gamma^c= 10.7084$ MHz/T.\n", "To model this interaction and to add the carbon spin to the NV, the `add_spin` method can be used as follows:" ] }, { "cell_type": "code", "execution_count": 3, "id": "0129e728", "metadata": {}, "outputs": [], "source": [ "GAMMA_C = 10.7084e-3\n", "azz = -130\n", "\n", "H2 = azz*tensor(jmat(1,'z'),jmat(1/2,'z')) - GAMMA_C*sys.B0*tensor(qeye(3),jmat(1/2,'z'))\n", "\n", "sys.add_spin(H2)\n", "\n", "sys.rho0 = tensor(basis(3,1),basis(2,0))" ] }, { "cell_type": "markdown", "id": "84760aa9", "metadata": {}, "source": [ "with `tensor` representing the tensor product, `jmat` giving the spin matrices, `basis` the $Z$ basis states, and `qeye` the identity matrices, all imported from QuTiP.\n", "The initial state of the nuclear spin in this application is polarized, where $\\ket{m_S=0}\\otimes\\ket{m_{I^c}=-1/2}$ is set to the `rho0` attribute as shown above.\n", "Therefore, the states are pure and can be represented as kets, instead of density matrices.\n", "Which makes the simulation computationally less costly, given that there are fewer ODEs to be solved in the ket state as compared to the whole density matrix.\n", "\n", "The energy levels of the system can be plotted with the `plot_energy` method:" ] }, { "cell_type": "code", "execution_count": 4, "id": "f9c09fc6", "metadata": {}, "outputs": [ { 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sys.plot_energy()" ] }, { "cell_type": "markdown", "id": "6da26fa4", "metadata": {}, "source": [ "At such magnetic field above GSLAC $B_0 > B_{\\textrm{GSLAC}}$, the $m_S=0$ state has a higher energy than $m_S=-1$.\n", "Furthermore, the nuclear states at $m_S=0$ are only split by its Zeeman interaction, while the sublevels at $m_S=-1$ have a contribution from the hyperfine coupling as well.\n", "In this application, it is important that the $\\ket{m_S=0} \\leftrightarrow \\ket{m_S=-1}$ transitions have very distinct frequencies at $m_{I^c}=+1/2$ and $m_{I^c}=-1/2$ nuclear states, in order to avoid unwanted excitations.\n", "This is ensured by the high intensity magnetic field $B_0$ and hyperfine coupling $a^c_{zz}$, which leads to these energy differences being much larger than the bandwidth of the pulses.\n", "\n", "The interaction with an external excitation field needs to be represented through the operator $\\hat{h}_1$.\n", "Assuming $\\mathbf{B}_1(t)$ along the $x$-axis and Rabi frequencies of\n", "$\\omega_{1,S} = 20$ MHz and $\\omega_{1,I} = 0.8$ MHz for the electron and nuclear spins, respectively, we have:" ] }, { "cell_type": "code", "execution_count": 5, "id": "c31df60e", "metadata": {}, "outputs": [], "source": [ "w1_S = 20\n", "w1_I = 0.8\t\n", "\n", "h1 = w1_S*tensor(jmat(1,'x')*2**.5,qeye(2)) + w1_I*tensor(qeye(3),jmat(1/2,'x')*2)\n", "\n", "w0_mw = sys.energy_levels[2]-sys.energy_levels[1]\n", "w0_rf = sys.energy_levels[1]" ] }, { "cell_type": "markdown", "id": "455ddc36", "metadata": {}, "source": [ "where we also define the frequencies of the pulses `w0_mw` and `w0_rf` in resonance with the transitions. By default, in QuaCCAToo, the lowest energy state in system is 0, `sys.energy_levels[0]=0`." ] }, { "cell_type": "markdown", "id": "3ec430a7", "metadata": {}, "source": [ "# 2. Electron Spin Rabi" ] }, { "cell_type": "markdown", "id": "1e5112e8", "metadata": {}, "source": [ "Finally, for simulating this interaction of the excitation with the electron spin, we use the `Rabi` class and the `square_pulse` function to model the $\\mathbf{B}_1(t)$ field.\n", "Typically, in a Rabi experiment, the MW (or RF) pulse length is varied, which causes a periodic oscillation of the observable with frequency $\\omega_1$.\n", "Given the necessary parameters defined previously and an array for the pulse durations, this is achieved by:" ] }, { "cell_type": "code", "execution_count": 6, "id": "81847733", "metadata": {}, "outputs": [], "source": [ "tp_S = np.linspace(0,0.15,1000)\n", "\n", "rabi_S_sim = Rabi(\n", "\tsystem = sys,\n", "\tpulse_duration = tp_S,\n", "\th1 = h1,\n", "\tpulse_params = {'f_pulse':w0_mw},\n", "\tpulse_shape = square_pulse\n", "\t)\n", "\n", "rabi_S_sim.run()" ] }, { "cell_type": "markdown", "id": "492baf94", "metadata": {}, "source": [ "The `run` method is used to execute the simulation, by setting and solving the coupled ODEs, where the results of the simulations are stored in the `results` attribute of the `rabi_S_sim` object. \n", "Here, the frequency of the excitation field $\\mathbf{B}_1(t)$ is passed to the object through the `f_pulse` key of the `pulse_params` dictionary variable.\n", "\n", "The resulting expectation value of the fluorescence observable as a function of the pulse length can be plotted with the `plot_results` method from the `Analysis` class.\n", "The electron spin performs full Rabi oscillations between the $m_S=0$ and $m_S=-1$ levels, conditioned to the 13C spin being at the $m_{I^c}=-1/2$ state.\n", "The $m_S=+1$ levels and the nuclear states are not affected by this pulse, as expected." ] }, { "cell_type": "code", "execution_count": 7, "id": "eeed470a", "metadata": {}, "outputs": [ { "data": { "image/png": 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HB7169cLw4cMBACdPnsSGDRtw+vRpxMXFAQDmz5+PLVu2YN26dXj++ecBAE1NTVi5ciWGDBliacMtt9yC9957z1K4ffvttygrK8Nf/vIXAEB8fDzmz59v2f6hhx7Cli1b8MEHH1gVbomJiVi+fDlUKhX69u2Lw4cPY/ny5e0Wbt9//z0OHz6M4uJiaLWmruWXXnoJn3zyCT788EPcf//9nf0JuiTp6dfevXsxdOhQDB06FAAwb948DB06FE8//TQAoLCwEPn5+ZbtU1JSsHnzZmzbtg0XXXQR/va3v+HVV1/t9lQgrXmrvXDPyBR4eZnGyX35WyG7FqhLP54oQXah6S7lYD8f3Hl5cpdTMLTO2v8OMWvUtZ0nSpF1tiVr00YkdTtrXx5m1uQm2NcHIX4al34FaL3hpzHN3K/2UiE8wP7lt1qPQR8xYoTVz0eMGIHs7GwAwF/+8hfU1dUhNTUV9913Hz7++GPo9aYTlf3790MQBPTp0wcBAQGWr+3bt+PkyZOW19NoNBg8eLDVe0ydOhXbtm3D2bNnAQDvvvsurrvuOoSGmoYTGAwGPPfccxg8eDDCw8MREBCAr7/+2qr2AIDLLrvM6vcwYsQIHD9+3LKShNi+fftQXV1teT3zV25urlV77SXpFberr7660z7i9evXt3nsqquuwv79+x3ell7hfrjponhs2n8aggB8dvAsHvpDusPfh5TBYBSw+XDLWKPpV6QgQGvbf6de4X648aI4fLz/DABmjTpnMAr43+Gzlu+nX5GCQJ1tQ0PExzWAWZObp2/o79L3EwQBZ8rroDeYPpcjAjRQd7KaQ+/evaFSqZCVlYWbbrqpzc+PHDmC0NBQREREdPga5mIoMTERR48exdatW/HNN99g5syZ+Pvf/47t27fDaDRCrVZj3759bZaDEi/K7uvr26bIHD58ONLS0vD+++/jr3/9Kz7++GOsW7fO8vOXX34Zy5cvx4oVKzBo0CD4+/tjzpw5aGy0/0qn0WhEbGys1Rg8s5CQELtf10xWY9ycbdyAaHx3pBjltY04WFCOU6U1nAeJ2vVL7gUUV5rmB+wfF4QBccHdev64/jH47kgxKmqbmDXq1J68lqxlxNqRNR7XyEY1jQZL0abzUcNX03mJEB4ejrFjx2LlypWYO3eu1Ti3oqIivPvuu5g2bZqlmPrpp5+snv/TTz+hX79+lu99fX0xadIkTJo0CbNmzUK/fv1w+PBhDB06FAaDAcXFxRg1alS392vKlCl49913kZCQAC8vL0ycONHysx07duDGG2/E7bffDsBUdB0/frxN9297be9oQfiLL74YRUVF8Pb2RnJycrfb2xWOVBXxUXvhukEtg30/OXC2k63JU+kNRnz2a0s2Jg6O7fZraLy9MHFQy/OYNWqP3mDEpwdbsnH9kO5njcc1soUgCFbj6YL9bLuq+9prr6GhoQHjx4/HDz/8gIKCAmzZsgVjx45FfHw8nnvuOcu2O3fuxIsvvohjx47h9ddfxwcffICHH34YgKmHbc2aNfjtt9+Qk5ODd955B76+vkhKSkKfPn0wdepUTJs2DZs2bUJubi727NmDF154AZs3b+6yjVOnTsX+/fvx3HPP4c9//jN0Op3lZ71798bWrVuxa9cuZGdn44EHHmgzewVgmqtu3rx5OHr0KDZs2IB//vOflra3ds0112DEiBG46aab8NVXXyEvLw+7du3Ck08+ib1799r0e+0MC7dWRqVHItRfAwDNyxZVStwicjffZBejuLIeANAnJhB9owPtep0r+zBr1Dlx1tKjmTVynsp6veVqm9bHCzpv28qD9PR07N27F2lpabjllluQlpaG+++/H6NHj8bu3but7qB85JFHsG/fPgwdOhR/+9vf8PLLL2P8+PEATF2Ib731FkaOHInBgwfj22+/xeeff26Z6mvdunWYNm0aHnnkEfTt2xeTJk3Czz//3GZS/Y7aeMkll+DQoUOYOnWq1c+eeuopXHzxxRg/fjyuvvpqxMTEtNvtO23aNNTV1WH48OGYNWsWHnrooQ5vMlCpVNi8eTOuvPJK3HPPPejTpw9uvfVW5OXltVlEwB4qobNBZgpUWVmJ4OBgVFRUWOZ0a+3H4yVYtzMXANAvNhCPju/X7nbkeYxGAY99dAhlNY1QqYCnrx/QoyWsmDXqiNEo4NEPD6G81vFZG5QQjDnX9HFUU6mH6uvrkZubi5SUFKurQa4iCAJOl9XB0Lw6QmyIDlrvtl2AgGkw/4EDBzB06NB2uwnJPt3JAK+4tWNk73BEBZl+cUcKqyxnvERZhZWWJa0GxYf0eN1RZo068vvZSkvX1eAEx2QtrPmq229nKjpcLos8T32TwVK0+WrUHRZt5B5YuLVDpVLhyvSWu2B+ypVmyQ5yPzuOt6yJe0V6x3dK2YpZo478eMLxWTO/jiBYvz55tqrm+QEB2Hx3PEmHhVsHLk0Nh/mu4t0nSzudtoQ8Q2V9Ew7klwEwzSw+JKF7d/d1hFmj1lpnbXC8Y7I2Kj3SkrUfjp23XGUhz2UwGlHbYJqLzMtLZZnDjdwXC7cOhPlr0DfGNBC4uLIev5/lYF5P9232OcsH3Yi0cIctH8SsUWvOzNrghBAAQFmNaXoQ8myV9eKrbWq7J9sl12Hh1okx/aIs//4m+5yELSGpNeqN+Da7GIDprHRs/7ZrRPYEs0ZmrbN2TUbP70ITG923JWtbfivsZEtyNVdfbTcKAqpEa6EG2TixMzled/72LNw6cVFiqGUw7+HTFTjHgeMe6/ezFahrNHUnXJoSZsmFozBrZNY6a+EBWoe+/sD4ICSEmiZKzTlfg8KKOoe+PnWfj4+pYKqtrXXp+9Y3GmDuLffXejvsyi51n3mlBlvu1OUoxE6ovVQY0y8KH+4zLRezJ+8Crh8cJ3GrSAr788st/74kOazjDe3ErJGZs7OmUqkwsncENu4pAADsO1WG6wf7dvEscia1Wo2QkBAUF5uutPr5+bmky7K8phGGJlNXqbdGQH1911d9zGtz1tfXczoQBzEajTh//jz8/Pzg7d11WcbCrQuXpIRZPkwPna7gh6kHMhgF/No8Fkjr44WM2Pbn/+spcdYOM2seyVVZuzgp1FK48bjmHmJiTMMvzMWbswkCUFbbaOqiU6nQ4OdjU7FoNBpRUlKCvLw8eHWyjil1j5eXF3r16mXT34CFWxciArSIC/HF2fI65JyvRmV9E8cBeJhj56pQ03y7/KD4EGhsnFG8u8RZO3m+GlX1TTYvJk7KIEXWeFxzDyqVCrGxsYiKikJTU1PXT+ihk8XV2PSraULmgfHBuG1gL5ueV11djYkTJ2Lv3r1WC7xTz2g0GpsLYRZuNhiSGIKz5XUQBGD/qTJcLRrcS8q3+2Sp5d8X9wpx6nuJs7aPWfM4UmWNxzX3oVarXdIF+UtBIcobTP/unxBu84oNjY2NOHXqFDQajSSrPBBvTrDJcNE4E/GBlZSvtlGPX5onxdVp1BiSGOLU92PWPJc4a74aNS5ycuHGrHkuVx/XyLFYuNkgMcwX8c13YZ0oruayRB5k36kyNBmMAIARqeHQ+Tj3TLh11nh3qecQZ+2y1HCnLzuUGOZrubuUxzXPsu9UGRr1rjuukWOxcLOBSqXC5Wnhlu938ezUYxw+U2H59whRBpzFlLWW5Y14JcRziLN2WaprsjZClDUe1zyHq7NGjsXCzUbicP96uly6hpDLGI0CsppXMfDVqJES7u+S970staULi1nzDK2zlhrBrJFzSJU1chwWbjYK8dNYuhUKLtRa7vwi5cotrbFMhNo/LgheXq5ZCibET4PEMD8AzJqnkDJrPK55FqmyRo7Dwq0bzHMqCYLptn1SNvGaoQPjHLPIt636Na9dKgjAUWZN8aTMmvi4xqwpnzhrA1ycNXIMFm7dYF4IHACyCrkQuNL9JhoH0j/OOROhdqSfaOLVLC46r3jMGrmKOGsDXJw1cgwWbt3QLyYI6ubLygfyy12+IDC5Tml1A04WVwMA4kJ8EeHg9SK70jc60JK1gwXMmpIxa+Qq4qzFhuhcnjVyDBZu3eCrUVvOhstqGpFTUiNxi8hZzHMcAcDwFMevF9kVZs1z7Mlj1sg1xFm7NIV3k8oVC7duykwKtfx7/6kyCVtCznSweb1IALhUgg9TgFnzFAdEi8q7Q9b2MWuK5Q5Zo55j4dZNQ3uFWhaB3Z9fxm4FBWrQG5DbfNUhOliHqCBplnVh1pTPLbN2illTInfJGvUcC7duCtB6o0+0aWHd4soGXKhplLhF5Gg552tgMJo+uPpGB3axtfMwa8rnjlk7X9WAUmZNccRZ6xPFxeHljIWbHfqIDrAnmgd6knKIp3pJj5b2AMesKZu7Zu0ks6Y44qz1iZHuJIF6joWbHXqLzlZOnudAXqURH+CkvAoCMGtKx6yRq7hT1qhnWLjZITXSH83DQXC8mBNWKoneYMTJYtOHVniABuES3y7PrCkXs0au4m5Zo55h4WYHP4034kNalomp5jIxinH0XBWaDEYA1l1HUmHWlItZI1dxt6xRz7Bws5N5qRBBsJ6JmuRNfLv8kMQQydohxqwpk3jKGWaNnMkdj2tkPxZudhqU0LLG2+HTPMApgSAIlg9TtZcKg+LdYx0/Zk15BEGwfJiqvVQuX5+0I8ya8rQ+rrlL1sh+LNzslB4VAJ2PGgBw+EwFjEbOeyR3xVUNKGueBqFfTKDl7ys1Zk15WmfNV8OskXOcq3TPrJH9WLjZyVvtZVkmpqZBj9xS3oUld+IpENzpdnlmTXnkkjUufyV/4htN+sZwUXklYOHWA+KutGNFvAtL7k6KPqTSIt1rgkpmTVnkkrXj55g1uRPP/yj1XIHkGCzcesB63iNOWCl35qsgKhWQEuEvcWusMWvKwqyRqxxvzpraS4XkcPfKGtmHhVsPxAbrLOMFcs7XcH0/GatvMuB0WS0AID7E123Gt5kxa8ohp6ydZNZkrbK+Cecq6gEASeF+0HjzI18J+FfsAZVKhdTms+WKuiau7ydjeaU1MH8+pbnhOn7MmnLIKWuVzJqsicdSpke5z1hK6hkWbj0kPvByfT/5On6u5W+XGuF+H6YAs6YUzBq5ynHR384dTxLIPizcekh84OX6fvL129mWOav6utFdfmLMmjKIs9Yv1j2zJr5hglmTr5O8MUGRWLj1kHh9vyNFldI2huxS26i3rOMXHaxDZKB7ruMnzlp2IbMmR62zFuGma0Yya/LXqDcit/nu5aggHYJ0PhK3iByFhVsP+Wu9LXeFnSmrQ0l1g8Qtou7KLqy0DMB2l9US2iPO2tlyZk2OsgurLFlz5xns/TTMmtydKq2BoXkC5d7sJlUUFm4OMCghxPLvo5xjS3ZyRF1B/dy0m9SMWZO3HNH0Ghlu2k1qxqzJ23GrGxNYuCkJCzcH6CMaO3CME1bKTp5oJQJ3m1Ortb7RLR/2zJr8MGvkKuKJd3nFTVlYuDlASoQ/VM0DQvK4RIysCIKAvFLTnFohfhqE+GkkblHnmDX5EgQBp5qzFuznw6yR0wiCYCnc/LXeiA3WSdwiciTJC7eVK1ciJSUFOp0OmZmZ2LFjR6fbv/vuuxgyZAj8/PwQGxuLu+++G6WlpS5qbfu03mrEh5j+Y5wpr0OD3iBpe8h25yobUN9o+nslh/tJ3Jquaby9kBDqC4BZk5viqgbUNWctRQYz2DNr8lVUWY+aBj0A09U2cwFOyiBp4bZx40bMmTMHixYtwoEDBzBq1ChMmDAB+fn57W7/448/Ytq0aZg+fTp+//13fPDBB9izZw/uvfdeF7e8reTmbg9BAAou1ErcGrKVuOsq2c27rsySmgtMZk1exFetkpg1ciJ2kyqbpIXbK6+8gunTp+Pee+9FRkYGVqxYgcTERKxatard7X/66SckJydj9uzZSElJwRVXXIEHHngAe/fudXHL2xKvAZdXwgOcXIg/TOWyjp+4wGTW5MNqfBuzRk507BxvTFAyyQq3xsZG7Nu3D+PGjbN6fNy4cdi1a1e7z7n88stx+vRpbN68GYIg4Ny5c/jwww8xceLEDt+noaEBlZWVVl/OYHWAK+V4ELnItboK4v5dpUCrkwRmTTZymDVykROiheWTZHKSQLaTrHArKSmBwWBAdHS01ePR0dEoKipq9zmXX3453n33Xdxyyy3QaDSIiYlBSEgI/vnPf3b4PsuWLUNwcLDlKzEx0aH7YZYQ6gu1V/NAXh7gZKG+ySCaoFIrmwkqmTX5qW8yIPc8s0bOV1nfhOJK08LyyRH+XFhegST/i7YeNCkIQocDKbOysjB79mw8/fTT2LdvH7Zs2YLc3FzMmDGjw9dfuHAhKioqLF8FBQUObb+Zj9oLCaGms+iiinrUNuqd8j7kOCeKqy0TVGbEBkncGtsxa/LDrJGrcHyb8klWuEVERECtVre5ulZcXNzmKpzZsmXLMHLkSDz66KMYPHgwxo8fj5UrV2Lt2rUoLCxs9zlarRZBQUFWX86SFtVyg4J4IWlyT0dEk4r2i5HPhynArMmNOGtyKtwAZk1uTnB8m+JJVrhpNBpkZmZi69atVo9v3boVl19+ebvPqa2thZeXdZPVajUAWJaRkZJ41n3ONO7+josmFXXXheU7wqzJC7NGrnJCtDpHGgs3RZK0q3TevHlYvXo11q5di+zsbMydOxf5+fmWrs+FCxdi2rRplu1vuOEGbNq0CatWrUJOTg527tyJ2bNnY/jw4YiLi5NqNyz6iGYaP8qZxt2a0Sggv3l6g4gALYJ95THmyEyctSP8MHVrgiCgoMyUtfAAjWzGt5kxa/LRqDda7pSPDubC8krlLeWb33LLLSgtLcXSpUtRWFiIgQMHYvPmzUhKSgIAFBYWWs3pdtddd6GqqgqvvfYaHnnkEYSEhGDMmDF44YUXpNoFK4E6HySE+uJ0WR1OldagQW+A1lstdbOoHYWV9WjUGwHI5w4/MXHW8i/UoL7JAJ0Ps+aOzlU2oKHJlLVeYcwaOU9BWW3LwvKRvNqmVJIWbgAwc+ZMzJw5s92frV+/vs1jDz30EB566CEnt8p+yRH+OF1WB0EATpfVIY3/edzSKRnO39aaOGtnypk1d2W+2gYAvZg1ciLxJMlyPEkg20h+V6nSJIa2/GfJ50zjbsu8PinQMju83DBr8nCqVP4fpsyaPJwpr7P8OyHMV8KWkDOxcHMwcRHAJWLcl3hOKrlOUMmsyUO+Aq6CMGvycLpMVLiFyjNr1DUWbg4m/s/CA5x70huMOFVqngxVhwCt5CMG7CLOWn4ps+aOBEFAfnPW/LXeCPWT52BxZs39CYKAM82FW7Cfj2yPa9Q1Fm4O5qtRIypICwAouFAHo1H6aUrIWkFZHfQG098lLVKeV9sA66ydLquzDEom91Fe24SqetOktUnhfh1OLu7umDX3V1bbhJoGU9YSQthNqmQs3Jwgsbk7pMlgRFHz0iPkPnJE8xylRMi3cAOss3aOWXM7x0TTAjFr5EziuQKTZZ416hwLNycQj2M5xW4FtyNeWD5V5nfHibPGtSTdzzHR8kPi+dDkiFlzb0rKGnWOhZsTiKeXEM9iTe7hZPNi395qFRJD5d2lIL6Kc7KYWXM35qsgKpX8141k1tybkrJGnWPh5gS9owJgHspynCsouJXqBj2Km7t5ksL94a2W93+BtMgAy7ipY1xH0q3UNuotg8V7hfnLftJaZs19KS1r1Dl5f2q5KZ2P2jLFxJmyOlQ3Dxgl6eWeF3WTKmAciClrpi6ss+XMmjspuNAyNUOKjG+CMWPW3JfSskadY+HmJOmiS9XsVnAfuaKxOXIfLG7GrLmnU+K5AmU6f1trzJp7EmdNrnMFku1YuDmJuCgQL3lD0jojmqBSrhPvtsasuSfxxLuJCvkwZdbckxImeSbbsXBzEvGBWjybNUnrTLnpAKf2UiEyUCtxaxyDWXNP5gm4VSoV4hUyrxaz5p6UmDXqGAs3J4kK1ELtZRrIe5pnpm5BbzDiXGUDACA2WGf5+8hddJCOWXMzjXojzlaYboKJC9FB462MQy2z5n6UmjXqGP/CTuKt9kJc85lPUUUDGvVGiVtExVUNlpUs4hR0Vqr2UjFrbqagrNaSNaV0yQOts1bPrLkBpWaNOsbCzYkSmucIEwQBRRWcaVxqZ8pbunaUVLgBzJq7ySsR3wSjrDFHLVkDCivYXSo1JWeN2sfCzYmsFpxnt4LkxKtYKK9wY9bcSZ4oa8kKuwoizhrHuUlPyVmj9rFwc6IE0az8HA8ivZOiVSzkvLh8exLDmDV3kltiypqXl8qq0FECZs29KDlr1D4Wbk6UGMo1S92F3mC0TL4bEaBFiJ9G4hY5VgKz5jbqmwyW7uqEUF/FDRZn1tyHOGvxIcrLGrWPf2UnCvbzQai/qUDILamB3sCBvFLJv1CLpubfvxLX8Qv29UEYs+YW8i/UQjCNFVfMJM9izJr7EGctVWG9CNQxFm5OZp5pvFFv5HgQCeWKBvCmRSnzANdblLUCZk0y4qwp9S4/Zs09eELWqC0Wbk4mvrpzgkvESKbAamZxZR7gmDX3YHWXn0I/TJk19+AJWaO2WLg5mfgAJx4cT65lviqgUlnfNKIk6VGBln/nMGuSOdV8kuCtViEuRCdxa5yDWXMPnpA1aouFm5PFh/jCq3mm8bPl7FKQgtEoWNYojQzUQuejlrhFzhEXomPWJKY3GFFsWZ3DF95qZR5imTXpeUrWqC3+pZ3MW+2FmCDTmVBhRT0H8krgXFW95cYEJd8uz6xJ71xVA4Tm0eKxwcq9AsKsSc9TskZtsXBzAfNkrwajgOKqBolb43kKLrRcERAvkq1E8aHMmpQKRVefYhU2yXNrzJq0PClrZI2FmwvEi8ZUnWG3gsudKhXdeaXwwk28IgSz5npnRcuNxSn8Kkg8syYpT8oaWWPh5gJWBzjeOu9y4klCk8KVXbgxa9LypKsgccyapDwpa2SNhZsLJPCKm2QEQbDceRXs66O4FRNaY9akddpy97IKUYFaiVvjXMyatDwpa2SNhZsLRAZo4dN8xw8PcK5VWtOI2gY9AM+YoJJZk05dowGFFabfeWKYr+XvoFTMmnQ8LWtkjX9tF/DyUiGmeQxCcWU9GvQGiVvkOazGtym8mxRg1qSUV1ojWn5IecuqtcasScfTskbWWLi5iLloEAQuzOxK4t91Lw8o3ABmTSriCbbTFLhGaXuYNWnknBct4echWaMWLNxcJE10VnSSS8S4jNWNCQq/o9TMarUOZs1lckUfpp5yFYRZk0ZuScvv2lOyRi1YuLkIl75yPUEQLF2l/lpvhPkr+8YEM6uTBGbNZcyDxbU+XogO8ozB4syaNMxzU3pS1qgFCzcXiQ3WwVdjWmrppOjMnJynvLYJVfXmGxP8oFKpJG6RazBrrlfXaEBJtWkS2oRQZo2cx1OzRi1YuLmISqVCcvNdjZV1Taisb5K4RconvtMtUcFLXbXGrLnemfKWLnnxNBlKx6y5nqdmjVqwcHMh8YSVheX1nWxJjlAkmlk8NsSzZhZn1lyrQDQBrad9mDJrruXJWSMTFm4uFCcqHs5y3iOnK6wUFW4etiQMs+Zap60+TD3n6i7ArLmaJ2eNTFi4uRDXkXStooqW33FMsGedmTJrriVe8inew5YfYtZcy5OzRiYs3FzIqkuhggc4Zyts7ir113ojQOstcWtci1lzHUEQLFeagv184M+skZN4etbIhIWbCwVovRGoM/1HO8uxIE5V32RARa1poLSndZMCzJorVdbpUdO8rJonXgFh1lzH07NGJnYXbuXl5Vi9ejUWLlyICxcuAAD279+PM2fOOKxxSmQ+O62sa0J1839AcjzxxLvxHjqAl1lzDXH3oKd+mJr/jzFrzsWsEWBn4Xbo0CH06dMHL7zwAl566SWUl5cDAD7++GMsXLjQke1TnFjRfzYO5HWe3JKWOaVSPHRJmDhmzSXEv9s4D/0wjQ1m1lyBWSPAzsJt3rx5uOuuu3D8+HHodC3dUBMmTMAPP/zgsMYpUYLoP1vBBa7t5yziws08z5SniWfWXOKU6HfrqR+mzJprMGsE2Fm47dmzBw888ECbx+Pj41FUVNTjRilZkmihc3FxQY5lXstP4+3lsQe4ZNGVRmbNeU4UVwEA1F4q9PKQ9XBbY9Zc40TzerCenDWys3DT6XSorKxs8/jRo0cRGRnZ40YpWa8wP3irTUuUcIkY56hu0KO0uhEA0CvcD2ovz1wSJjHUV5Q1riPpDNUNehRXmpYfSonwh8bbM+/3Ytacz5Q1080fnpw1srNwu/HGG7F06VI0NZnu2lOpVMjPz8eCBQtw8803d+u1Vq5ciZSUFOh0OmRmZmLHjh2dbt/Q0IBFixYhKSkJWq0WaWlpWLt2rT27IQlvtReSmrvuiivrOZDXCcTzHHnSUletWWetgVlzAqusefAVEGbN+Zg1MrOrcHvppZdw/vx5REVFoa6uDldddRV69+6NwMBAPPfccza/zsaNGzFnzhwsWrQIBw4cwKhRozBhwgTk5+d3+JzJkyfj22+/xZo1a3D06FFs2LAB/fr1s2c3JJMq7lbgVTeHO13GtfzMmDXnYtZaMGvOxayRmV2z9wUFBeHHH3/Ed999h/3798NoNOLiiy/GNddc063XeeWVVzB9+nTce++9AIAVK1bgq6++wqpVq7Bs2bI222/ZsgXbt29HTk4OwsLCAADJycn27IKkxGMTzpTXYVBCsIStUR7xLfOefoBLZNacillrweOaczFrZNajaZfHjBmDMWPG2PXcxsZG7Nu3DwsWLLB6fNy4cdi1a1e7z/nss88wbNgwvPjii3jnnXfg7++PSZMm4W9/+xt8fdsPckNDAxoaGizftzc2z9ViOdO4U522WhLGs7sUOKu9czFrLXhccy5mjcxsLtxeffVVm1909uzZXW5TUlICg8GA6Ohoq8ejo6M7vDM1JycHP/74I3Q6HT7++GOUlJRg5syZuHDhQofj3JYtW4ZnnnnG5ra7gngm/6IKzjTuSIIgWMaChAdo4KtRS9wiaTFrzsOsWWPWnIdZIzGbC7fly5fbtJ1KpbKpcBNvLyYIQpvHzIxGI1QqFd59910EB5suw7/yyiv485//jNdff73dq24LFy7EvHnzLN9XVlYiMTHR5vY5g85HjVB/DcpqGnG2or7TfabuKattQn2TAQDPSgFmzZmYNWvirJ0pr2PWHIhZIzGbC7fc3FyHvnFERATUanWbq2vFxcVtrsKZxcbGIj4+3lK0AUBGRgYEQcDp06eRnp7e5jlarRZardahbXeE2GAdymoaUdugR2W9HsG+PlI3SRHEM4vHhnjeGqXtscpanR7BfsyaIzBrbZmzVtdoYNYciFkjsR5PBCMIAgRB6PbzNBoNMjMzsXXrVqvHt27dissvv7zd54wcORJnz55FdXXLPEHHjh2Dl5cXEhISut0GKXGJGOc4y7X82rDKGsceOQyz1haz5hzMGonZXbitWbMGAwcOhE6ng06nw8CBA7F69epuvca8efOwevVqrF27FtnZ2Zg7dy7y8/MxY8YMAKZuzmnTplm2nzJlCsLDw3H33XcjKysLP/zwAx599FHcc889Hd6c4K7EZ00cD+I4VmemwTwzBZg1ZykU/S6ZNZM4Zs0pmDUSs+uu0qeeegrLly/HQw89hBEjRgAAdu/ejblz5yIvLw/PPvusTa9zyy23oLS0FEuXLkVhYSEGDhyIzZs3IykpCQBQWFhoNadbQEAAtm7dioceegjDhg1DeHg4Jk+ebPP7uZM4npk6hfgA56lLXbXGrDkHF/xui1fcnINZIzG7CrdVq1bhrbfewm233WZ5bNKkSRg8eDAeeuihbhVSM2fOxMyZM9v92fr169s81q9fvzbdq3Ikvgoivs2b7Gc0CpbfZai/Bjof3nkFWGet4AKz5gjMWvvimDWHY9aoNbu6Sg0GA4YNG9bm8czMTOj1XOrEFkE6H4T5awAAeSU1MBi7P06QrJ0uq7PceZUa6d/F1p4jSOeD8ABT1k6VMmuOcKacWWtPILPmcMwatWZX4Xb77bdj1apVbR7/17/+halTp/a4UZ4iNTIAANCoN/IGBQfIKWm5aaV38++WTFIimDVHyilpWdIpjVmzIs7aGfYm9BizRq3Z3FUqngtNpVJh9erV+Prrr3HZZZcBAH766ScUFBRY3UxAnUuN9MfevAsAgJPnq7lwcA+Jl4TpFc7fpRiz5ljigqQXf5dWxFnLKanm/8UeYtaoNZsLtwMHDlh9n5mZCQA4efIkACAyMhKRkZH4/fffHdg8ZUsTXfbOK6kB+krYGAWwXhKGA3jFxFnLLanB1cxaj3DB744xa47FrFFrNhdu33//vTPb4ZESQlvOngp563yPiJeECfb1QaCOE3+KibPGaRp6RhBaBosza23xuOY4zBq1p8cT8JL9zEvEALAsR0T2qahrQk2D6caYeJ6VtsGsOQ6z1jlx1gqZtR5h1qg9dk0HAgB79uzBBx98gPz8fDQ2Nlr9bNOmTT1umKcQL0dU1aBHEM+o7CIe38buhPZxmTXHYNa6xqw5BrNG7bHritv777+PkSNHIisrCx9//DGampqQlZWF7777zmodUeqaeMLKwnJ2K9jrbDkn3u2KOGvsLrUfs9Y1Zs0xmDVqj12F2/PPP4/ly5fjiy++gEajwT/+8Q9kZ2dj8uTJ6NWrl6PbqGji5Us407j9CivES13xANceZs0xmLWuMWuOwaxRe+wq3E6ePImJEycCALRaLWpqaqBSqTB37lz861//cmgDlS4mmGv7OYL1Uldcy689zJpjMGtdE6/WwZ4E+zFr1B67CrewsDBUVVUBAOLj4/Hbb78BAMrLy1FbW9vZU6mVOKuuUp6Z2sv8uwv29YGfxu6hm4rGrDkGs9a12CBxVymzZi9mjdpjV+E2atQoy3qhkydPxsMPP4z77rsPt912G/7whz84tIFKF+TrDV+Nae053jpvn+oGParqTXdexfKstEPMWs8xa7YRZ+0ss2YXcdbEV8uJ7CrhX3vtNdTXm/4zLly4ED4+Pvjxxx/xpz/9CU899ZRDG6h0KpUKscE65JyvwYWaRtQ26nlm1U3iCSpjOA6kQ8xazzFrthFnrYxZs4t4xYRY3phAInZ3lcbFxZlewMsLjz32GD777DO88sorCA0NdWgDPUGvcOuZxql7Tha3/M5SwrkIc2eYtZ5h1myXxKz1yMnzLWsvM2skZlfhNnr0aKxZswYVFRWObo9HSovgAa4nckQHuN5RXIS5M8xazzBrtktl1nrkZHFL1tKiWLhRC7sKt0GDBuHJJ59ETEwMbr75ZnzyySdtJuEl26VGtnwA5J7nAa67zEvCaH28EB2klbg17o1Z6xlmzXbMWs+IsxYTxDFu1MKuwu3VV1/FmTNn8OmnnyIwMBB33nknYmJicP/992P79u2ObqPiRQdpLQN5eWbaPfVNBpRUNwAwLSyvUqkkbpF7Y9bsx6x1D7NmP2aNOmP3WqVeXl4YN24c1q9fj3PnzuHNN9/EL7/8gjFjxjiyfR5BpVKhV5hpYeaKuiZUN69NR107LRrAG88BvF1i1uwnXn6IWesas2Y/Zo060+NF5ouKivDGG2/ghRdewKFDhzBs2DBHtMvjiO8a4rxHthPf5ZcQ6idhS+SDWbNPwQVmrbuYNfswa9QZuwq3yspKrFu3DmPHjkViYiJWrVqFG264AceOHcPPP//s6DZ6hFjRGAbOsWU78Vp+8VyE2SbMmn2Yte5j1uzDrFFn7JpYJzo6GqGhoZg8eTKef/55XHLJJY5ul8cRT7DIJWJsd1bcpcADnE24HJF9mLXuY9bsw6xRZ7pduAmCgH/84x+4/fbb4efHS7iOEifqUuCZqe3MC1j7a70RpPORuDXyIF6smlmzHbPWfcyafcy/K2aN2tPtrlJBEPDggw/izJkzzmiPxwr184HWx/TnKKrkWBBb1DUaUFHbBACI5ZIwNmPWuo9Zsw+z1n11jQaU15qm12LWqD3dLty8vLyQnp6O0tJSZ7THY6lUKkQ3jwc5X9WAJoNR4ha5v0LRYGce4GynUqkQ07wI+PmqBjTqmbWuMGv2Yda6r6iy5coks0btsevmhBdffBGPPvoofvvtN0e3x6PFNXcrCAJQXNUgcWvcX5Go64XrRnaP+QPBlDV2YXWFWbMfs9Y9haLxbcwatceumxNuv/121NbWYsiQIdBoNPD1tQ7XhQsXHNI4TyO+QeFseR3n7+mCeK6juBCemXaH1c0wFfWccqALzJr9mLXuOSs6SWDWqD12FW4rVqxwcDMIABLDWg5ouedrcElymIStcX85otnYe4Xxw6A7mLXuYdbsx6x1j3g93EQWudQOuwq3O++809HtIACpkS0LCedwiZhOGYwC8pp/R+EBGoT4aSRukbwwa7Zj1npGnLWTJdWdbElGo2BZHiw8QINQf2aN2rJ75YSTJ0/iySefxG233Ybi4mIAwJYtW/D77787rHGeJkjng/AA03/UvJIa6HmDQoeKq+otA52TI/y72JpaY9Zsx6z1jDhrp0pqmbVOFItu4EgKZ9aofXYVbtu3b8egQYPw888/Y9OmTaiuNp1FHTp0CIsXL3ZoAz1NamQAAKDJYLSaPZusidco5ZgZ+zBrtmHWeo5Zs02BaAm/RHbJUwfsKtwWLFiAZ599Flu3boVG03Ipd/To0di9e7fDGueJkkVnWeJ1OMma+HeTyJnF7cKs2YZZ6zlmzTbWay8za9Q+uwq3w4cP449//GObxyMjIzm/Ww+J7yLiTOMdO32BS8L0lDhrZ5m1DjFrPces2UacNRZu1BG7CreQkBAUFha2efzAgQOIj4/vcaM8mfWt85xpvCPmLgWtjxciA7QSt0aexFkrYtY6xKz1HLNmG2aNbGFX4TZlyhQ8/vjjKCoqgkqlgtFoxM6dOzF//nxMmzbN0W30KBH+WvioTX8WXnFrX32TAaXVpiVh4kN8oVKpJG6RPDFrXWPWHEOcNV5xax+zRrayq3B77rnn0KtXL8THx6O6uhr9+/fHlVdeicsvvxxPPvmko9voUby8VIgOMp1pFVc18A6sdpyr5Cz2jsCsdY1Zcwxx1s4za+1i1shWdhVuPj4+ePfdd3H8+HH897//xX/+8x8cOXIE77zzDtRqtaPb6HHM/2mNRgHnq7n0VWviq0Ncy69nYkOYtc4wa47DrHWOWSNb2TUBr1lqaipSU1NhMBhw+PBhlJWVITQ01FFt81itb1CI5dmXFS747TixwcxaZ5g1x4m1WtKPWWuNWSNb2XXFbc6cOVizZg0AwGAw4KqrrsLFF1+MxMREbNu2zZHt80gxQeKBvBwP0pr1mSkP/j0h/v0Vcn6tNpg1xxH//nhca4tZI1vZVbh9+OGHGDJkCADg888/R05ODo4cOYI5c+Zg0aJFDm2gJ4oTLS5/tpx3YLVm/p2ovVSIDOSdVz0Ry7uYO2UuZpm1nmPWOseska3sKtxKSkoQExMDANi8eTMmT56MPn36YPr06Th8+LBDG+iJooN0UHuZ7ijKK+U6kmJ1jQbL2XpciK/l90T2YdY6Vt9ksBQYzFrPMWsdY9aoO+wq3KKjo5GVlQWDwYAtW7bgmmuuAQDU1tby5gQH0Hh7WZY7KSyvR22jXuIWuY+ckmoIgunfaVEB0jZGAZi1juWcr2HWHIhZ6xizRt1hV+F29913Y/LkyRg4cCBUKhXGjh0LAPj555/Rr18/hzbQU6VGtiwRk1vCs1OzggstS8KkcsFvh2DW2pd/oeV3waw5RlpkS1GSc55ZM2PWqDvsKtyWLFmC1atX4/7778fOnTuh1Zr649VqNRYsWODQBnqq1IiWA9xJHuAsCkRLwvTiIswOway1T5y1RC4u7xApoqIkhycJFswadYfd04H8+c9/bvPYnXfe2aPGUAvxVRDxVSZPZ16E2ctLZbWMDtmPWWufOGuxIcyaIzBr7WPWqDvsuuIGAN9++y2uv/56pKWloXfv3rj++uvxzTffOLJtHi0yQAtvtWmAKu/AMmkyGC3L5cQF6yxL6FDPMGttibMWy6w5DLPWFrNG3WVXQl577TVce+21CAwMxMMPP4zZs2cjKCgI1113HV577bVuvdbKlSuRkpICnU6HzMxM7Nixw6bn7dy5E97e3rjooovs2AP35+Wlsszndq6SS8QAprmfjEbTCN4Edic4DLPWljhr7LpyHGatLWaNusuuwm3ZsmVYvnw5NmzYgNmzZ2P27Nl47733sHz5cjz//PM2v87GjRstc78dOHAAo0aNwoQJE5Cfn9/p8yoqKjBt2jT84Q9/sKf5ssGlr6ydLms5Q48P5QSVjsSsWWPWnIdZs8asUXfZVbhVVlbi2muvbfP4uHHjUFlZafPrvPLKK5g+fTruvfdeZGRkYMWKFUhMTMSqVas6fd4DDzyAKVOmYMSIEd1uu5yIl746y1ntUVTZcoATT1JMPcesWWPWnIdZsybOGpe6IlvYVbhNmjQJH3/8cZvHP/30U9xwww02vUZjYyP27duHcePGWT0+btw47Nq1q8PnrVu3DidPnsTixYttep+GhgZUVlZafcmF1XJEHA9idZDnAc6xmDVr4qzFMWsOxaxZs8oaTxLIBjbfVfrqq69a/p2RkYHnnnsO27Zts1z1+umnn7Bz50488sgjNr1eSUkJDAYDoqOjrR6Pjo5GUVFRu885fvw4FixYgB07dsDb27amL1u2DM8884xN27obcXHCtf1aDvJqLxUiArgkjCMxa9bEWQtn1hyKWbPG4xp1l82F2/Lly62+Dw0NRVZWFrKysiyPhYSEYO3atXjyySdtboBKZb20hyAIbR4DTIvZT5kyBc888wz69Olj8+svXLgQ8+bNs3xfWVmJxMREm58vpeggHVQqQBDYpWAwCiiuNI2HiQnWcUkYB2PWWjBrzsWstWDWyB42F265ubltHispKYFKpUJ4eHi33zgiIgJqtbrN1bXi4uI2V+EAoKqqCnv37sWBAwfw4IMPAgCMRiMEQYC3tze+/vprjBkzps3ztFqtZYJgudF4eyEyUIviygYUVdZ1WNR6gvNVDTA033kl7mohx2DWWjBrzsWstWDWyB7dHuNWXl6OWbNmISIiAtHR0YiKikJERAQefPBBlJeX2/w6Go0GmZmZ2Lp1q9XjW7duxeWXX95m+6CgIBw+fBgHDx60fM2YMQN9+/bFwYMHcemll3Z3V2TBPO1FQ1PLXD+eKKek2vLvBN555RTMmgmz5nzMmok4a7yjlGzVrZUTLly4gBEjRuDMmTOYOnUqMjIyIAgCsrOzsX79enz77bfYtWsXQkNDbXq9efPm4Y477sCwYcMwYsQI/Otf/0J+fj5mzJgBwNTNeebMGfz73/+Gl5cXBg4caPX8qKgo6HS6No8rSWqEP/afKgMAnCyuRryHDl49WdxygOvNRZidglkzYdacLy2SWQOss5bOrJGNulW4LV26FBqNBidPnmzTnbl06VKMGzcOS5cubTMeriO33HILSktLsXTpUhQWFmLgwIHYvHkzkpKSAACFhYVdzummdGlR4nUkq3Fln0gJWyOdvFLTkjAqlfV6h+Q4zJoJs+Z8qZHMGsCskX261VX6ySef4KWXXmp3DFpMTAxefPHFdqcJ6czMmTORl5eHhoYG7Nu3D1deeaXlZ+vXr8e2bds6fO6SJUtw8ODBbr2f3CSH+8OrecDqyfPVXWytTAajgDPNk1RGBemg81FL3CJlYtaYNVdh1qyzFhnIrJHtulW4FRYWYsCAAR3+fODAgR1O5UH20Xh7WboRiirq0aj3vCViiirr0dS8NA6XhHEeZo1ZcxWNt5dl/KCnZu2cKGu9wpg1sl23CreIiAjk5eV1+PPc3Fy77jClzpkPcIJg+s/uafKbuxMAHuCcjVlj1lzFfJLgqVk7xayRnbpVuF177bVYtGgRGhsb2/ysoaEBTz31VLtLYVHPiG8TP1vueTONF1zgAc5VmDVmzVXEqwQwa8wa2a5bNyc888wzGDZsGNLT0zFr1iz069cPAJCVlYWVK1eioaEB77zzjlMa6snEa/sVeuCt82fKuQizqzBrzJqriFdQYNaYNbJdtwq3hIQE7N69GzNnzsTChQshCKaJA1UqFcaOHYvXXntNNqsSyIn4zPSMB56ZmpeE0fmoEernI3FrlI1ZY9ZchVlj1sg+3SrcACAlJQVffvklysrKcPz4cQBA7969ERYW5vDGkUlEgBbeahX0BsHjFmWubzKgtNrUNR8XovPYGdZdhVlj1lyFWWPWyD7dLtzMQkNDMXz4cEe2hTqg9lIhJkiH02V1OFfZAL3BCG91txe9kCXxItRcEsb5mDUTZs35mDWTGGaNuskz/pcoQGxzt4LRKKC4qkHi1rjOWdGZuHj8FTlPHLPGrLkIswbEM2vUTSzcZEI8HuR0med0K5wR7SuvgrhGLLPGrLmIp2btbDmv7pL9WLjJRJLodvEcD5pp/IRoX5PDuSSMK4iz5kmz2p88X2P5d1I4p2dwheRwz8zaCdEapcwadRcLN5kQryN5vNgzDnB6gxF5JaYP08hALYJ555VLiLN2woOyllti2tfIQC1C/DQSt8gziNcs9aSsiY9rzBp1Fws3mQjQeiO2eSxE/oVaNOgNErfI+Qor6qE3mKac4QLMrsOsMWuuIs7aqdJa1Dd5RtbMS10xa2QPFm4y0rv57NRoFJBXUtvF1vLHmcWlw6yRq6RHBQIABEGwWgZKqQrKWvYxkVkjO7Bwk5Fk0dmZ+INGqfIv8AAnFWaNXMXjssY1SqmHWLjJiPgDRXzWplTiD9NeHMDrUswauUqCaLknT8gar7hRT7Fwk5H4EF+YJ9hW+q3zgiBYPkyD/XwQpOONCa7ErJGriLNWcEH5WTN3Bwf7+SDYl1mj7mPhJiM6HzUiA00Dec+U1cFgFCRukfOU1jSirtE0UJndCa7HrJGr6HzUiAoyZe1sObNG1BUWbjKTGGbqVmgyGFFcVd/F1vKVz8HikhNn7Vwls0bOY+4uVXrWeBMMOQILN5lJDBWNPVJwtwIPcNITZ03J3aXMmvSsj2vKHefGkwRyBBZuMmM1kFfJBzjeeSU5qxsUmDVyInHWlHySwKyRI7BwkxmPOcA1FwqmsVZaiVvjmTzlbj9mTXqekjXzvjFr1BMs3GQm3F8DX40agHIPcNUNelyoaQQAJIT5QmW+5YxcSpw1pZ4kMGvuwVOyVlrNrFHPsXCTGZVKhYTm8SBlNY2obtBL3CLHE3fLJYVxSRipqFQqyxVeZo2cqXXWquqbJG6R43EsJTkKCzcZShZNEHpSgQszW89i79vJluRsSWHMGrmGOGs552skbIlz8MYEchQWbjKUHh1g+fdxBX6Y8szUfTBr5CrirB07VyVhS5yDWSNHYeEmQ2mRLQe4U6XKPTP18lIhLoRXQaTErJGriLOWr8C7mAuYNXIQFm4yFOzrg0CdNwDTAU4QlDPTeKPeiLPlpgk444J18FEzolISZ+1UKbNGzqP0rJ1h1shBmB4ZUqlUlkvt1fV6lNUqZyDv2fI6ywGbCzBLT5y1mgZmjZxHpVKhV7jpBhFmjahjLNxkynyAA5TVrcABvO6HWSNXEf8dmDWi9rFwkymPOMCF8wDnDpg1chVmjahrLNxkqpdClyMS74t4/UKSDrNGrsKsEXWNhZtMRQVqofUx/fmUcrefIAiW1SDCAzTw13pL3CICgOggZo1cg1kj6hoLN5ny8mpZQaG0uhG1jfKf1f5cZQMamowAOA7EnahUKstVgtLqRtQoYAUFZs09MWtEXWPhJmOJChsPIp50MzmCyw+5kwRxF5YC1shl1txXIrNG1CkWbjImXiImr0RZB7h+MUEStoRaU3bWAiVsCbXWi1kj6hQLNxlLjWw5e1PCEjG5JaYxLWovldV6rCS9tKiWWe2PFsk/a3mlLVlLCudVEHfCrBF1joWbjMWH+FpmGj92rkrWM43XNxlwrtI0s3hCqB+8ObO4W4kL1lmydrxY/lkrqjBlLT7Ul7PYuxmlZi0uhFkjx2CKZEylUiElwnR2WtdowPmqBolbZL+CC7UwH5+TI3i1zd0oNmu8AuJ2lJs1HtfIMVi4yZy4yDkl4xsU8ko5s7i7E2dN/PeSG3Hbk/hh6pYUmTXemEAOwsJN5sRXDMxjxORIPGcTx4G4J3HW8mQ8xxaz5v6UmDVe3SVHYeEmc+IrBnKesFI8gDch1Ffi1lB7mDVyFaVlzctLhfgQZo0cg4WbzIX4aRDs5wMAOFVaK8uBvBzAKw/MGrmK0rIWH+ILjTezRo7BJCmA+RK8XAfyni7jAF65YNbIVZg1ovaxcFMAcbeCHAfyiifZ5ABe98askauIVxmQ4/hdZo2chYWbAlgN5JXhAe6oaPLgFA7gdWvMGrmKeLWOUzI8SWDWyFkkL9xWrlyJlJQU6HQ6ZGZmYseOHR1uu2nTJowdOxaRkZEICgrCiBEj8NVXX7mwte5JfBUkV2YDeQVBsMyO7qtRcyoQN8eskatY3THPrBFZSFq4bdy4EXPmzMGiRYtw4MABjBo1ChMmTEB+fn672//www8YO3YsNm/ejH379mH06NG44YYbcODAARe33L2E+GkQHqABAJwsrkaD3iBxi2x3rrIBNQ16AECf6EB4eakkbhF1hlkjVwn280FEgBaA/LJWXNWStfQoZo0cS9LC7ZVXXsH06dNx7733IiMjAytWrEBiYiJWrVrV7vYrVqzAY489hksuuQTp6el4/vnnkZ6ejs8//9zFLXc/A+KCAQAGo4CTxfI5O80pqbb8W7z2KrkvcdZOFFd3sbX7YNbkp39cEAD5Ze3keWaNnEeywq2xsRH79u3DuHHjrB4fN24cdu3aZdNrGI1GVFVVISwsrMNtGhoaUFlZafWlROnRLQsziz+g3J140HEKB/DKgjhrcho0zqzJj1yzJr4xgYUbOZpkhVtJSQkMBgOio6OtHo+OjkZRUZFNr/Hyyy+jpqYGkydP7nCbZcuWITg42PKVmJjYo3a7q9QI0QHuvHwOcOK28sNUHsRZy2HWyInkmrUc0RU3Zo0cTfKbE1Qq675/QRDaPNaeDRs2YMmSJdi4cSOioqI63G7hwoWoqKiwfBUUFPS4ze4oOkgLX40aAJBTUiOLCSubDEbkN6+vGhOsg5/GW+IWkS3EWctl1siJooO08NOa/lY556tll7VoZo2cQLLCLSIiAmq1us3VteLi4jZX4VrbuHEjpk+fjv/+97+45pprOt1Wq9UiKCjI6kuJVCoVUpvP7CrrmlBa0yhxi7pWcKEWBqPpQMyzUvlg1shVVCqV5e9VVa+XXdZSmTVyAskKN41Gg8zMTGzdutXq8a1bt+Lyyy/v8HkbNmzAXXfdhffeew8TJ050djNlJTVSXuNBxF0faaK2k/tj1shVUmU2ES+zRs4maVfpvHnzsHr1aqxduxbZ2dmYO3cu8vPzMWPGDACmbs5p06ZZtt+wYQOmTZuGl19+GZdddhmKiopQVFSEiooKqXbBrYivJIjHWLgrDhaXL7llLU80D1gysyYrzBqRNUk732+55RaUlpZi6dKlKCwsxMCBA7F582YkJSUBAAoLC63mdHvzzTeh1+sxa9YszJo1y/L4nXfeifXr17u6+W4nJVJ8gHPvM1NBEHC82DRBpbdahYRQX4lbRN0hu6ydM33ge6tVSGTWZIVZI7Im+ajJmTNnYubMme3+rHUxtm3bNuc3SMaCdKYJK0uqG3CqtBZ6gxHeasnvP2nXucoGlFabxqv0jgpw23ZS+4J0PogM1OJ8lftnrbiqASXVpkXKmTX5YdaIrDFVCpMWZTo7bTIYkePG40GOFLXMp2ee0JXkxTw/VZPBiJNufCUku5BZkzvzWDFmjYiFm+IMjG85WBw67b5j/8SzoPeJDpSwJWSvgaIPpsNnmDVyngHxLbMBMGvk6Vi4KYz4LO/4uSoJW9I58wHOW62yWric5INZI1dh1ohasHBTmGBfH0QFmRZmzi2pQaPeKHGL2iqvbcT5KtM4kJSIAPhwHIgsBfu5f9YqapssWUuO8GfWZEoOxzVmjVyFyVKg3lGmS/QGo4D8C+43HkTcndA7ivMcyZnbZ+18y9WZ9Ch2XcmZOGunSpk18lws3BQoXVQMHTvnfvMeiQu3dBZusubuWTt+jllTCvHf73ixe2eNJ6TkTCzcFCg9uuWgccIdD3CiNqXxACdr4g8oZo2cSXxcO+6OJwnsSSAXYeGmQDFBOvg3L8x8oti9FmZu0BssCzDHhugQoJV8KkHqgdhgZo1cQ3xcO+lmC84za+RKLNwUSKVSWc74ahr0KKyol7hFLY4WVcHYvAAzx4HIn0qlsnRhMWvkTMwakQkLN4USjwc56ka3z/8qmltOPOccyZe4W+hoEbNGzsOsEbFwU6yM2JYJKw/kl0vXkFbMM4t7eakwIC6oi61JDqyzViZhS6wxa8rDrBGxcFOspHA/hPlrAABHCivdYt6j8tpGnGvu3kiN8IfORy1xi8gRrLJWVMWskdO4e9ZSmDVyARZuCqVSqdC/+czPYBRw8rz0d2FlF7Z0bfSN4TgQpVCpWq4yGIyCW9xdyqwpk7tnrR+zRi7Awk3BxN0K4sWPpSJeWF7cNpK/fqK/p/jvLBVmTbncOWv9Ypg1cj4WbgomPvs74gYDeY80n5mqvVRIi+Q8R0rCrJGruHPWOH8buQILNwUL8dMgJlgHAMg5X4P6JoNkbSmpbkBJtWkdv95RAdB4M3pKEuKnQWyI+2UtjVlTHGaNPB1TpnDmbgVBECSdbfyIeBwIu64UqW+M+2WN3aTK1E+UtWMSTnfErJEUWLgpXP/Ylm4FKce5iW/dF7eJlINZI1fJEP1dxcWTqzFrJAUWbgrXNyYIKpXp37+eLpdkmZgGvQG/nTVNUBns64PUCI4DUSJ3ydrvZ01FI7OmXOKsHWTWyMOwcFO4AK030qNNZ4JFFfUouFDn8jYcKayC3mA6sF7UKwReXiqXt4Gcz12y1mQwze3FrCmXOGvnJMra0aKWrA1JZNbIdVi4eYDhyWGWf/96utzl73/oTMtyMIO4HIyiSZ21w8yax5A6a4dEy1wNSmDWyHVYuHkA8UFF/MHmCoIg4HDzQVXtpeIAXoWTOmuHmDWPIc7aIRcXbq2z1p9ZIxdi4eYBIgK0iAvxBQDknK9GVX2Ty967qLIepdWNAEwz2HM5GGVzl6z1iWbWlE6ctdySGmaNPAYLNw9hPjsVBOC3M66740/cnTCQXVcewR2yxq4rzzDYDbLG4xq5Ggs3DzHYqgur3GXvK+7CGMwPU48wJCHE8m9mjZxpMLNGHoiFm4foHRkAncZ0Of+3M5UwGJ1/+/yFmkYcbV6SJipIi5ggndPfk6SXFunPrJFLuEPWYoOZNXItFm4ewlvthYFxpjPDmgY9ss46v1vhl9wLME+vdFlqOFQq3i7vCZg1chUpsrYnj1kjabFw8yCXprbcPr/rZInT32/fqQst750S7vT3I/fBrJGriLO20wVZ25vHrJG0WLh5kMHxwfDXegMADuSXO3Vx5pLqBuScrwEAJIT6Wha7J8/ArJGriLN20MlZK2XWyA2wcPMg3movXJIcCgBoMhiR5cT1JPfmtazhd0lKWCdbkhIxa+QqLs3aqZasDUtm1kgaLNw8zJDEEMu/fy0od9r7iLuuhiXxAOeJxFk7mF/utPdh1shVWRN3k17Cwo0kwsLNw/SLCYLG2/RnP1hQDn3zWnuOVFRRz+4Essrar6eZNXIeZo08CQs3D6Px9rLMfVRdr8c+0aV/R/nq9yLLv0ekRTj89UkeNN5elishrskaB4p7Kldk7essZo3cAws3DzS6X6Tl39uOnXfoa1c36LHzhOnOLp1GjSv7sHDzZFf3dWXWIrt4BimZy7Lmw6yRtFi4eaC+0YGIDTFd5j9WVIXTZbUOe+1fckstk2CO6h0BP423w16b5IdZI1dxdtb0huaspTNrJC0Wbh5IpVLh6j5Rlu+3HXXc2enOE6WWf4/szattno5ZI1dh1shTsHDzUJf3DrcM5v0ppxQN+p7PfXTsXBXySkyDd3uF+yExzK/Hr0ny5+ysJYYxa2TSOmuN+p7fpMCskbth4eah/DTelnmI6hoN+OFYz2cc/+JQoeXfYzOie/x6pAzOztq4/swambTNWs+vujFr5G5YuHkwcXH1v0NnezTjeG5JDX4/UwEACA/QYDgnQiURZo1cRZy1L5g1UiAWbh6sV7ifZab5qno9vs46Z/drbT7cclZ63aBYeKsZLWrhrKxNYNaoFWaNlI4p9HB/HBoPlUoFwDQnVlV9U7df40x5HfY3z5sU7OfDwbvULqus/eagrHGeQGoHs0ZKxsLNw0UH6SxzrdU3GvDl4aIuntHWJwfOWP597YAY+PCslNphlbUmg9XVDFu1zpp5IDqRGLNGSsYkEm4YHGcptr7JPodTpTU2P/eX3AuWs9IAnTcnpqROibP2bXYxs0ZOw6yRUrFwI4T6azBugGlAr8Eo4I3tOTbdRl9e24j//HTK8v2U4b2g81E7rZ0kf8wauQqzRkrFwo0AAJOGxCE5wh8AUFxZj48PnO50e6NRwLqdeahp0AMAhiWH8Y4rsgmzRq7CrJESSV64rVy5EikpKdDpdMjMzMSOHTs63X779u3IzMyETqdDamoq3njjDRe1VNm81V6YfkUK1F6mAb1f/34Onxw4A0EQ2mzbZDDizR9y8FvzbfLBvj64Y0SSZTAwUWeYNXIVZo2USNLCbePGjZgzZw4WLVqEAwcOYNSoUZgwYQLy8/Pb3T43NxfXXXcdRo0ahQMHDuCJJ57A7Nmz8dFHH7m45coUF+KLycMSLd9//utZrN+VZ3VHVnFlPf7xzXHszbsAAPDyUmH6qBQEaLl2H9mOWSNXaS9rbzNrJGMqob1TDxe59NJLcfHFF2PVqlWWxzIyMnDTTTdh2bJlbbZ//PHH8dlnnyE7O9vy2IwZM/Drr79i9+7dNr1nZWUlgoODUVFRgaCgoJ7vhAJtzTqH939pKZ69vFToHRUAg1FAzvlqmBPjo/bCzNFpGJwQIk1DSfaYNXKVb7LOYQOz1mP8DJWeZKcTjY2N2LdvHxYsWGD1+Lhx47Br1652n7N7926MGzfO6rHx48djzZo1aGpqgo+PT5vnNDQ0oKGhwfJ9ZWWlA1qvbGP7R8Nfq8Y7u0+hUW+E0SjgWFGV1TYBOm88NCYdvaMCJGolKQGzRq5yTf9o+DFrpACSFW4lJSUwGAyIjrZe+y06OhpFRe3PJVZUVNTu9nq9HiUlJYiNjW3znGXLluGZZ55xXMM9xOVpEUiPCsS2o8XYnVOKilpTt0JUkBaj0iNxdd9I+GnYjUA911nWrugdidH9mDVyDB7XSAkkT2jrgZ+CIHQ6GLS97dt73GzhwoWYN2+e5fvKykokJia2uy1ZiwzU4i/DEvHnzATUNBrgpQJ8fdQcrEsOx6yRqzBrJHeSFW4RERFQq9Vtrq4VFxe3uapmFhMT0+723t7eCA8Pb/c5Wq0WWq3WMY32UCqVioN0ySWYNXIVZo3kSrK7SjUaDTIzM7F161arx7du3YrLL7+83eeMGDGizfZff/01hg0b1u74NiIiIiIlkXQ6kHnz5mH16tVYu3YtsrOzMXfuXOTn52PGjBkATN2c06ZNs2w/Y8YMnDp1CvPmzUN2djbWrl2LNWvWYP78+VLtAhEREZHLSHqd+JZbbkFpaSmWLl2KwsJCDBw4EJs3b0ZSUhIAoLCw0GpOt5SUFGzevBlz587F66+/jri4OLz66qu4+eabpdoFIiIiIpeRdB43KXAOGiIiIvvwM1R6ki95RURERES2YeFGREREJBMs3IiIiIhkgoUbERERkUywcCMiIiKSCRZuRERERDLhcet9mGc/qayslLglRERE8mL+7PSwmcTciscVbqWlpQDAheaJiIjsVFVVheDgYKmb4ZE8rnALCwsDAOTn53tU6CorK5GYmIiCggKPmjSR+8399gTcb+63qwiCgKqqKsTFxbn0famFxxVuXl6mYX3BwcEe9R/dLCgoiPvtQbjfnoX77Vmk2m9PuujhjnhzAhEREZFMsHAjIiIikgmPK9y0Wi0WL14MrVYrdVNcivvN/fYE3G/utyfw1P0mE5XAe3qJiIiIZMHjrrgRERERyRULNyIiIiKZYOFGREREJBMs3IiIiIhkQhGF28qVK5GSkgKdTofMzEzs2LGj0+23b9+OzMxM6HQ6pKam4o033mizzUcffYT+/ftDq9Wif//++Pjjj53VfLs5er/feustjBo1CqGhoQgNDcU111yDX375xZm7YBdn/L3N3n//fahUKtx0000ObnXPOWO/y8vLMWvWLMTGxkKn0yEjIwObN2921i7YxRn7vWLFCvTt2xe+vr5ITEzE3LlzUV9f76xdsEt39ruwsBBTpkxB37594eXlhTlz5rS7ndKOa7bstxKPa7b+vc3c+bhGdhBk7v333xd8fHyEt956S8jKyhIefvhhwd/fXzh16lS72+fk5Ah+fn7Cww8/LGRlZQlvvfWW4OPjI3z44YeWbXbt2iWo1Wrh+eefF7Kzs4Xnn39e8Pb2Fn766SdX7VaXnLHfU6ZMEV5//XXhwIEDQnZ2tnD33XcLwcHBwunTp121W11yxn6b5eXlCfHx8cKoUaOEG2+80cl70j3O2O+GhgZh2LBhwnXXXSf8+OOPQl5enrBjxw7h4MGDrtqtLjljv//zn/8IWq1WePfdd4Xc3Fzhq6++EmJjY4U5c+a4are61N39zs3NFWbPni28/fbbwkUXXSQ8/PDDbbZR4nHNlv1W4nHNlv02c+fjGtlH9oXb8OHDhRkzZlg91q9fP2HBggXtbv/YY48J/fr1s3rsgQceEC677DLL95MnTxauvfZaq23Gjx8v3HrrrQ5qdc85Y79b0+v1QmBgoPD222/3vMEO4qz91uv1wsiRI4XVq1cLd955p9sd4Jyx36tWrRJSU1OFxsZGxzfYQZyx37NmzRLGjBljtc28efOEK664wkGt7rnu7rfYVVdd1e4HuRKPa2Id7XdrSjiuiXW23+5+XCP7yLqrtLGxEfv27cO4ceOsHh83bhx27drV7nN2797dZvvx48dj7969aGpq6nSbjl7T1Zy1363V1taiqakJYWFhjml4Dzlzv5cuXYrIyEhMnz7d8Q3vIWft92effYYRI0Zg1qxZiI6OxsCBA/H888/DYDA4Z0e6yVn7fcUVV2Dfvn2W7rKcnBxs3rwZEydOdMJedJ89+20LJR7X7KGE45qt3Pm4RvaT9SLzJSUlMBgMiI6Otno8OjoaRUVF7T6nqKio3e31ej1KSkoQGxvb4TYdvaarOWu/W1uwYAHi4+NxzTXXOK7xPeCs/d65cyfWrFmDgwcPOqvpPeKs/c7JycF3332HqVOnYvPmzTh+/DhmzZoFvV6Pp59+2mn7Yytn7fett96K8+fP44orroAgCNDr9fjrX/+KBQsWOG1fusOe/baFEo9r9lDCcc0W7n5cI/vJunAzU6lUVt8LgtDmsa62b/14d19TCs7Yb7MXX3wRGzZswLZt26DT6RzQWsdx5H5XVVXh9ttvx1tvvYWIiAjHN9aBHP33NhqNiIqKwr/+9S+o1WpkZmbi7Nmz+Pvf/+4WhZuZo/d727ZteO6557By5UpceumlOHHiBB5++GHExsbiqaeecnDr7eeMY5ASj2vdoaTjWmfkdFyj7pN14RYREQG1Wt3mrKS4uLjN2YtZTExMu9t7e3sjPDy80206ek1Xc9Z+m7300kt4/vnn8c0332Dw4MGObXwPOGO/f//9d+Tl5eGGG26w/NxoNAIAvL29cfToUaSlpTl4T7rHWX/v2NhY+Pj4QK1WW7bJyMhAUVERGhsbodFoHLwn3eOs/X7qqadwxx134N577wUADBo0CDU1Nbj//vuxaNEieHlJO4LEnv22hRKPa92hpONaV06ePOn2xzWyn6zHuGk0GmRmZmLr1q1Wj2/duhWXX355u88ZMWJEm+2//vprDBs2DD4+Pp1u09Frupqz9hsA/v73v+Nvf/sbtmzZgmHDhjm+8T3gjP3u168fDh8+jIMHD1q+Jk2ahNGjR+PgwYNITEx02v7Yyll/75EjR+LEiROWAzoAHDt2DLGxsZIXbYDz9ru2trZNcaZWqyGYbtZy4B7Yx579toUSj2u2UtpxrStyOK5RD7j6bghHM99GvWbNGiErK0uYM2eO4O/vL+Tl5QmCIAgLFiwQ7rjjDsv25ukC5s6dK2RlZQlr1qxpM13Azp07BbVaLfzf//2fkJ2dLfzf//2f294278j9fuGFFwSNRiN8+OGHQmFhoeWrqqrK5fvXEWfsd2vuePeVM/Y7Pz9fCAgIEB588EHh6NGjwhdffCFERUUJzz77rMv3ryPO2O/FixcLgYGBwoYNG4ScnBzh66+/FtLS0oTJkye7fP860t39FgRBOHDggHDgwAEhMzNTmDJlinDgwAHh999/t/xcicc1Qeh6v5V4XBOErve7NXc8rpF9ZF+4CYIgvP7660JSUpKg0WiEiy++WNi+fbvlZ3feeadw1VVXWW2/bds2YejQoYJGoxGSk5OFVatWtXnNDz74QOjbt6/g4+Mj9OvXT/joo4+cvRvd5uj9TkpKEgC0+Vq8eLEL9sZ2zvh7i7nrAc4Z+71r1y7h0ksvFbRarZCamio899xzgl6vd/audIuj97upqUlYsmSJkJaWJuh0OiExMVGYOXOmUFZW5oK9sV1397u9/7tJSUlW2yjxuNbVfiv1uGbL31vMXY9r1H0qQXCDvgEiIiIi6pKsx7gREREReRIWbkREREQywcKNiIiISCZYuBERERHJBAs3IiIiIplg4UZEREQkEyzciIiIiGSChRsRERGRTLBwI3JjV199NebMmSN1MySxZMkSXHTRRS55r++++w79+vWzWrdVLg4fPoyEhATU1NRI3RQicgEWbkROctddd0GlUkGlUsHHxwepqamYP3++W33AXn311ZY2arVaxMfH44YbbsCmTZtc2g6VSoVPPvnE6rH58+fj22+/dcn7P/bYY1i0aJFl8fnCwkJMmTIFffv2hZeXV6fF85IlS3DrrbcCAJKTk6FSqfD++++32W7AgAFQqVRYv3695bHk5GSsWLGi3de0tWgdNGgQhg8fjuXLl9u0PRHJGws3Iie69tprUVhYiJycHDz77LNYuXIl5s+fL3WzrNx3330oLCzEiRMn8NFHH6F///649dZbcf/99/fodQ0GQ4+uYAUEBCA8PLxHbbDFrl27cPz4cfzlL3+xPNbQ0IDIyEgsWrQIQ4YM6fT5n332GW688UbL94mJiVi3bp3VNj/99BOKiorg7+/v2MY3u/vuu7Fq1SoYDAanvD4RuQ8WbkROpNVqERMTg8TEREyZMgVTp061XFm66667cNNNN1ltP2fOHFx99dUdvt7KlSuRnp4OnU6H6Oho/PnPf7b8TBAEvPjii0hNTYWvry+GDBmCDz/8sMs2+vn5Wdp42WWX4YUXXsCbb76Jt956C9988w0AYNu2bVCpVCgvL7c87+DBg1CpVMjLywMArF+/HiEhIfjiiy/Qv39/aLVanDp1Cnv27MHYsWMRERGB4OBgXHXVVdi/f7/ldZKTkwEAf/zjH6FSqSzft77qZDQasXTpUiQkJECr1eKiiy7Cli1bLD/Py8uDSqXCpk2bMHr0aPj5+WHIkCHYvXt3p/v//vvvY9y4cdDpdFZt+sc//oFp06YhODi4w+cWFBTgt99+w4QJEyyPTZ06Fdu3b0dBQYHlsbVr12Lq1Knw9vbutC0dMV8VFX+Zf08AMH78eJSWlmL79u12vT4RyQcLNyIX8vX1RVNTk13P3bt3L2bPno2lS5fi6NGj2LJlC6688krLz5988kmsW7cOq1atwu+//465c+fi9ttvt+vD/M4770RoaGi3u0xra2uxbNkyrF69Gr///juioqJQVVWFO++8Ezt27MBPP/2E9PR0XHfddaiqqgIA7NmzBwCwbt06FBYWWr5v7R//+AdefvllvPTSSzh06BDGjx+PSZMm4fjx41bbLVq0CPPnz8fBgwfRp08f3HbbbdDr9R22+YcffsCwYcO6tZ9mn332Ga688kqEhIRYHouOjsb48ePx9ttvW34nGzduxD333GPXewCmrlvz14kTJ9C7d2+rv71Go8GQIUOwY8cOu9+DiOTBvtM/Iuq2X375Be+99x7+8Ic/2PX8/Px8+Pv74/rrr0dgYCCSkpIwdOhQAEBNTQ1eeeUVfPfddxgxYgQAIDU1FT/++CPefPNNXHXVVd16Ly8vL/Tp08dyNc1WTU1NWLlypVX34pgxY6y2efPNNxEaGort27fj+uuvR2RkJAAgJCQEMTExHb72Sy+9hMcff9wynuyFF17A999/jxUrVuD111+3bDd//nxMnDgRAPDMM89gwIABOHHiBPr169fu6+bl5SEuLq5b+2n26aefWnWTmt1zzz145JFHsGjRInz44YdIS0vrcMza448/jieffNLqscbGRvTv39/yvfn3IggCbr75ZgQHB+PNN9+0ek58fHy3/15EJD+84kbkRF988QUCAgKg0+kwYsQIXHnllfjnP/9p12uNHTsWSUlJSE1NxR133IF3330XtbW1AICsrCzU19dj7NixCAgIsHz9+9//xsmTJ+16P0EQoFKpuvUcjUaDwYMHWz1WXFyMGTNmoE+fPggODkZwcDCqq6uRn59v8+tWVlbi7NmzGDlypNXjI0eORHZ2ttVj4vePjY21tKEjdXV1Vt2k3WnT9u3bMWnSpDY/mzhxIqqrq/HDDz9g7dq1nV5te/TRR3Hw4EGrrxkzZrS77RNPPIHdu3fjk08+ga+vr9XPfH19LXkgIuXiFTciJxo9ejRWrVoFHx8fxMXFwcfHx/IzLy8vCIJgtX1n3aiBgYHYv38/tm3bhq+//hpPP/00lixZgj179lhuAvjf//6H+Ph4q+dptdput9tgMOD48eO45JJLLG0FYNXe9trq6+vbpti76667cP78eaxYsQJJSUnQarUYMWIEGhsbu92u1q/dXnEp/h2bf9bZTRIREREoKyvrdlu+/PJLZGRkICkpqc3PvL29cccdd2Dx4sX4+eef8fHHH3f6/r1797Z6LCwsrM12//nPf7B8+XJs27YNCQkJbX5+4cIFpKWldXs/iEheeMWNyIn8/f3Ru3dvJCUlWRUUABAZGYnCwkKrxw4ePNjp63l7e+Oaa67Biy++iEOHDiEvLw/fffed5WaA/Px89O7d2+orMTGx2+1+++23UVZWhptvvtnSVgBW7e2qrWY7duzA7Nmzcd1112HAgAHQarUoKSmx2sbHx6fTOyKDgoIQFxeHH3/80erxXbt2ISMjw6Z2dGTo0KHIysrq9vM+/fTTdq+2md1zzz3Yvn07brzxRoSGhvakidi9ezfuvfdevPnmm7jsssva3ea3336zdJ0TkXLxihuRRMaMGYO///3v+Pe//40RI0bgP//5T6cfvl988QVycnJw5ZVXIjQ0FJs3b4bRaETfvn0RGBiI+fPnY+7cuTAajbjiiitQWVmJXbt2ISAgAHfeeWeH7aitrUVRURH0ej3OnDmDTZs2Yfny5fjrX/+K0aNHA4ClAFyyZAmeffZZHD9+HC+//LJN+9m7d2+88847GDZsGCorK/Hoo4+26eZLTk7Gt99+i5EjR0Kr1bZb6Dz66KNYvHixZbzYunXrcPDgQbz77rs2taMj4hsJxMyFaXV1Nc6fP4+DBw9Co9Ggf//+0Ov1+PLLLy133bYnIyMDJSUl8PPz61H7ioqK8Mc//hG33norxo8fj6KiIgCAWq22FNR5eXk4c+YMrrnmmh69FxG5P15xI5LI+PHj8dRTT+Gxxx7DJZdcgqqqKkybNq3D7UNCQrBp0yaMGTMGGRkZeOONN7BhwwYMGDAAAPC3v/0NTz/9NJYtW4aMjAyMHz8en3/+OVJSUjptx1tvvYXY2FikpaXhj3/8I7KysrBx40asXLnSso2Pjw82bNiAI0eOYMiQIXjhhRfw7LPP2rSfa9euRVlZGYYOHYo77rgDs2fPRlRUlNU2L7/8MrZu3YrExMQOC9fZs2fjkUcewSOPPIJBgwZhy5Yt+Oyzz5Cenm5TOzpy++23IysrC0ePHrV6fOjQoRg6dCj27duH9957D0OHDsV1110HANi+fTsCAgKQmZnZ6WuHh4e3KVK768iRIzh37hzefvttxMbGWr7M3dgAsGHDBowbN67dblsiUhaV0HqQDRGRh3nsscdQUVHR5k7NjsyePRt6vd6quJVKQ0MD0tPTsWHDhjY3bxCR8vCKGxF5vEWLFiEpKcnmlQcGDhyIv/71r05ulW1OnTqFRYsWsWgj8hC84kZEREQkE7ziRkRERCQTLNyIiIiIZIKFGxEREZFMsHAjIiIikgkWbkREREQywcKNiIiISCZYuBERERHJBAs3IiIiIplg4UZEREQkE/8PViZCkz6yBoUAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Analysis(rabi_S_sim).plot_results()" ] }, { "cell_type": "markdown", "id": "9fa07509", "metadata": {}, "source": [ "# 3. Nuclear Spin Rabi" ] }, { "cell_type": "markdown", "id": "945ac9b5", "metadata": {}, "source": [ "Apart from a conditional rotation of the electron spin, the carbon nuclear spin can also be excited by setting `f_pulse` in resonance with `w0_rf`.\n", "Now, we consider $\\ket{m_S=-1}\\otimes\\ket{m_{I^c}=+1/2}$ as the initial state and define an observable for the nuclear spin as\n", "$$\n", " \\hat{F}_{I^c} = \\hat{1} \\otimes \\ket{+1/2}\\bra{+1/2} .\n", "$$\n", "Experimentally, this is indirectly measured through the electron by electron-nuclear double magnetic resonance (ENDOR).\n", "To model the decoherence of the spin, we assume $\\hat{C}=\\hat{I}^c_z$ as the collapse operator, with rate $\\Gamma_2 = 0.5$ MHz.\n", "Altogether, the time-evolution of the nuclear spin within these considerations is simulated by:" ] }, { "cell_type": "code", "execution_count": 7, "id": "f2c80e53", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sys.rho0 = tensor(basis(3,2),basis(2,0))\n", "sys.observable = tensor(qeye(3),basis(2,0)*basis(2,0).dag())\n", "\n", "gamma2 = .5\n", "sys.c_ops = gamma2*tensor(qeye(3),jmat(1/2,'z'))\n", "\n", "tp_I = np.linspace(0,2.5,1000)\n", "\n", "rabi_I_sim = Rabi(\n", "\tsystem = sys,\n", "\tpulse_duration = tp_I,\n", "\th1 = h1,\n", "\tpulse_params = {'f_pulse':w0_rf}\n", "\t)\n", "\n", "rabi_I_sim.run()\n", "Analysis(rabi_I_sim).plot_results()" ] }, { "cell_type": "markdown", "id": "ee852a96", "metadata": {}, "source": [ "where the `c_ops` attribute of the `NV` instance, which was previously empty, is now set to the operator.\n", "The `pulse_shape` parameter is set to square pulses by default, which will be omitted from now on.\n", "\n", "Differently from the electron spin, the oscillation is damped by decoherence of the nuclear spin and has a much smaller Rabi frequency due to the smaller gyromagnetic ratio and thus, weaker coupling to the excitation field $\\mathbf{B}_1(t)$.\n", "The software component accurately reproduces the results presented in the reference, apart from the fact that the simulations present a much larger contrast.\n", "This can be attributed to an imperfect initialization of the spins in the experiments, which are not accounted in the simulations.\n", "Together with unconditional excitations, these two rotations form the computational basis for arbitrary quantum gates with the NV-$^{13}$C pair, which will be further explored in the subsequent tutorials." ] } ], "metadata": { "kernelspec": { "display_name": "quaccatoo-env", "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": "3.13.3" } }, "nbformat": 4, "nbformat_minor": 5 }