{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# TLS description of optical absorption" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we present a two level system (TLS) based description of optical absorption. We discuss the equation\n", "of motion of the system (EQM) in the rotating frame (RF) and we derive the _Bloch vector_ representation of the model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Hamiltonian of the system is written as\n", "$$\n", "H_0 = -\\frac{1}{2}\\omega_0 \\sigma_z \\, , \n", "$$\n", "where $\\sigma_z$ is the Pauli matrix. $H_0$ is diagonal in the chosen representation with a energy shift \n", "between the two levels given by $\\omega_0$. The eigenstates are represented as\n", "$$\n", "|1\\rangle = \\left(\\begin{array}{c}\n", "1\\\\\n", "0\\\\\n", "\\end{array} \\right) \\, , \\quad\n", "|2\\rangle = \\left(\\begin{array}{c}\n", "0\\\\\n", "1\\\\\n", "\\end{array} \\right) \\, .\n", "$$\n", "Note that in this notation $|1\\rangle$ describes the GS of the system, while $|2\\rangle$ is the excited state." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The interaction of the optical pump with the system is described by an Hamiltonian $H^I$ that has only non-diagonal \n", "non vanishing matrix elements. \n", "\n", "The equation of motion (EQM) of the density matrix (DM) are expressed by the Liouville equation\n", "$$\n", "i \\dot{\\rho} = \\left[H_0+H^I,\\rho\\right]\n", "$$\n", "and we can explicitly write the associated equations for the matrix elements of the DM in the chosen basis using\n", "the structure of both the Hamitonian defined above. We obtain:\n", "$$\n", "i \\dot{\\rho}_{11} = H^I_{12}\\rho_{21} - H^I_{21}\\rho_{12} \\\\\n", "i \\dot{\\rho}_{22} = H^I_{21}\\rho_{12} - H^I_{12}\\rho_{21} \\\\\n", "i \\dot{\\rho}_{12} = -\\omega_0\\rho_{12} + H^I_{12}(\\rho_{22}-\\rho_{11}) \\\\\n", "i \\dot{\\rho}_{21} = \\omega_0\\rho_{21} - H^I_{21}(\\rho_{22}-\\rho_{11})\n", "$$\n", "where $H^I_{12} = \\langle 1|H^I|2\\rangle$ and $H^I_{21} = \\langle 2|H^I|1\\rangle$, furthermore\n", "$H^I_{12} = H^{I*}_{21}$ since $H^I$ is hermitian. These equations imply that $\\rho_{21}$ is the complex\n", "conjugate of $\\rho_{12}$ and that $\\rho_{11}+\\rho_{22}$ is constant, that is the conservation of the charge\n", "(in what follows the total charge is assumed to be equal to 1).\n", "\n", "It is convenient to describe the system in terms of _polarization_ and of the _inversion_ variables defined as\n", "$$\n", "p = \\rho_{12} \\, , \\quad I=\\rho_{11}-\\rho_{22} \\, , \\quad H_I = H^{I}_{12}\n", "$$\n", "In terms of these variables the EQM for the density matrix read\n", "$$\n", "\\dot{p} = i\\omega_0 p +i H_I I \\\\\n", "\\dot{I} = -2i\\left(H_Ip^*-H_I^*p\\right)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interaction Hamiltonian and rotating wave approximation (RWA)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider an interaction between the system and the optical pump described by a dipole interaction, that is\n", "$$\n", "H^I = - \\mathbf{\\mu}\\cdot\\mathbf{E}(t)\n", "$$\n", "where $\\mathbf{\\mu}$ is the dipole operator. We choose a linear polarized electric field (say along the $x$ axis).\n", "The time dependece of the field is described by a monocromatic wave of energy $\\omega$ times a real slow enevelope function $E_0(t)$.\n", "Due to this assumption the matrix element $H^I_{12}$ can be expressed as\n", "$$\n", "H^I_{12} = - \\mu^{x}_{12} E_0(t) e^{-\\frac{(t-t_0)^2}{2w^2}}sin(\\omega t) \\doteq - \\Omega(t) sin(\\omega t)\n", "$$\n", "where $\\mu^{x}_{12}$ is matrix element of the component of the dipole parallel to $\\mathbf{E}$ evaluated between the states 1 and 2 and\n", "we have introduced the (time-dependent) _Rabi frequency_ $\\Omega(t)$:\n", "$$\n", "\\Omega(t) = \\Omega_0e^{-\\frac{(t-t_0)^2}{2w^2}} \\, , \\, \\mathrm{where} \\,\\,\n", "\\Omega_0 = \\mu^{x}_{12}E_0\n", "$$\n", "here $\\Omega_0$ is the usual (constant) Rabi frequency (we have set $\\hbar=1$ in this analysis). Note that since $\\mu^{x}_{12}$ is a complex\n", "quantity so it is the Rabi frequency and we introduce its real and imaginary parts $\\Omega_R(t)$ and $\\Omega_I(t)$ (as well as the associated constant factors $\\Omega^0_R$ and $\\Omega^0_I$) for the susequent analysis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The RWA can be used if we are interested in probing the system with energy of the pump not very different from the energy gap of the system, that is if we introduce the energy shift $\\delta$ as\n", "$$\n", "\\omega = \\omega_0 + \\delta\n", "$$\n", "where the condition $\\delta \\ll \\omega_0$ is satisfied. \n", "This fact allows us to introduce the rotating wave approximation. To understand this point consider that, for instance, the \n", "generic solution for $p$ can be written as\n", "$$\n", "p = p_0e^{i\\omega_0t} -i e^{i\\omega_0t}\\int_{0}^{t}dt'e^{-i\\omega_0t'}\\Omega(t')sin(\\omega t')\n", "I(t')\n", "$$\n", "\n", "Due to the presence of the factor $e^{-i\\omega_0 t'}$ in the integral the sine can be splitted into complex exponentials and only the\n", "addend $e^{i\\omega t'}$ gives relevant contributions since the fast oscillating terms cancel. So the interaction matrix element in the RWA\n", "reads\n", "$$\n", "H_I = \\frac{i}{2} \\Omega(t)e^{i\\omega t}\n", "$$\n", "Accordingly the EQM are expressed as\n", "$$\n", "\\dot{p} = i\\omega_0 p -\\frac{1}{2}\\Omega e^{i\\omega t} I \\\\\n", "\\dot{I} = \\Omega e^{i\\omega t}p^* +\\Omega^* e^{-i\\omega t}p\n", "$$\n", "Note that this argument is usually discussed and justified for __constant__ Rabi frequency, however if the envelope function $E_0(t)$ is slow we can split the previous integral into various terms in which the frequency is constant and apply the same argument to all the addends." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the RWA is adopted it is possible to discuss the physics of the system in the rotating frame (RF), where the fast oscillating terms are absent. The change of variables to the RF is\n", "$$\n", "p' = e^{-i\\omega t}p \\, , \\quad I' = I\n", "$$\n", "In this frame the EQM are\n", "$$\n", "\\dot{p}' = -i\\delta p' -\\frac{1}{2}\\Omega I' \\\\\n", "\\dot{I}' = \\Omega p'^* +\\Omega^* p'\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bloch vector representation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Bloch vector representation is a change of variables from the polarization and inversion\n", "to the 3-dimensional vector $u$ defined as\n", "$$\n", "u_1 = 2Re(p) \\, , \\quad u_2 = -2Im(p) \\, \\quad I = u_3\n", "$$\n", "This formulation is particularly useful for computational reason since the components of the\n", "Bloch vector are real quantities and can be easily managed for numerical integration of the EQM.\n", "\n", "The EQM in this basis read\n", "$$\n", "\\dot{u}_1 = -\\delta u_2 - \\Omega_R u_3\\\\\n", "\\dot{u}_2 = \\delta u_1 + \\Omega_I u_3 \\\\\n", "\\dot{u}_3 = \\Omega_R u_1-\\Omega_I u_2\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Inclusion of the coherence dephasing time" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The polarization-inversion or equivalently the Bloch equation description allows us to add an explicit dephasing time for the coherence.\n", "\n", "This is done by adding the term $-\\eta p$ in the EQM for the polarization. In the Bloch vector notation the complete equations read\n", "$$\n", "\\dot{u}_1 = -\\delta u_2 - \\Omega_R u_3 -\\eta u_1\\\\\n", "\\dot{u}_2 = \\delta u_1 + \\Omega_I u_3 -\\eta u_2\\\\\n", "\\dot{u}_3 = \\Omega_R u_1-\\Omega_I u_2\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Representation of the polarization and of the number of carriers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is useful to express some observables like the polarization or the density of charge in the excited states in this formalism. \n", "These quantities can be compared with the results provided by the abinitio real time simulations.\n", "\n", "The density of charge in the excited state is given by $\\rho_{22}$ that, using the condition $\\rho_{11}+\\rho_{22} = 1$\n", "can be expressed as\n", "$$\n", "\\rho_{11} = \\frac{1-I}{2}\n", "$$\n", "\n", "For what concerns the polarization, assuming that the only non vanishing matrix elements of the dipole operator (say $x$ component) are the non diagonal ones we have\n", "$$\n", "P = p x_{12}^* + p^* x_{12}\n", "$$\n", "that can be expressed in the terms of the components of the Bloch vector as\n", "$$\n", "P = u_1 Re(x_{21}) + u_2 Im(x_{21})\n", "$$\n", "So we observe that the elemnts $u_1$ and $u_2$ are responsible for the behavior of the polarization.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Complex rotation to real dipoles and Rabi coupling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is possible to reabsorb the complex phase of the dipole $d=d_{12}$, and consequently of the\n", "Rabi coupling, since $\\Omega_0 = Ad/\\hbar$. This procedure preserves the value of the observable\n", "(the mean on the k point index is understood)\n", "$$\n", "\\mu = Tr(\\hat{\\rho}\\hat{d}) = pd^*+p^*d\n", "$$\n", "Indeed we can express the complex dipole as $e^{i\\alpha}|d|$ and if we define complex rotated polarization as\n", "$$\n", "\\hat{p} = e^{-i\\alpha}p \\, , \\,\\, \\mathrm{where} \\,\\,\n", "\\alpha = atan\\left(\\frac{Im(d)}{Re(d)}\\right)\n", "$$\n", "The EQM in terms of these variables read \n", "$$\n", "\\dot{\\hat{p}} = -i\\delta\\hat{p} -\\frac{1}{2}\\Omega I \\\\\n", "\\dot{I} = \\Omega\\left(\\hat{p} +\\hat{p}^*\\right)\n", "$$\n", "where in these equations the envelope function $\\Omega(t)$ is real and depends on the module of the\n", "Rabi coupling $|\\Omega_0|$.\n", "The observable polarization in this basis is expressed as\n", "$$\n", "\\mu = |d|(\\hat{p}+\\hat{p}^*)\n", "$$\n", "So in this basis we deal with EQM with real parameters that provide equivalent results for the observable.\n", "\n", "The equations for the Bloch vector in this basis read\n", "$$\n", "\\dot{u}_1 = -\\delta u_2 - \\Omega u_3\\\\\n", "\\dot{u}_2 = \\delta u_1 \\\\\n", "\\dot{u}_3 = \\Omega u_1\n", "$$\n", "while the observable polarization is computed as $\\mu=|d|u_1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analytic solution for constant field (to be updated...)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We seek for the general solution of the EQM in the RF for a constant field. \n", "We start from a guess for $x$ of the form\n", "$$\n", "x(t) = Asin(\\Delta t) + Bcos(\\Delta t) + C \\,\\,\\, , with \\quad\n", "\\Delta = \\sqrt{\\delta^2+|\\Omega|^2}\n", "$$\n", "the constants $A,B,C$ will be determined imposing the boundary conditions. Plugging this guess in the EQM \n", "for $x$ we obtain\n", "$$\n", "y(t) = \\frac{B\\Delta}{\\delta}sin(\\Delta t) - \\frac{A\\Delta}{\\delta}cos(\\Delta t) \n", "$$\n", "and pluggin this expression in the EQM for $y$ allows us to derive the expression of $z$ \n", "$$\n", "z(t) = \\frac{A\\Omega_r}{\\delta}sin(\\Delta t) +\\frac{B|\\Omega|}{\\delta}cos(\\Delta t) -\\frac{C\\delta}{|\\Omega|}\n", "$$\n", "pluggin this expression in the EQM for $z$ we obtain $-|\\Omega| y(t)$ as expected, so the guess is correct." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The constants are determined through the boundary conditions\n", "$$\n", "x_0 = B+C \\, , \\quad\n", "y_0 = - \\frac{A\\Delta}{\\delta} \\, , \\quad\n", "z_0 = \\frac{B|\\Omega|}{\\delta} -\\frac{C\\delta}{|\\Omega|}\n", "$$\n", "and their solution reads\n", "$$\n", "A = -\\frac{\\delta}{\\Delta}y_0 \\, , \\quad\n", "B = \\frac{\\delta^2}{\\Delta^2}x_0 + \\frac{\\delta|\\Omega|}{\\Delta^2}z_0 \\, , \\quad\n", "C = \\frac{|\\Omega|^2}{\\Delta^2}x_0 - \\frac{\\delta|\\Omega|}{\\Delta^2}z_0\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The general solution reads\n", "$$\n", "x(t) = -\\frac{\\delta}{\\Delta}y_0 sin(\\Delta t) + \n", "\\left(\\frac{\\delta^2}{\\Delta^2}x_0 + \\frac{\\delta|\\Omega|}{\\Delta^2}z_0\\right)cos(\\Delta t) + \n", "\\left( \\frac{|\\Omega|^2}{\\Delta^2}x_0 - \\frac{\\delta|\\Omega|}{\\Delta^2}z_0 \\right)\\\\\n", "y(t) = y_0cos(\\Delta t) + \n", "\\left( \\frac{\\delta}{\\Delta}x_0 + \\frac{|\\Omega|}{\\Delta}z_0\\right) sin(\\Delta t) \\\\\n", "z(t) = - \\frac{|\\Omega|}{\\Delta}y_0sin(\\Delta t) +\n", "\\left( \\frac{\\delta|\\Omega|}{\\Delta^2}x_0 + \\frac{|\\Omega|^2}{\\Delta^2}z_0\\right)cos(\\Delta t) +\n", "\\left( \\frac{\\delta^2}{\\Delta^2}z_0 - \\frac{\\delta|\\Omega|}{\\Delta^2}x_0 \\right)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution can be expressed in terms of the Bloch vector in the rotating frame by using the linear relations between the\n", "$u'_i$ and the $x_i$ components defined above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analytic solution for time-dependent field (at $\\delta=0)$ (to be updated...)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For $\\delta=0$ the solution can be parametrized like in the time-independent case. The only modification\n", "is that the argument of the sine and cosine function becomes \n", "$$\n", "\\theta(t) = \\int_0^t dt' |\\Omega(t')|\n", "$$\n", "We observe that $\\dot{\\theta}(t) = |\\Omega(t)|$ and so the $x$ vector written in terms of $\\theta(t)$ satisfy the correct EQM with\n", "a time-dependent Rabi frequency\n", "$$\n", "x(t) = x_0 \\\\\n", "y(t) = y_0cos(\\theta(t)) + z_0sin(\\theta(t)) \\\\\n", "z(t) = - y_0sin(\\theta(t)) + z_0cos(\\theta(t))\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the basis of these equations we see that the area of the module of the pulse is the object that realizes the $\\pi/2$ or the $\\pi$ conditions:\n", " * $\\theta=\\pi/2$ : the system initially in the ground state $u^0=(0,0,-1)$ reach the state with $u_2=-1$ and $u_3=0$, that correspond to an occupation level of the excited state equal to $1/2$.\n", " * $\\theta=\\pi$ : if $x_0=0$ the Bloch vector changes sign. If the system starts from the ground state the occupation level of the excited state is maximum.\n", " \n", "Since $\\Omega(t)$ is parametrized as\n", "$$\n", "\\Omega(t) = \\Omega_0 e^{-\\frac{1}{2}\\left(\\frac{t-t_0}{w}\\right)^2}\n", "$$\n", "the $n\\pi$ condition becomes\n", "$$\n", "\\sqrt{2}w|\\Omega_0| = n\\sqrt{\\pi}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical solutions for arbitrary field and detuning (to be updated...)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# useful to autoreload the module without restarting the kernel\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from mppi.Utilities import Constants as C\n", "from mppi.Models import TwoLevelSystems as TLS\n", "from mppi.Models import GaussianPulse as G\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We present various example to discuss the features of the dynamics of the TLS. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dynamics for a single gaussian pulse" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the parameters for the numerical analysis and show the results" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "T = 600 #fs\n", "tstep = int(1e4)\n", "dipole = 1 +1j # the weight of the real and imaginary part can be changed\n", "time = np.linspace(0,T,tstep)\n", "\n", "fwhm = 100 # fs\n", "energy = 1.5 # pulse energy in eV\n", "h_red = C.Planck_reduced_ev_ps*1e3 # hbar in eV*fs\n", "omega = energy/h_red # angular frequency of the pulse" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time unit: fs\n", "the width parameter of the pulse is 42.466090014400955 fs\n", "Rabi coupling (fs^-1): (0.010434524642511517+0.010434524642511517j)\n", "Rabi coupling (module) (fs^-1): 0.014756646266356059\n", "field amplitude (V/m): 129788828.49284193\n", "field intensity (kW/cm^2) : 4471405.517491325\n" ] }, { "data": { "text/plain": [ "{'Omega0': (0.010434524642511517+0.010434524642511517j),\n", " 'Omega0_abs': 0.014756646266356059,\n", " 'field_amplitude': 129788828.49284193,\n", " 'intensity': 4471405.517491325}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta = 0.5*np.pi # set the area of the pulse\n", "pars = TLS.pulseParametersFromTheta(dipole,theta,fwhm=fwhm)\n", "pars" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time unit: fs - energy unit: eV\n", "period of the oscillations 2.757111798154881 fs\n", "width of the pulse 42.466090014400955 fs\n", "fwhm of the pulse 100 fs\n" ] } ], "source": [ "pulse = G.gaussianPulse(time,energy=energy,amplitude=pars['field_amplitude'],fwhm=fwhm)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(time,pulse)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "Omega = lambda t : G.gaussianPulse(t,energy=energy,amplitude=pars['Omega0_abs'],fwhm=fwhm,envelope_only=True,verbose=False)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "uprime0 = np.array([0.,0.,1.])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "delta = 30 # in meV\n", "delta_fsm1 = 1e-3*delta/h_red # in fs^-1" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "uprime = TLS.solveBlochEq(uprime0,time,Omega,mu12=dipole,delta=delta_fsm1)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,7))\n", "plt.title('Carriers')\n", "plt.plot(time,(1+uprime[2])/2,label='carriers')\n", "plt.legend()\n", "plt.show()\n", "\n", "plt.figure(figsize=(10,7))\n", "plt.plot(time,uprime[0],label=\"u'1\")\n", "plt.plot(time,uprime[1],label=\"u'2\")\n", "plt.title(\"u'1 and u'2\")\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "u = TLS.convertToRotatingFrame(omega,time,uprime,invert=True)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,7))\n", "plt.plot(time,u[0],label='u1')\n", "plt.plot(time,u[1],label='u2')\n", "plt.title('u1 and u2 in the original frame')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Global response of many $k$-points to a gaussian pulse. Emergence of the FID." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider the global response of the system with a large samplings of $k$-points.\n", "\n", "To each point there is an associated detuning and we assume a uniform distribution in a given energy\n", "range." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "import random as rand" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "numk = 1000\n", "delta_range = 40 # meV\n", "deltas = [0.] # the first kpoint has zero detuning\n", "for i in range(numk-1):\n", " deltas.append(delta_range*(rand.random()-0.5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We set the properties of the system and of the pulse. Here we assume for symplicity that all k the points have\n", "the same value of the transition dipole" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "T = 4000 #fs\n", "tstep = int(4e3)\n", "dipole = 1 +1j # the weight of the real and imaginary part can be changed\n", "time = np.linspace(0,T,tstep)\n", "\n", "fwhm = 100 # fs\n", "energy = 1.5 # pulse energy in eV\n", "omega = energy/(C.Planck_reduced_ev_ps*1e3) # angular frequency of the pulse\n", "\n", "h_red = C.Planck_reduced_ev_ps*1e3 # hbar in eV*fs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We choose a field that realizes the $\\pi/2$ condition (for the points with zero detuning)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time unit: fs\n", "the width parameter of the pulse is 42.466090014400955 fs\n", "Rabi coupling (fs^-1): (0.010434524642511517+0.010434524642511517j)\n", "Rabi coupling (module) (fs^-1): 0.014756646266356059\n", "field amplitude (V/m): 129788828.49284193\n", "field intensity (kW/cm^2) : 4471405.517491325\n" ] }, { "data": { "text/plain": [ "{'Omega0': (0.010434524642511517+0.010434524642511517j),\n", " 'Omega0_abs': 0.014756646266356059,\n", " 'field_amplitude': 129788828.49284193,\n", " 'intensity': 4471405.517491325}" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta1= 0.5*np.pi # set the area of the pulse\n", "pars1 = TLS.pulseParametersFromTheta(dipole,theta1,fwhm=fwhm)\n", "pars1" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "Omega = lambda t : G.gaussianPulse(t,energy=energy,amplitude=pars1['Omega0_abs'],fwhm=fwhm,envelope_only=True,verbose=False)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "#plt.plot(time,Omega(time))" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "uprime0 = np.array([0.,0.,1.]) # set the system in the GS before the pulse" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "uprime = np.zeros([3,len(time),numk])\n", "for k in range(numk):\n", " delta_fsm1 = 1e-3*deltas[k]/h_red\n", " uprime[:,:,k] = TLS.solveBlochEq(uprime0,time,Omega,mu12=dipole,delta=delta_fsm1)\n", "uprime_global = np.mean(uprime,axis=2)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "k = 3\n", "plt.plot(time,uprime[0,:,k],label=\"u'1\")\n", "plt.plot(time,uprime[1,:,k],label=\"u'2\")\n", "plt.plot(time,0.5*(1+uprime[2,:,k]),label=\"carriers\")\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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hMKbWAvnM4kwA2ia0tRtUsyUiIhL2FGyFwl0CxlNjZmtH0Q4A2sW3sxtUsyUiIhL2FGyFwh841VCz5c9spcen2w2xyVBauCeOTERERFooBVuhKPUvQl1DsFWUSWpsKtGR0XZDTBKUFYLXu4cOUERERFoaBVuh8Be71zCMmFmcSXpC+u4N/v1UtyUiIhK2FGyFonwYsYZgqyhzd70WQEyivVSwJSIiErYUbIXCHzTVNIxYnLl7JiLsru1SkbyIiEjYUrAVCv8wYoDMlsfrYVfxLtrGVwi2yocR1WtLREQkXCnYCkV5Zqt6sJXtysZjPFUyW779lNkSEREJWwq2QuGqeTZiZpGvoWnAzJaCLRERkXClYCsUtRTI7yzeCVTosQWq2RIREREFWyEpLYDoBIiIrHZTjisHgLS4tN0bVbMlIiIS9hRshcKVX2Pbh+ySbABaxbbavVE1WyIiImFPwVYoSgtqbGia48oh0okkueJSPjGJgKOaLRERkTCmYCsUroIae2xlu7JpFduKCKfCS+o4WoxaREQkzCnYCoUrv8ZFqHNKckiNTa1+Q2ySarZERETCmIKtUJTm1zqM2DqudfUblNkSEREJawq2QuEqqLFAPsdVW2ZLwZaIiEi4UrAViloK5LNLsivPRPRTZktERCSsKdgKRQ2ZLWOMzWzFBcpsJSuzJSIiEsYUbAXL4wZ3McSmVLspvywfj/HQOrZ19fvFJO1e5kdERETCjoKtYPlnFAYYRswpyQGoIbOlmi0REZFw1ijBluM4xzmOs8JxnNWO49wS4PYbHcdZ6jjOQsdxvnccp3tjPO8eVcu6iP6lemrObCnYEhERCVcNDrYcx4kEngGOBwYB5zqOM6jKbvOBUcaYocCHwEMNfd49zp+dCpTZ8gVbgWcjJoPHBZ6yJjw4ERERaakaI7M1BlhtjFlrjCkF3gVOqbiDMeZHY0yR7+oMoEsjPO+eVZ7Zqt7U1L8uYo2ZLVDdloiISJhqjGCrM7CpwvUM37aaXAp81QjPu2fVVrPlH0YM1NTUv39pYdMcl4iIiLRoUXvyyRzH+TMwCjishtuvAK4A6Nat2x48siD4M1MB1kbMLskmyokiKTpADy5/ZktF8iIiImGpMTJbm4GuFa538W2rxHGco4DbgZONMa5AD2SMedEYM8oYM6pt27aNcGiNqI4C+dZxrXEcp/r9/MGZiuRFRETCUmMEW7OBvo7j9HQcJwY4B/i84g6O4wwHXsAGWjsa4Tn3vPIC+eqZrRxXTuB6LaiQ2VLNloiISDhqcLBljHED1wFTgWXA+8aYJY7j3O04zsm+3R4GkoAPHMf5w3Gcz2t4uJbLP4wYILOVXZIduMcW7K7ZUmZLREQkLDVKzZYxZgowpcq2Oyr8fFRjPE+zKi2AiCiIiq12U44rh96tewe+n2q2REREwpo6yAerJNcu1ROgLqvWYUTVbImIiIQ1BVvBKsmDuFbVNnuNVzVbIiIiUiMFW8Fy5UFcgEWoS/PxGm/NNVtRsXb4UZktERGRsKRgK1gleXYYsYpa10UEO+wYk6iaLRERkTClYCtYrsDDiP6lemrMbIFd4keZLRERkbCkYCtY9c1sgW3/oJotERGRsKRgK1g11GzVugi1X0ySMlsiIiJhSsFWMLxe29Q0wDCiP7NV6zBibJJqtkRERMKUgq1guPIAE3AYMduVTXRENAlRCTXfX5ktERGRsKVgKxiuPHsZYBgx15VLamxq4EWo/WKTldkSEREJUwq2glHiC7YCZbZKsmkd17r2+8ck7V5bUURERMKKgq1g1JLZqrV7vJ+/ZsuYxj82ERERadEUbAWjPLMVuM9WncFWTBJ43eB2Nf6xiYiISIumYCsY5ZmtwLMRa52JCLsXo1bdloiISNhRsBWMklx7WWUY0eP1kFeaF1xmC1S3JSIiEoYUbAXDFbhAvs5FqP1ifcGWMlsiIiJhR8FWMEryIDIGouMqbc52BdE9HipkthRsiYiIhBsFW8Eoya3/uoigmi0REZEwpmArGHWtixhMny1QsCUiIhKGFGwFoySv1sxWamyQNVsaRhQREQk7CraCUVdmK9iarVoyWzlFpZR5vPU9QhEREWmhFGwFozgH4qtnr3JcOcRGxhIfFV/7/f01WzVktr5cuJUR93zLmc9Px+X2NPBgRUREpCVRsBWM4uyAwVZ2STapcXUsQg0QGQ2RsVBavc+Wx2u498ulREVGsGBTDh/N3dxYRy0iIiItgIKtuhhTc7Dlyq67XssvNilgZmvuhmy25pbwyFnD6N8+mY/mZTT0iEVERKQFUbBVl9IC8JZBfFq1m3JKgliE2i8mKWDN1i+rMomMcDiif1smDOnI3A3ZZBeWNvCgRUREpKVQsFWXYlsEX1Nmq862D36xyQEzW39syqFf+2SS46I5qE8bAGauy6rv0YqIiEgLo2CrLrUFWyXZpMVVz3gFFJNUrWbLGMPCjFz272oXuB7apTXx0ZHMWLurQYcsIiIiLYeCrbrUEGyVecooKCsIfhgxQM3WltwScovL2K+TDbZioiLYr1MKizfnNvSoRUREpIVQsFWXIt+QXpVgK+iGpn4BarbWZRYC0LttUvm2wZ1bsXRrHh6vqd/xioiISIuiYKsu/sxWQuXhwqwSG4SlxtV/NuK6nfZ6r7aJ5dsGdUqhqNTD+l2F9TxgERERaUkUbNXFH2xVKYQvz2wFG2zFJFfLbK3dWUhCTCTtkmPLt+3XyXaqX7Ilr16HKyIiIi2Lgq26FGdDdAJEx1XanO0Kcqkev1jfMKLZPTy4fmchPdokVmqK2rttEhEOrN6hdRRFRET2BQq26lJL93gIJbOVBMYLZUXlmzbsKqJHekKl3eKiI+malsCaTAVbIiIi+wIFW3WpIdjKKckBoFVsq+AeJ8ZXl+Wr2zLGsDW3hE6tqq+r2LttEmuU2RIREdknKNiqSy1L9STHJBMdER3c4/gXo/bVbeUVuyku89ChVVy1XXu3TWTdzkK8mpEoIiKy11OwVZeiXTVmtoJuaAp2GBHAZRubbs0rBqgh2ErC5fayOac49OMVERGRFkXBVl0KMyGpXbXNWa6s4IvjwRbIQ3lma2tuCQAdAwVb7ey+qtsSERHZ+ynYqo2nzA4jJlYPtnJKcoJvaAq29QOU12xt9wVbHQLUbPVMt/Vd63aq15aIiMjeTsFWbQp32svE9Go37SrZRVp8CMOIATJbjkOlHlt+bRJjSIiJZGNWUbXbREREZO+iYKs2hZn2MrFtpc0er4eskizaxLUJ/rGq1Gxtyy2hbVIs0ZHV3wLHceiWlsAmBVsiIiJ7PQVbtakh2Mp2ZeM1XtLjq2e8alQls7UtryRgcbxft7QEZbZERET2AQq2auMfRqxSIL+reBdAaMGWP7NVauuwdha4SE+qPoTo5w+2jFH7BxERkb2Zgq3aFO6wl1VqtuoVbEVE2mV/fMOIWYWltEmMqXH3bm0SKCnzklngCu2YRUREpEVRsFWbwkyIjIHYlEqbd5bYjFdIwRbY7FZpAcYYdhWWkpZUc7DVNc0u46O6LRERkb2bgq3aFO60bR8qLBQNsLO4nsFWbBK4CihwuSl1e2vPbPmCLdVtiYiI7N0UbNWmYHvAtg87i3cSHxVPQnRCgDvVwpfZyiosBaBNYs01W51bx+M4sHFXLV3kS3Lh54dh7iTwekM7FhEREdkjopr7AFq0vK2Q2qPa5p3FO0PPaoFdH9FVwC5fsFXbMGJcdCQdUuJqzmx5PfDWWbBppr2+fQlMeDj0YxIREZEmpcxWbfI2Q0qnapt3Fe+qX7AVkwSl+ewqsMFWei2ZLbB1WzXWbC141wZapz4PB1wFs16EzfNCPyYRERFpUgq2alJaBCU5kNKx2k2ZxZn1zGzZmq2sQjvDsLbMFti6rQ1ZNSzZM/N5aDcIhp0DR9xuF8v+5dHQj0lERESalIKtmuRvtZcpnSttNsawvXA77RPah/6YvpqtXeU1W3UHW9vzXJSUeSrfsHM1bFsIIy60xftxKTDiAljxFeRvD/24REREpMko2KpJ3mZ7WWUYMb8snyJ3ER0SO4T+mP6arYJSEmMiiYuOrHX3rml2kerNOVWK5Fd+bS/7H7972/DzwXhg0QehH5eIiIg0GQVbNcnbYi+TKwdbWwtsxqtewVZMEpQVkl1QUucQItTS/mHVVGg7EFK7796W3hfaD4HlX4Z+XCIiItJkFGzVpDyzVblma3uRHaarX2bLLtlTUJBLWh3F8QBdU22wlVEx2HKXwsaZ0Ht89TsMmACbZuxeZkhEZG/mLlVbG9knKNiqSd4WiGsNMYmVNvszWx0TqxfO18m3PmJpYS6pCdF17t42OZbYqIjKma3ti8Djgq6jq99hwAlgvLuHGRtTSZ5tNyEi0tQ2z4PXT4L7OsB/OsInV0FBZnMflUi9KdiqSda6gD22thVtI8qJok1cm9AfMzYZAE9JPq3i6w62HMfxtX+oULOVMddedgkQbHUYCkkdYM2PoR9bTXIz4LUJ8EBXeKQv/PF24z224PUaflu9kw/nZrBxl1YLEGHRh/DqsZC5Ag66AfY/DxZ/BC+Ph5yNzX10IvWipqY1yVoLnYZX27y1cCvtEtoRGVF7cXtAvsyWN8hgC6Brajybsiv8Ed48xwZUVWZJAnZmYq/DYM0PYEy1ZYb8Sso8xEZF4NRwe7niHJh0AhRlwWE3w/pf4dOrweu2sx+lQbbllnDlm3NYkJELQIQD/zxuAFcd1ruZj0ykmaz+Dj6+ArqNg4lvQkKa3T78PHjzNHjnXLjsO4iOb97jFAmRMluBeMogdxOk9ax209aCrfWr14Lymi1cBUEHW93SEioPI2bMgS6jagyk6HmYXUB7x9JqN5W6vdzy0UIG3fE1Bz/4IzPX7qr9yb++BXI2wXkfwhG3wfmfQq8jYMo/YMfyoI5fAssuLOXsF6azekcBj5w1jG/+dijHD+nIA18t543p6/fYcZR5vLw/ZxM3fbCAB75azvqdNfR1E2lquZvhg4uh/SD407u7Ay2AziPhjFdg+2L4/u7mO8YWyuX2MGPtLj6el8EPy7eXLwknLYcyW4HkbrLZm7Re1W7amL+RgzsfXL/H9WW2EigOPrOVlkB+iZvcojJaRZVC1hrbyLQmvQ6zl2unQfv9Kt304NfLeXf2Js4d05WZ67K4eNJsvrzhEHqmJ1Z/nC1/wIJ34OAbodsBdltUDJz+IjwzBr76J1zwWc1BX0tVlGVfm7hW0PNQiAzufWhMxhj++t4fbMsr4Z3LxzKyeyoAT54znJJSD/dOXsZBfdLp3TapSY8jr6SMK96Yw4y1WaQnxZJbXMqrv67j/tOHcMbILk363CLVfPVP+0X37DfLSy4q6Xs0jLoUZr5gW920H7Tnj7GFMcbw3uxNPPrtSjLzXeXbIyMcjh7Ynr8e3ZcBHVKa8QjFT5mtQLLW2cvUypmtwrJCdhbvpHtK9wB3CoLvAySRElKCDLa6pFZo/5C5wm5sN7DmO7TqAm36wNqfKm1etT2f135bx3kHdOP+04fy9mVjiYxwuO3jRRhjqj/OtPvtBIGD/1p5e1I7OOwWWPcTrPo2qHNoMZZ+Bv8dCh9eDP87HV48ArI37PHD+Hbpdn5amcltxw8oD7TAfkDef8YQ4qIjuPPzJU16DB6v4YZ35jN3QzaPnDWM2bcfyW83j2d0z1T+/sECPvtjc5M+v0gly76A5ZPhiFsDjiiUG/9/9nP0m/8DYFNWEZe/MYdBd3zN+Een8cWCLXvogJufx2u46YOF3PLxInq2SeSF80fy402H8/6V47js4J78vmYnE574hX9/tpiiUndzH27YU7AVSNZae1kls7UxzxZndkvuVr/H9WW2kpzgM1v+XlubsotgxzK7sV0d3+h6Hmbrqzxl5ZuenbaGhJgo/n5MfwA6tIrj70f3Y/raXUyvOpyYs9HOaDzgKpsBqmr0pdC6G/z8kK0N2xus+QE+vATaDYBLv7NDErmb4PUTbbZrDyl1e/nPlGX0bZfEn8dWD9rbJcdx3fg+/LJqJ3PWN91xvTVzA9NWZHLnyftx5sguOI5Du5Q4XrlwNAf0TOMfHy5k+ba8Jnt+kXIlubY0ocMQGHtt7fsmpMEhN8Ka79m06GdOe/Y3pq/ZxRkjupAYE8X178xn0m/r9sxxNyNjDLd+vJCP5mXwlyP78u4VYzl2vw70TE9kTM80bp0wkJ//eQTnj+3OGzM2MOGJX5i7Yc99zkl1CrYCyVwBMcmQXLk2a0O+zYLUP7Nlg61ESkIYRrSFoBuzimwdVlRcwFmSlfQ6DMoKYbOduZhbVMaURVs5bXhn0iosEXTOmG60S47luWlrKt9/wXv2cv8/BX78yGg48AbImA0bfg/qPJpVcbadOp7eD/78sW2bMeRM+3P+Nvjsuj0WNL45YwPrdxVx+wkDiYoM/Ov357HdSU+K4akfVjfJMewqcPHI1BUc0jedP42p/MUhLjqSZ84bQUpcNH9554/qS0XJXsft8bJyez6LN+e2zAzHd3dBwXY46UmIDKKyZdQlmLjWbPz0HsDh02sP4p5TB/PJNQdyzKD23D15KQs25TT1UTert2Zu5P05GVw/vg9/O7ofERHVyzlaJ8Rw1ymDeefysbi9hrOen85/pizT73QzUbAVyPYltt6pSj3ShlwbbHVN7lq/x41OwOCQGEJmKzkumtSEaDZl+TJb6f2grpmQPQ4BnPKhxM8WbMbl9jJxdOXjjouO5Pyx3fll1U427PIVRhtja7W6H1y5Q31Vw/8MCenw6+NBnUez+uFe2+j11OfsOpJ+XUbaYYkVX8LKqU1+GNmFpTzx3UoO7deWw/u3q3G/hJgoLhjXg59WZrI2s6DRj+P5n9ZQWOrh3ycNCjgjNT0plofPGsqK7fnVA3HZaxS43Dz2zQpG3/cdxzz+Myc+9Ssj7vmW2z5ZRE5RCymg3jgD5rwCB1wNnUcEd5/YZKalnslBnlm8dHwCfdrZL7FRkRE8cvYw2qfEcfNHC/F495Kse4hWbc/n7i+Wcnj/tvztqH517j+2Vxu+/uuhTBzdjRd/Xstx//257slR0ugUbFVlzO5gq4pVOavonNSZhOiE+j224+COSiAphMwW2CL5jf5gq64hRLCp9o5DYd3PAExeuJX+7ZMZ3Ln6kOBZo7oSGeHw7uxNdkPGnLqL8MFOvT7gKlj97e7hzZYoewPMnQSjLoZO+1e/few1NoCdeqvtVt2Envh+FQUuN/93Qi01dz7njOlKdKTD/2Y0bl+hnKJS3p65kZOHdaJPuwBFyD5H9G/HScM68dxPa1inGYp7nSVbcjnhyV948ofVHNCzDY9PHMZz543gtOFdeG/2Jo5/4hdWbs9v3oN0l8IXf4FWXe1s5yCt3pHPPzaMpsyJYfi2jyrdlhIXzW0TBrJ8Wz6TF+579Vter+G2TxaREBvJI2cNC5jRCiQpNor7Tx/C25cdgMcYJr44g6v/N5dVzf1/IIwo2KoqNwNcuQGDrRVZK+if2r9BD++KTCQphNmIYJftyc7aCflboG2Qz9/zMMiYRXZODnM3ZHPMfu0D7tahVRxH9G/Hh3Mz7DfBBW9DVDwMOqXu5xh9qd13+tNBn8se9/PD4ETCIX8PfHtkNBxzr63TW/hekx3GmswC/jdjA+eO6Ua/9jUHOX7tkuM4bnBHPpi7qVHT/m9O30BhqYcrD6s+07aqf50wkNjICO74bHHgSRR7Gben+ZZ9yS4sZfLCLTzz42qem7aGrxdvJbe4rO47BqO0EH55DJ4/BB4bRPaLJ/P4c89RUubhvSvG8vz5IzlteBeOH9KR+08fwqfXHITHa8pbjzSb356AzOVwwmO72+IE4T9TluOKScUz6DRY8K5d3aKCE4Z0ZECHZJ74fhXePZDdyi4s5e4vlnL8E79wwauz+HH5jiZ7rg/nZTB7fTa3Hj+A9KS6l3yr6sA+6Uz966HccGRffl6ZydGP/8zEF6bzzqyNdvRkL7UwI4eHpy7n358t5rM/Njfr73pN1Pqhqi3z7GWHoZU2F5UVsSFvA8f3PL5BD18ckUSriCISYoJvito1LYHNSzdANNAmyIaXvQ6D359k6cypeLxJHDUwcLAFcPqIzny3bDuzVm1h3OKPYOCJlYfbapKQZuu65r8J4++A5Jqfo1nkb7NDoqMugZRONe/X9xjouD/8+hgMOze4upEQ3T9lGfHRkfzt6LrT/n7njO7KFwu28N2y7Zw4tJbjD5Lb4+WNGRs4vH/boKaDt0uJ4+/H9OPOL5by5aKtjXIMe1peSRlPfLeKz/7YzM6CUrqkxnPGiC5ceVgvEmKa/uNvR14Jj3+3kg/nZlDmqfyHPyYygjNGdubaI/qUzzoO2fal8N559stCt3Fsj++NZ+3PvBz5E0X7XUZCj+prqA7p0ooPrzqQ05/7jYsnzeKzaw+uVMu5R2SusF+E9jsd+h0T9N0WbMrhh+U7uPm4AcT1vQqWvGcDrgOuKN8nIsLhqsN689f3/uDX1Ts5tF/bpjgDADbnFPOnl2awObuYA/ukszazgIsnzeaGI/tyYzC/6zmbYNYLdhSiKNvWCfc50ra2aFW5cXVxqYeHp65gZPdUzhpZz1IWbJnCjUf346IDe/D2zA18MDeDWz9eBNgSgl5tE+mVnki3Ngl0S0uge1oi3dISaBXEEnN7WkmZhzs+W8z7czKIinCIi47k9ekbePHntbx0wSg6tW45zW8VbFW1cYYtQu84rNLmVTmrMBj6pzUss1UQkUybiKK6u7dX0DUtng1mm72SWsu06Iq6jYOIaAqX/0C75LMYEmAI0e+I/u1IiIlkze8fM64kt+4hxIrGXQtzXoXZL9n6p5Zk7uu2X9oBV9W+n+PAof+wf7SWfAxDz27Uw/ht9U6+W7aDW0L8Njq2Vxs6pMTxybzNjRLo/LQyk8x8V7Wi+Nr8eWx3PpyXwd1fLOWwfm1JjtsDH7jGwB9vweyXIW+rHf497J+2sWUI1mYWcMGrs9iaW8JxgzvQu20SCzNyeOL7VXw8P4MXzx/FwI5N14Po68VbufmjRRSXeZg4uiunj+jCwA4peI1hyZY8Pv1jMx/OzeDT+Vv4+zH9uOSgnkEPCwGwZb7tqh4ZCxd9yTRXP654cy790y/gg95fkTD3RYg0cOJj1e7arU0CL184mrOfn84/P1zASxeMCukzqUG8HjspJSYBjn8wpLs+/9MaUuKiOH9cd4iNsv8nZr8EYy6vVGN7/JAO3DM5hjemb2iyYKukzMNVb84lq6CU964cx8juqZS6vfzfp4t48vtVpCfFcMG4HoHv7PXC9Kfg+3vs9e7joO0A23Zo2gO2Fnbcdfb/fZT9zHhj+noy810886cRof0/qUFaYgzXje/LtUf0YfWOAn5fs4slW3JZt7OQ75ZtZ2dB5bKKVvHRjOyeysF90pkwpCMdWsU1+BgaoqTMw0WvzWLG2iyuPrw31xzem8SYKL5avI1bPlrIWc9P57PrDqpXBrApKNiqauN06DzKNvCsYP72+QAMSR/SoIfPJ5HWEVtDuk+3tAS6O9vtlbpmIvrFJGK6jKbLxlkcMuiaWn8542MiOXpQe7osfwiT1AGn1xHBH1yb3tB/Asx+xTZAjannN/TG5imzQWCfo4LLBvafAG0H2g+5IWexs7CUJVvyKHV76ZmeQO+2SfX6Y+T2eLn7i6V0SY3nogN7hHTfyAiHU4Z34pVf1rGrwEWbBn5ovD9nE+lJMRwxoObi/KqiIiO479QhnPrsbzz6zUruPLn68Hqj8rjhkyvsWngdhtpv+au+hVeOgZOesBMzgrA9r4Q/vTSTMo+XD64ax4huu/uZzVqXxXVvz+OM537ntYtGc0CveqxzWocP5mzinx8tZGiX1jx29rBqDWrH9ExjTM80rjm8N3d8toR7v1zGTysz+e/E/YN7n3M2wltn2VnTF37Oj5mJXPnGXPq2T+KNSw8gLuEIiI2D35+0LRVGXVztIfbv2ppbjh/A3ZOX8sb0DVwY4v/Pepv5PGTMgtNfsn37grQms4Cvl2zj2sP7kBTr+9M1+nL49CpY/4ttUuwTGxXJxNFdef6nNWzOKaZzE2Q4Xvp5LYs25/Li+SPL++XFREVw/+lDyfINLY7snsp+nap80fWU2SWJlnwMA0+C4x6w/RH9stfDD/fBL4/AqqlwxivkJffiuZ/WcHj/tozpmUZjchyHvu2T6VulvKHA5WZTVhEbs4rYlFXEmswCZqzN4oflO7j3y6WMH9Ce68f3YVjX1o16PMHweg1/eXc+M9dl8d+J+3Pq8N1ZwBOGdqRLajxnvzCda9+axzuXj22U4LShVLNVUXE2bF1ov2VUMWf7HHqk9KBdQvAfDoHkmkRSCK1OomtqAt2c7bhiUoMb3vPZ2W4sA8w6Du1a95Dlaf1iOcj8waYuJ9Y927GqA6+D4iw7ZIcNMH5amcn7czY1X03Isi+gYBuMuaLufQEiIuCgv8COpTzyzFOMuvc7Lnx1Fpe/MYejHvuZox77iQ/nZoRcA/LmjA2s2J7Pv04cRFx06Otpnj68C26vaXCzxp0FLr5ftoPThncmuoaWEzUZ1rU1fz6gO29MX8/izbkNOo5aGQNf/s0GWkf+G678GU59Fq6bbf+QfnadfV/r4PF9EOcWl/HmpQdUCrTABjpfXH8wHVvFcfGk2Y3ef+jtmRv5x4cLObhPOu9ePrbWlQC6pCbwyoWj+M9pQ5i5LosJT/5S90wxV4FdI9BdCn/+sDzQ6tchibcuO4DUxBib5TnqTuh9JHx1M+xcFfChLj6oB4f3b8sDXy3fMzU7W+bDd3dCv+NhyFkh3fWln9cSExnBRQf12L1xv9MgPtVmQas4Z3Q3vIYmadC7OaeYZ6atZsKQDhyzX+UWQZERDo+cNYzUxBhu+mAhZRXrhzxueP9CG2gddaftll8x0AL7hfqMl+Dcd21m98XD+f3DJ8kpKuWmYxo2shKKpNgoBnZM4dj9OnDZIb24//Sh/HjT4fx40+FcdVhv5m7I4pRnfuPq/81le17JHjsugNd+X8/UJdv5vxMGVQq0/IZ1bc29pw5m5ros/jdzzzeuDkTBVkUrvwHjgX7HVdrs9rqZt30eozqMavBTZHsTSDahze7q1DqebhE7yIoJsPh0LWYzhAjHcFBU3esYHlwyjWjHw7ulB4X0HIAdsuw0AmY8y8adBZz41K9c+Oos/vnhQo567Cf+/dniPV+wOPtl+6HV56igdt+RX8KNy/qw2bThyF1vlzcK/Ozag7jvtMEkxERx0wcLOOfFGWzJKQ7uMfNKeOwb2+rhmEH1q2fr3yGZQR1T+GR+LX8wjLGLhntrLqT/dP5m22tnVIi1Hl4PLPmUf3mf5Zm45/j97ftwF2aH9hjBWvQBzHvDTmY45Mbdw0LxrWHiW3Zh+E+vrbPr/8u/rGXG2izuOXUwgzoF/nLSPiWOty8fS7vkWC5+bTbLtjZOA9fXf1/PbZ8s4oj+bXnpglHEB1Gb6TgOfzqgG59ccyDx0ZGc+9IMHvtmReDfGWPgkyvtDOCzXuOTjN2B1v8uPYDWCRUy8hGRNliNjreBqrf64zmOw39OG0KEA//3aRNPhCjKsoFGYjs45ZmQlvrakVfCx/M2c/aorpWHhaLjbLZz+Zc2MKmgW5sEhndrzed/NP6sxOemrcbrhdsmBJ5Z3DohhntPHcyyrXlM+m397hum3mpbzRz3IBz8t9pfg/7Hw9W/UdZhBMetvpv32k5icHroX9gaW8/0RP553AB+uXk8fzuqHz+u2MFRj/3ER3Mz9sjzr9yez4NfL+eoge25pGLgXcWZI7twSN90Hvp6RaWljJqLgq2Kln8BSR1s4FDBnO1zyC/L56BO9QhEqtjpSSDeFFXq7l6XmKgIekVmsiUitAWwJ2d1pIg40nfMqHPfqEXvkhHXjzfXJIY++81xbHZr12qefP4ptuWV8NS5w/nxpsO5+KAevD59A//8cOGem9G2Yxls+M0WxteRpTPG8On8zRz92M9MXryTlT0vZLhZxt8G5DC2VxuGdW3NeQd057NrD+KhM4eyZEsuE578hR+Wb6/1cb1ew98/WECZ18udNfSzCtbpIzqzICOXNVV7bpXk2mVLHu4ND3aH/3SCDy6qtki4MYb352xiWNfWQc2ELLdzNbx0BHxwITGrpnBY3GquKHyBkv+OLG8r0mjytsCXN0HXsXDE7dVvj0mAM18FDHx2bY1NaLfnlfDE96s4amB7zqxjfcf2KXH877IDbF+zV2ft7jVXTy//spZ/f76Yif3ghQNziVv1Jaz+3p5bEPbr1Iovrj+YU4d35skfVnPWC9NZuqVKEPjbE7B8MmXj7+Se5R3523sLGNk9lbcuHVs50PJL7gDH3Q+bZsD8NwI+b6fW8dx0bH9+WpnJ50213E1pIbw90b4WZ02CxNCGbif9vp4yr5fLDglQszrqElubOa/6+Z26f2eWb8tv1NUQMvNdfDAng9NHdK51YsOx+3XgsH5tefKHVewqcMGsl2DWi7YWa2wddaR+yR14qN0DPO4+kzEF38OLh8G2RY10Jg2TFBvFX47qy9d/OZSBHVL4+wcLuPXjRbjcTdc0tdTt5a/v/kFybBQPnDGk1s9Vx3G46+T9KC7z8MyPTdMgOhQKtvzyt8GKr2DwGXZIqYIpa6eQEJVQ/wWoK8h0+2oHSkIYjnGX0sHsZJ0n+EJPr9fw+/p81icNt72wagt0ti+FrQtw7Xc2+S4301aEPnW5rP9J7Ihox8Syz3jn8rGcNKwTPdMT+fdJ+/G3o/rx8fzNvDmjadK5G3YV8tg3K7j4tVmc9/IMfnn3YTxONJu6n1br/TbuKuLyN+by1/f+oHfbRKb85RCO+NNNdlji1/9W2jciwuHsUV354vqD6dQqnksmzeE/U5ZVHiKo4NFvV/DLqp3cceJ+9GrggtInDetEhAOfVcxubV8Kzx4I05+xTWyPvgf2Pw9W/wDPHwQzXyx/zxdm5LJyewFnjwphcenMFTBpgm2FcsYr8I81JNy8nGd6P882VyzeN0+HVd816Lwq+e4ucJfAac/VHCCn9YSj/m3rcxZ9GHCXB75ajttruOPE4BYp7pKawJuXjqHM4+X8V2axoz7DIcbw7hdfUTr138xJ+jsPbvwTMe+cCe+fb9fgfGwgPH+wzba6a/+GnRwXzWNn78+T5w5nbWYhJzz1C9e8NZevFm0lY+7XmO/vYnW7ozn81/145dd1XDCuO69fMqb2mWLDzrXZ5+/vqfFz54JxPRjWtTV3f7GU7MJG7jdXnG0Drc1z4MxX7AoOISgqdfPWzI0cO6gD3dskVt8hrZcdLp07yQ7TVXDC0I5ERjh8Or/xgshJv6+j1OPlikPrbp/yfycMpKjUwxefvGWHc/seC0ffHfRzbcst4fWZGWQMvQHngs/tEPJLR9rPp9IQhn2Ls23mryS30VfL6JGeyDtXjOWaw3vzzqyNnPPiDLIa+/+Qz3+/W8nSrXk8cMbQoArfe7VN4uxRXXhr5oZmb22hYMtv5gv229HoSytt3lm8ky/XfsmEXhOIi2rY7AtjDNvLfI9RnBP8HXM3EYGXJSXBF0au2J5PTlEZxb2OswWXtX0bmv8/iIim+2EXkp4UU69vt2/O3MxzrmMZ7SxjYMHMSrddP74PR/Rvy71fLquenWkAt8fLQ18v58hHf+LpH1ezLc+Fx1XI/llfMdk9mkOeXsRhD//I/326iKlLtrEjv4TteSX8tDKTf3ywgCMfm8avqzO5fcJAPrjqQNuJOibR1nmt+LJahgjsL+/H1xzIn8fabsxnV8k+lLq93P/VMp75cQ3njunGuWPqP0Xbr31KHAf1SeeTPzbb7ODWhfDa8XbI+9Lv4OzX4aAb7KyzG+ZBn6Phq3/AV/8Er5cP5m4iNiqCk4YFOaNxx3KYdKL9UL5oil3ayBcAXXrO2dyW+ijLPZ3xvHdBwNcoZJvnwcJ3Ydw11dYjrWbkxXY48Zvbq/VXWrY1j0/mb+ayg3vSrU3wEzX6tk9m0sVj2Fng4vxXZpFbFGTWeecqzLQH2fXQcM6Zew5XRk0mrft+MOER+7pd9StcONkGwhFR8OXf4ckRsHxKnQ998rBO/PyPI7jy0N5MX7OLe976hrjPL2e1pyOnbDyHzqkJvHP5WO4+ZTAxUXV8jDuOzW4V7YKfHwm4S2SEwwOnDyG3uIx7Ji8N7vyDsXkuvHyUneV92ovB9e+r4oM5GeQWl3H5obXMxB59me1DuPKrSpvTk2I5pG86XyzY0ig9t0rdXt6ZtYmjBrYP6ktU3/bJ/GWY4fTVt+NK7QNnvBxSTexTP6zCGMNfj+oLPQ+Bq3+D3kfAd/+G/w6BKf+0dYxbF9ovYOt+sa0wfrwfProMXhoPD3SHB3vAYwPggW7wUE/7+/3r45C5sgGvxm6REQ7/PG4Az503gqVb8jjz+d/JyG7c4Gb2+iye/2kNE0d15egQyjJuOLIvjuM0e3arUWYjOo5zHPAEEAm8bIx5oMrtscAbwEhgFzDRGLO+MZ67UexaYzMEQ86qNHPNGMNjcx7Da7xcOOjCBj9NcZmHbK/vm1lJTvB3zLYLqy4uakNJmSeoQuvpa2yRbaexZ8Ciu2DZ57arfFXuUvuHbsAEolLaMWFIR96bvYn8krKgp/lnF5by3+9WMqLnOZjiGThf/RN6ziifshwR4fDQmcMY/+g07vx8CW9cMgbH64F5r9sPhl2rbDap/wRbpB7EDKWSMg9X/W8u01ZkcubILvzj2P60T4mD+W/BZ0WMOuNG7irqyy+rMvl43uZqndgTY+xspevH97X3q2jMlfDbk3Ym16nPVnvuuOhI7j11CGN7teG2jxcx4clfGNU9lQ6t4pi7IZutuSWcd0A37j5lcKNNpz9teGdufH8BC1asYf+v/mSDwounVJ+dmpgO57wN3/4Lpj+Nu7SEz/+YwPGDO5ASzPu5fSm8fpINDi78AtpW7hUUFx3JM5cdybXP3cEzhX8j9vWJJN/wG04ITSkrMQam3m6Xfjr4xrr3j4iEEx61f0R+eaRSluDpH1aTFBvFlYcG2Yuugv27tubF80dxyaTZXPL6bN68dEz1Plxer+3Dt3yyrRHauRIHWO0dwLTOf+fUP11NRHKA7HPPQ+DA62HtNHuu754Lg06FCQ/X+n+9VUI0txw/gL8f0g73y8cQVeBl+ZEv8c3AEaHPrus03PbEm/EcjLwo4AzdgR1TuOqw3jz942pO3r9TrUtK1WnnatvseN7rkNQeLvgMeoRehuHxGl75dR3Du7VmZPdavmz2OxZSutjs4cCTKt108rBO3Pj+AuZvyq79MYLww/LtZBWWBt8+pSiLa7feTq4TxR0xt/N4bDLBfiJsyirivdmbOGdMV7qm+b48JKbDn96za9LOeNa+vrNeCHBvx3bmb9PLjtak9bSfGa4Cu0JIxlw7UeG7O6HrATDiQjvZoIGzyY8f0pE2SbFc+vpsznjud9645AD6dwihdKEGBS43N77/B51T4/nXScFlrf06torn7FFdWLEtH4/XENlMMxMbHGw5jhMJPAMcDWQAsx3H+dwYU/Hr0aVAtjGmj+M45wAPAhMb+tyNInczvHOO/U9W4YO7xF3C0/Of5ou1X3DVsKvo0apHg5+qwOUm1/iCrVAyW1k22Npo2rFuZ2FQvYFmrcuiS2o8HTt1he4HwZJPbS1M1T/+K76033iHXwDYD6Y3pm/g26XbOX1EcMNOj3+3kgKXm9tOGoZT8JDt/TP1djhh97fotsmx/P1o2yBz1g+fcsCKh+zC2h2G2saGeVvsH4IF78JZr1Waxl2Vf7bZtBWZ3HfaYM47oMIajnNfg/R+dB52FBc6Dhce2INSt5d5G7NZsS2fCAd6picxsntqzcXLiW1gxPkw5zX7mrUKPDHhxKGdOKRPW16fvp4flu9g0eZcBnVM4ckj4xi9+Rl47AdbFJze1/buGnNlvT/Mjt2vA0nRC0iefAUU74BLvq65DUhEhO2KHxVH1C+P8G/PWjqMeKXuJ9m2CN44BSJjbEYmvU/A3domx/LsNSfy7GuZ3LHrZj5//Cp2HHQ3gzqlkJYYQ1SEQ2xUJCnx0aTERdUecC77Ajb+Dic+HvxM284jYViFwCGtFyu35zNl8VauPbxPvZsvHtw3nSfO2Z9r357H1f+bxwvnjyQuwmvr05Z9YcsMCrZBRBSebgfxacRxPLyxL8cfNJJ/nTCo9unljmMzElf+BL/9F356CNb9ZAulh55dc6F0cTbR704kOn8D/PkjDu7ZgLrRI++ApZ/BN/+Cc98OuMt14/swZfFWbv9kMd/87VASY0P4E2GMrZWc/ox9rSKjbT3VkXdAXM19/mrz7dJtbMwq4pbjB9S+Y0QkjLrIroO6c3Wl/7tHD2pPTFQEXyzY2uBg673Zm2ifYrNldXKXwnvnE5m/memjX+TTX6I4YdmOoLMy//1uFZERDteP71v9xu4H2n+lRbYLf26GHZmJT7WzG1t3K/+yW6PczXZW5NxJ8Nk1dphzyJn2s6/TiJAmMFQ0pmcaH1w1jgtfncXZL0zn1YtGl7fGqK+7Pl9CRnYx7185bnfbjxD83wmDiI2K2HO95AJojMzWGGC1MWYtgOM47wKnABWDrVOAO30/fwg87TiOY5pzDZCyEv75vz+RVrQYr2NwD5+Ae9HzuL1udhTvYOnOpeSX5TOx/0SuHnZ1ozxloctDLvXJbK3HGxnLDlqzekdBncGWMYbZ67M4zN/Mb9g5tqh4w2/Q4+CKO8LvT0Pr7vYPATCiWyqdW8fz+YItQQVbK7fn89bMjZx3QHdbfN1+vC0Anf607dpeYcbNn/uW0Tf5KQ74ZTreVt2IOPtN+y3U/wuwYzl8cKHtH3TO27bHUgAPT13B1CXb+fdJgyoHWtsWQ8ZsOPY/lT4oYqIiGNurDWND6ac07jrbO2zGs3DsfTXu1iohmhuO7MsNR/a1r+cvj8DXD9oPugEn2ALljDn2G+TcSXDW64HXaKxDYmwUT6V/Su/suZSd/CzRdS3a6zhw5L94749MJua/jpn3d+j1as0fwBlz4a0zIDrBZrTq6E2WnhTL7ddeyao3FnLy+rc456th3Out/o0zNSGaA3unc97YbhzYu8ofKLcLvr3D9jfzBftBqxg4nPMWT/2wmoToSC49OMimvzU4fkhH/nPaEF765Gu+f/gxjnV+J8qVCzFJdmbrgBOYGzOaW7/ayKodBdx0bH+uObx38B/ikdG2ge7Ak+3vpL+n2AmP2D+QFW1daIeCstfZurlavoAEJbmDnen5/V2w5gfoXb27fFx0JA+eMZSznp/Ow1NXBNdXzeux2b5f/2szfwltbDPO0ZeF1EerKmMMz01bQ9e0eI6t0l4hoOEX2Iagc16F4/5Tvjk5Lprx/dsxeeFW/nXioHpnNrbl2hKEqw/vTVRd7VM8ZfDRpbDhVzj9JY7Z7xT6rPiF+75cyqH90omNqn10YsGmHD6en8EVh/SqnnmvKCbBLuAd7CLeFbXqbDOu466zmbL5b9ovu3Nfs7+T/Y6x/+faDoTkjtVqmWszoEMKH151IOe/MpM/vzyTF84fWe/msl8u3MoHczO47og+jO5Rv2C5Pm13GltjBFudgU0VrmcAB9S0jzHG7ThOLtAG2FlxJ8dxrgCuAOjWLfgu1/VRUGaY6V1JYUIsXieepKwlROdGEeVEkRaXxjE9juHEXic2SrsHv0KXm1zjG24pDmH6fPZ6SO2BUxTBqiD6Vq3dWciuwtLdze8Gn2Fnrc18oXKwtf5XW7R6wqPldQQREQ4nDuvIy7+sIzPfRdvkmr8dGWO4Z/JSEmOqLENz1F2Qv9V+qK+YYr+BZa4katVUxkbG8VDZ2SQN/gvXDBpc+QHbDYCLv4LXT4b3L4DLvoN2ladW/7pqJ8//tIZzx3Tl4oOq/GGd8Zxdq3HYuXW+RnVK7W5ftzmv2g70reuovXKXwufX2yHZwWfA8Q9XnnG17hc7Zf+VY+DsN6D/cTU/ViALP+CI7Pd5zX0snWKP5Ngg7rJhVyE3Zx5Lh0FtOWz5I/Dm6bZ/T9Wli5Z+Dp9ebYcozv/UDjkEITLCoe+fHobnp/M/9+vMOu5Lcj0xlHkNJWUecovKWLk9n++X7+DLRVs5br8OPHDGkN2z5ma9aAOJP38U+hJJKR3hkL/BD/eyef5UJi90c9VhvW2PqYbI2cQ5G+7gnNhPcJVG84VnDOvaHUVk36ModWKY/usu5m1cSoeUON64ZAyH9K1nd/K2/eGSqfZ38vu74Yn97VT/7gfZIdwNv9lsWkKafX0aGmj5jb3GDj19fStc9VvA1310jzQuGNedSb+v59B+6YwfUEsmZuMMmHKTzYqm9rTrHO7/J9tuooF+WL6DBRm5PHjGkOACpOT2Noid/6YN9uJbl9900rBOfL1kGzPX7uLAPnVkpbwem5lbMQV2rgTjhdbdWF7an3amM2eNPLz2+5cW2qalyyfbhqVDzyYaWyx/0WuzmfTbeq48rOYvM16v4Y7Pl5CeFMt14wNnlxuV49gh3h4H2Y7+iz60XwCmP2tnvwJERNvALirOrjXrRPj+Obt/jm9t1xTuMhr6HkPXtA58cNWBXPDqLC59fTb/nTicE4Z2DOnQNucUc9snixjWtTV/OSpAhm8v0qI6yBtjXgReBBg1alSTZr2SEuL5duIvvDY3iwe/Xs6Qvm159aLRTTqeW+hy1y+zlbWOiLRedCtOYE0QwdbsdbZJ42h/sBUdb4dbfv0vbPnDZlY8bph6m/3Gsv95le5/9qiuvPDTWt6ZtdFmbGrw44od/LJqJ/86cVDltdUio+D0l21gN/NF+0ub0gnGXUfkgTew7tONTPs5g9PH9Km+5ENCGpz3Prx4uB3evfxHuw3YVeDib+//QZ92SdxxYpVv3Hlb7ULSIy8q37/BjvyX/YP39S1wzls17+fKh/f+bGtyxv8fHHJT9RR8z0Nsk863zrTLAp3+og3KgrHlD/j8eky3A3l+88UMn7c5qG/6H8zJIMKBfqfcBBv6wxd/gWfH2q7bPQ+xx/3HO3YoudMIOPcdm/0IRUwinPIMUa9N4MB1T1UaOvYrKfPw6m/r+O+3qzj9ud95/eIxdI0tskNpfY4KuhdaNeOug7lv4Hx9K/FR93BZQ7JaxtjM49e32uuH/gPX0EtZPz+fKYu2snraJiIjHPq3T+a2CQM4f2yPoHpo1Soi0k4KGHSy7aq+6EP7Bxpsdmjs1TYT1Vj/n8H2pTrmPvt/cM6rldYUrOi2CQOZvT6bv723gMnXH7y7ZsjP67Ffpn57AlI629/3waeH3hC5BsYYHv9uJd3SEoIuZwBsJn3Jx/b1PPyW8s3jB7QjMSaSLxZuqT3YWv+b/T3ZtQri02z3fScCkzGbw3M/YUYc8Nn/bOnDoFNs0F9Rxhz4/AZbInHcg5VaPBzevx1HDWzPY9+u5MiB7ejTLnAt06Tf17NgUw6PnjVszyyPVVFcKztJbPSltr5r81z7WuRm2CFLd4kNPo3xXVb4V7gDlk3e3YKj6wG0HX4+7150Ipe9s4zr3plHbvEQ/nRAcImUQpeby16fg9dreGLi/iE3Y25xjDEN+geMA6ZWuH4rcGuVfaYC43w/R2EzWk5tjzty5Eizp7w5fb3pfvNk8/rv65r0eb5fts10v3mycd/T3pivbwvuTl6vMfd2NGbKzebSSbPM0Y9Nq/Muf3tvvhl5zzfG6/Xu3liUbcyDvYx5+gBjsjcYM/lGY/6dYszijwM+xvmvzDSj7/3WlLo9AW8vKXObwx/+0Rzx8I/GVRZ4n5ps3FVo+t4+xfz13fk177RptjF3pxvzxqnGeNzG6/Wai1+bZfreNsUs2Zxbff9v7jDmztbG7Fob0rHU6edH7ev0xzuBb8/fYczzhxpzZ6ox89+q+/GKc4155Th7rPPerHv/vG3GPDrQmEcHGZO/3dz5+WLT97YpJqvAVevdSt0eM+a+b81Fr87cvTFzpTHv/Mmej//f/V2NmfagMWW1P16dptxsH2/tzzXuMnPtLjP0zqnmkAd/MIUfX29fsx3LG/S0u2a+Y8y/U8znr9xb/wcpLTbmw8vs8b9+iv39qMLt8ZqyGn4XGo3Xa/8/5W21Pzfl80w6yZj7uxlTuKvG3dZlFpjBd3xtjnx0mtmZX7L7hqJsY9483b5eX/zVGFdBox/ip/MzTPebJ5v3Zm8M/c7v/MmY/3S1x1nBX96ZZ4bdNTXw55XXa38P/p1izOND7Oeix11+8/TVmWb8LS+Yxe/8y5hnD/T9/rSyv8tTbzfmq1uNeelIu/3hfsas+jbgoW3PKzbD7/7GHP/fn01BSVm12xdl5Ji+t00xl7w2q/Ln997C6zVm6yJjfnrImKdG2dfjvk6m7JNrzX3Pvmx63Py5eer7lXWeW3HOdvPI00+Zx2+/2Gx/5RxjPrnamN+fNiZr/R46kfoB5pgaYprGCBVnA30dx+npOE4McA7weZV9Pgf80/nOBH7wHViLcN4B3RjXqw2PfbuSolJ33Xeop0KXbfZmYlsFXyBfmAllhZDWkz7tklm3s7DObuyz12cxqnta5TqS+Na2x03WGjtlePbLNjOwX+BeVBcf2IMd+S4+q6H78mu/rWfdzkLuOGlQ3VPPq+ialsAVh/Tik/mbmbuhhuHULqPsFPo1P8AP9zLpd1uEfuuEAdW7gudvs0NSg04NeggsaAfeYPtYffEXWPtT5du2LoBXjrY9qc59xw6f1CUuxQ4L9Trc1uzMDDSTyKck12b3irPt4ye145zR3Sj1eHl71saa7wdMWbSV7XmuyjVt6X1thu6m1XDB57ZtxE2rfIvdNnD47cg77DDSZ9faYZQAxvRMY9LFo2mbv4zYBW/iHnmpHU5rgKe3DWGWdwATMl8JrXedX0ku/O8MWPQ+HPF/8OePq9dOYYdM66zTaSjHgaS2NrvYlIW8jmOHt0oLbDuKGj6Ke6Qn8tKFo8jILuK8l2faPkWZK+1M0LU/wYn/tRMbYgL0vmqA/JIy7vtyGUM6t+KMULJafofdDK5cWz9ZwUnDOpFTVMZvq3dW3t9dCp9eAz/eB0PPgWum28/FClm69+dksCOmO71O/7dtv3DtbDjiNvv/Z9bLNkvoddtJVtfPqTFb2y45jkfPHsaK7flc9b+5FLp2/71ZtT2fi16bTZukGB46c2izFnPXm+NAh8G2LvHaWXaofNApRC35mNu238ic5JuI/+FfPPPs42St+8NOjNq1Btb8aOuHP7wUz+NDiXu8L3/PvJ2/RH1Mu/xltjnw1Nvgyf3tKhKhTDBrIRo8jGhsDdZ12OxVJPCqMWaJ4zh3Y6O8z4FXgDcdx1kNZGEDshbDcRz+fkw/znx+Op/M31z5D1Qj8v9imbjWwQ8j+mYiktqTPlFJlHkMG7OKauzxsjW3mE1ZxVx0YICgo9fhcPXvdmis49Bah28O69eWwZ1TeOybFZw4tGOlAsO1mQU88d0qjhrYrt7Tw68+vDcfzN3E3V8s4ZNrDgo8k2vkhTaN/etjzHXDkQMmBF7M+cf/2ILUI/9Vr2OpVWQUnPkavHGybVDp7/O08XdbTJrYDi78HLqOCf4xYxLsumcfXmJ7YeVmwPh/VQ548rbAu3+yRf8T3yxv29G/QzKH9E3njenrufyQXgEDXWMML/68lt5tExkfaNHppLaQdFior0Td53Tqs/DaBPj23wGHEwGGd0pgUtpr7MxJ4YXiU7mjAU+ZXVjKO7M3kdTnRsasuxJ+ftjOwgxW/nYbaGUuswXoQ85swNHsZdoPssNsP9xra8WGnh1wt7G92vDyBaO5+n9zeeipJ3g08mmiY+JwLvyifA3Z4lIPK7bns3RLHku35pKRXYyrzEtaUgz92iVzaL909u/aOujg4b4vl5FZ4OLFC0bVr6yj41DbymD6szB0oh0KBA7p25aUuCi+WLBl92Lsxdnw3vm2Ue7ht9kvHlWOM6+kjCmLt3L6iC67h47b9rP7HvbPkA/viP7tuP/0Idzy0UImPPkLE0d3JbuwlLdmbiQhJpI3Lx3b4EXnWwTHgW5j7b8JD8OyyaQtfJcL1/1AVOZX8Ppd1e5SGNeBGa4ezPUcxNhDjubQw46GWN9wa/YG+6V6xnN2hvD5H9svkHuJRqnZMsZMAaZU2XZHhZ9LgNBWHd3DRnZPZVDHFN6bvanJgq0CX7DlxLcOPjLPXm8vU3vQN94GWCu3F9QYbM3y1WuNqWnWRnpfu+5cHSIiHG6fMIhzX5rBQ1+v4A5fb5MCl5vr35lPbHQE9546JLhzCCAxNopbjh/A395bwEfzMmpcs6/wyPvZ+MfvPBj1LGVHnF79A3vtT7bgd+y1dTfErK+ktran1bd32Lqe2S/ZQvyRF9kP6BCXHgHsrMCzXrfNR39/ElZOtfUzqT3szMCZz9nZehPftH8MK7jkoJ5cPGk2n/5h14qr6qeVmSzZkscDpw/Zs6vddz/Q1hnNeNbOjgqU6Zt6O8m5K/lqwGO8OjeHYX03c8r+oa356ff69PUUl3k48bgJMP08mPG8DYbrmEkJ2C8xb54KBTts36L61o3tzQ6+0a4C8MVf7edCp+GBd+udxs/j5tJqxkMsKe3ODa6bSPnCQ2zUdHYWuli/sxB/v9Dk2Ch6pCcSGxXBks25TFm0lce/W0m/9klcMK4HZ1QMWAL4YM4m3p29iasP783+XVvX/9yOutP2Qvv4Srj0G4hNIiYqguMHd+TLRVttv8LCzXbm8641tuHqsMDdiD7/YwslZV4mhrquaC3OHtWVLqnx/GfKMh76egURDhwzqAN3nbJf7bMP91YxiTBsIs6wiUS5XWQsm8nXv81m7abNFJsYtpHGCm9XskpSGNGtNfecOpj9OlVpF5La3c4M3+80uyLBq8fCxV9X6wXYUrWoAvnm5DgOJw3rxINfL2dLTjGdQm0aGAT/MGJEQirkbqpjb5/sdYADqd3p540iMsJhyZZcjhscuJB59vosEmMiGdix4Y3kxvVuw0UH9uDV39YRExXBQX3a8MjUFSzfls/LF4yqXtweolOGdebN6Ru4e/JSRvVIo2d65eEIt8fLDR8sZVnxDUxrdSeJH50Df/5w9wzFnavs9Oo2fW1helOKT4WTn4Jj74eC7baXTV19bOoSGWWHYfocbWekffn33bf1Hm8LbAN8kBzevy3DurbmsW9WctLQTpX+eLk9Xv4zZRnd0hI4bUT9gpgGOfpuWxz8+Q22X5c/W2SMLYif/RKMu47TjrqY93NmcPsnixneNTWkju9gg/5Jv6/nqIHtbcuRI++ApZ/aGaEXfGZbLNRk+1LbC85dYttcdGm8Gcd7lYhIu07hK8fYoONP71dvIZC/Hb64gdSVX2MGn0nRkLs4bIVdp7PM46Vfu2ROHNqJQR2T2a9TK7qkxlf6QpRdWMq3S7fzxoz1/N+ni3n0mxWcP64HF4zrXm25lfdnb+KWjxdyYO82/P3oBv4BTUizk1DeOtPObJ74JsQkctKwTrw3ZxOLf/qIUfNvt19ozv+41tme78/ZxIAOyQztUr9eYTU5sHc6k68/hNyiMmKjI1pEe4I9IiqWLkMO5bIhh7Itt4RfVmWyNbeEo2OjGNMzjf06pdSeBe0yygbQrx4Lb58Fl31vZ1K3cE4LKp2qZNSoUWbOnDl79DnXZhYw/tGfuOvk/bgw0HBVA90/ZRmTfl/PilFf2JlrNwaxLMbHV9oWDTcuAeD4J36hbXIsb1wSeNhq/CPT6NYmgUkXhzCsVYsyj5fbPl7EB74V3VPionj4rGHB9b0JwqasIk5++ldSE2J487IDyjtju9we/vnhQj77Ywv3nDqY87vn2g/OkjzbdC8qzmaZImNsg8+9KJ0ckDGQtdbW6KX2qHNW4Kx1WZz9wnQuPbgn/6qwDuAzP67m4akreO68ERw/JLRp1o2mJBfePscOtfY/wa6Ft/p7O1Qz9Bw73BgRSUZ2Ecc/8Qu92ibx4VXjQppt9OT3q3js25V8eu1BuzMgC9+Hjy+3jTRPeCxw3dPan2wvt6g4OP+Taq1FwtLOVTb4LNhhZ88N8C3VtPpbW1NYVmyX+xl9Wb1ryYwxzF6fzYs/r+W7ZduJiYrgpKGdGN6tNW6Pl2+Xbee31bs4qE8bXrpgVPXu/fU170344gb7OzX6MjxR8fw+5U0OMfOg3SBbItCu5oapy7bmcfwTv3DHiYO4pIE93KSRZcyBSSfYDvjnfxpSH7Cm4jjOXGNMwG9vymxV0KttEl3T4vl9zc4mCbYKXG7b/TahDRTutB9odX14Za+vVPQ9tHMrpi7dhjGmWvSfkV3E2p2FnDe28YZBoyMjePisYVxxaC+25JYwvFvr4JZ9CVLXtAReumAUF0+azUlP/cqlB/ckISaSd2ZtZOX2Av55XH/O95/P5T/aNcHmvg7eMpsRmvBQzZ3U9yaOY4e/ghkCwxabXzCuO6/8uo7ubRI4f2x3Ppm/mce+XclJwzrVmPncI+JawQWfwi+P2UzWii/tUioTHqn0B7tLagIPnD6Ua9+ex2PfruTm4+roEu6TXVjKSz+v5ZhB7SsPNQ09G7Yvtu0I3C44/iHwLyNUVmzXgvv5YZsJPe/9feP/TWNI72t/t6beZl87f28lHLuE1tF317iaQLAcx2FMzzTG9Exj9Y4CXvl1HZMXbOGjefZLXMdWcfzfCQO5+KCejdt+Z8T5dsLD1Nth6m1EAsOjUnm8dCKXX/AoSUm1jwC8N3sTMZERnDa8GbLEUrsuo2xfsC/+YptoH3RDcx9RrRRsVTG6Rxo/rcgMGMw0VKHLbZe/SEwHj8vOBoqtY7gvex30Pbr86tCurXhvziYysour9b75dZWdZXNoMEtJhKhv+2T6tm/40GQgo3qk8fHVB/Kvzxbz8NQVAPRqm8grF47iyIEVGiq26mwXcj3Vt1BwbUNFYeC2CQPJyC7mjs+W8J8pyygp83JAzzTuP31I889kioqFI261M8PKCm0H9gDHdMLQjvy6uivP/7SGg/ukc1BdDSeBp39cTUGpm78fE2Am41F3QWQs/PwQrP7O/u54PbDqWyjaaQumT3hsdxAmVlJb2/D2mHtgy3zbpLLjsND7rgWhT7sk7j99CPedOphteSVERTi0TY5tuv+zvQ6Dq3+1vfg8pSzLSeSJF2bSbUUuZ4ys+TMtv6SMD+dmcNzgDg1vlitNY8SF9nf7+7vtiiPtg1jxoJko2KpiTI80Pp63mTWZhfRp17gfyIWlHhJiIiHR13W6MLP2YKu00NYHpVbMbLUGYN7G7GrB1i+rdtI+JbbRj3tP6Ns+mXevGMeuAhdlHkP7lFo+fMM8yPKLi47kpQtG8dkfm/ljUw6DO7XitBGdW1bzv4iIOr9Q/OvEQcxal8Xf3vuDr/5ySK0zsZZuyWPS7+uZOKpr4AVuHQfG324/eH97AlZ+YwOHHgfBmCsqr6Ag1SV3qDYho6lERDhNUhtbI18D0pGtDH3aJfHqb+s4fUTnGj9n3pu9iQKXm8sO0fBhi+U4tpb26VG2TvTSbxqtsW5ja0Gfyi3DCN+CmQszchr9sQvLhxF9394Ld9V+h+wN9rLCMOLAjsmkxEVV6xXjcnv4eWUmh/Vr2/xZjQZokxRLh1Zxe/U57EmREQ6nj+jC3acM5uzRXVtWoBWkhJgonjp3BDlFZfzjw4XUVEda6vZyy8cLaR0fXffCxN3G2t5k/1gFN62wSyQp0BJskHfpwT1ZsiWPGWuzAu7jcnt47bf1jOmZxtAurffsAUpoEtJs37jNc2y/sxZq7/tkbmK90hOJiYpg2da8Rn/s3cOIvlYBRTtrv0O2v8dWj/JNUZERHNw3nZ9X7qz0R+mXlTvJd7mZ0FxF0SINMKhTCrdNGMAPy3fw8NQV1QIuYwx3fbGEhRm53Hvq4N3rK4rUw2nDO9MmMYanflgVMLh/a8ZGNucUc83hwdVQSjMbcpadwf3dXbZHYQukYKuKqMgI+rVPYtnW/EZ/7MJSj81sVRxGrE2FhqYVHdq3LdvySli+bfcxfrFwCylxURzYu+VPgRUJ5MIDe3DumG48O20Nt3+6uHw1B5fbwx2fLeGtmRu58tBezTfLUvYZcdGR3HBkX35fs4tvlm6vdFtmvounfljFgb3bcFi/ei40LnuW49haTK8bpvyjxlURmpOCrQAGdkhh2da8Gocz6qvQ5bY1W+XDiEFktmJbVVuI9qhB7YmOdPjQ145hR34JUxZt5dThnUNeOkekpXAch/tOHcyVh/Xi7ZkbGXf/D5z/ykwOfvBH3pyxgcsO7ln38KFIkM47oBv92ydz+yeL2JpbDNhWN3//YAGFpR7uPHk/lTPsTdJ62kk5yyfD0s+a+2iq0V/mAPp3SGZXYSlZhaWN+rgF/mHEmASIToCiOmq2stYFXOsvPSmWYwZ14MO5GWQXlvLsj2twe03gpWxE9iIREQ63Hj+Qj64ex/gB7cgrLmN0j1TevuwA/u/EQfrjJ40mKjKCZ84bTkmZlzOe/Z2Xfl7L+a/M5OeVmdx18n62Wa7sXcZeCx33hyk3QVHgerzmotmIAfg7mW/IKmq0NaqMMbsL5MG2f6hrGDF7nZ1+HcB14/swdck2Tn32NzZmFfHnA7rXuISPyN5mZPc0RnavYckpkUbSp10y71w+lr+9/wf3TVlGq/hoHjpzaMBlsGQvEBkFpzwNLx5ue6ud9lxzH1E5BVsBdG9jg631OwsZ0S21UR7T5fbiNZAQ65uWmpBe+zCixw05G+06UAEM7JjC4xP358nvV3HWyC7cfoI6YYuIhGpIl1Z8+7dDySxwkZoQs1fO6JUKOgyBg/9mGxgPPBEGnNDcRwQo2Aqoa1o8EQ6s31XUaI/pX4S6UmarYHvNd8jdZIv9Umvu8XLSsE6cNKxTox2jiEg4chyHdsn74ALQ4erQf9imxp9cBVdMC3pljqakED6A2KhIOrWOZ8OuwkZ7zEJfsJXoX/MrsS0U1DKMmLXWXqb1arRjEBER2edFxdreehFR8PbZdvWAZqZgqwY92iQ2amar0OUBINE/jJjcwWa2vJ7Ad/D32ApQIC8iIiK1aN3NNjbO3wavHgsZc5v1cBRs1aB7m4TGzWz5egYl+ocRUzqB8dRcJJ+1DqLiIakZFxQWERHZW3UbCxd8ZpMaH14EnrJmOxTVbNWgU+t4corKKC71EB/T8LWW/DVb5cFWsq/WKm9z4MVes9bazvERiodFRETqpcsouxB5zqZmXVdXf8lr0LGVLZbcllfSKI9XWLVAPsUfbNUwlpy1TvVaIiIiDRWfCh2HNushKNiqQQdfsLU1p7hRHq/IV7OV4M+SlQdbAdZx8nptzZbqtURERPZ6CrZq0KlVPABbcxsns1Wt9UNCOkRE22HEqnI3gbsE0vs2ynOLiIhI81GwVYMOTTSMmOBv/RARASkdIT/AMGLmCnvZVuvAiYiI7O0UbNUgLjqS1IRotjTSMGJhqYeYyIjKC0Und4LcAJmtzOX2Mr1fozy3iIiINB8FW7Xo2CqebY00jFjocu/useXXuhvkbKi+c+YKSGoPCVobTkREZG+nYKsWHVrFNVrNlg22qnTaaNMbcjOgrEr2LHM5tO3fKM8rIiIizUvBVi3aJsWys8DVKI9V4HLvXqrHL603YGybBz9jbGZL9VoiIiL7BAVbtUhPjmFXYSler2nwYxWVeqoPI7bx9dHKWrN7W/Y6KM2HdoMa/JwiIiLS/BRs1aJNYiweryGnuOEt/gsCDSOm+VYi31Uh2No8z152HtHg5xQREZHmp2CrFunJsQCNMpRY6HLv7rHlF9/arn24Y+nubVvmQ2SsMlsiIiL7CAVbtUhPigEaJ9gqKvXs7rFVUafhsOWP3dc3z4UOg5t1DScRERFpPAq2atE2yZ/ZKm3wYxW43CRVrdkCG2ztXAmufHAVQMYc6HFwg59PREREWoYAqRbxS/cHW/kNy2wZYwK3fgC7IjkGNs4A4wVvGfQ6okHPJyIiIi2Hgq1atIqPJjLCafAwosvtxe01gYOt7gdBdCIsnwylhRDbCrqNa9DziYiISMuhYKsWEREObRJjGhxsFZV6AEiMCTCMGB0H+50GcyfZ62OutNtERERkn6Bgqw7pSbHsamDNln8R6oCZLYAjboVNMyEmAQ67uUHPJSIiIi2Lgq06pCZGk13UsGCrwBdsVWv94NeqC1w/p0HPISIiIi2TZiPWoXVCDDlFDWtqWlRqg62EmoItERER2Wcp2KpD6/joBneQL3DZmq2ArR9ERERkn6Zgqw6pCTHkFDVsfcQ6a7ZERERkn6Vgqw6tE6LxGsgvcdf7Mfw1W4mBOsiLiIjIPk3BVh1SE+ySPTnF9S+SL1JmS0REJGwp2KpD6wS7RmF2A4rkC/19tlSzJSIiEnYUbNWhtS+z1ZD2DwUuN1ERDjGRerlFRETCjf761yHVl9nKaUCwVeRbF9FxnMY6LBEREdlLKNiqQ3nNVgOGEQtcnpobmoqIiMg+TcFWHVLio3GcBtZsudyq1xIREQlTCrbqEBnhkBIX3aBhxMJSNwlq+yAiIhKWFGwFITUhukHDiIUut4YRRUREwpSCrSC0Sohp0GzEQpdHw4giIiJhSsFWEFLiohrcQV7d40VERMKTgq0gpMRHk1dS/2HEolK3useLiIiEKQVbQWhoZssOIyrYEhERCUcKtoKQEhdNXnH9Mlulbi+lHi+JMarZEhERCUcKtoKQEh+Ny+3F5faEfN+iUi1CLSIiEs4UbAUhOc4GSvUZSixw2fuo9YOIiEh4UrAVhJQ4uz5ifYYSC102G6bMloiISHhSsBUEf2YrrwGZrQT12RIREQlLCraCkBJvM1v59Wj/4K/Z0jCiiIhIeFKwFYTyzFZx6JmtQl9mS01NRUREwpOCrSD4a7bqk9kqKK/Z0jCiiIhIOFKwFQT/MGJ9usir9YOIiEh4U7AVhMSYSCKc+g0jqvWDiIhIeFOwFQTHcUiOi67XMGKhy02EA7FReqlFRETCkSKAICXHRdWr9YN/XUTHcZrgqERERKSlU7AVpPquj1jocmsIUUREJIwp2ApSSnxUvZbrKSx1qzheREQkjCnYClJyXHS9ZiMWuDwkxqjtg4iISLhSsBWk+g4jFrmU2RIREQlnCraClBxXv2HEAgVbIiIiYU3BVpBS4qPJd7nxek1I9yssdWsYUUREJIwp2ApSkm+5ncLS0LJb/tYPIiIiEp4UbAUpKdYu2VPoW+swWGr9ICIiEt4UbAUpKc4GTAWu4Ivk3R4vLrdXmS0REZEw1qBgy3GcNMdxvnUcZ5XvMjXAPvs7jjPdcZwljuMsdBxnYkOes7n4hxFDKZL3Z8ESVLMlIiISthqa2boF+N4Y0xf43ne9qiLgAmPMfsBxwH8dx2ndwOfd4+ozjOiv79IwooiISPhqaLB1CvC67+fXgVOr7mCMWWmMWeX7eQuwA2jbwOfd4/wBUyjDiIUuG2xpGFFERCR8NTTYam+M2er7eRvQvradHccZA8QAa2q4/QrHceY4jjMnMzOzgYfWuPzBVijDiAXlwZaGEUVERMJVnSkXx3G+AzoEuOn2ileMMcZxnBqbUDmO0xF4E7jQGOMNtI8x5kXgRYBRo0aF1tCqifkL5P3ZqmD4hxwTY5TZEhERCVd1RgHGmKNqus1xnO2O43Q0xmz1BVM7atgvBfgSuN0YM6PeR9uM/NmpglCCrVINI4qIiIS7hg4jfg5c6Pv5QuCzqjs4jhMDfAK8YYz5sIHP12xioyKJiYogP6TMloItERGRcNfQYOsB4GjHcVYBR/mu4zjOKMdxXvbtczZwKHCR4zh/+P7t38DnbRZJsVEhDiOqZktERCTcNSjlYozZBRwZYPsc4DLfz/8D/teQ52kpkmKjKAilz1app/x+IiIiEp7UQT4ESbFRodVsudw4DsRHK7MlIiISrhRshSDUYKvA5SYxJgrHcZrwqERERKQlU7AVgqS40DNbqtcSEREJbwq2QlCfmi3NRBQREQlvCrZCkBgbRUEoayP6hhFFREQkfCnYCkFyXFTIayNqGFFERCS8KdgKQVJsFCVlXtyegKsNVVPo8qjtg4iISJhTsBUCf/1VYZBDiYWlbhI0jCgiIhLWFGyFINkXbOUHOZRohxEVbImIiIQzBVshSIqzgVOw7R8KXG6SVLMlIiIS1hRshSCpfBix7mDL4zWUlHmV2RIREQlzCrZC4A+c8oPotVVY6luEWjVbIiIiYU3BVgiSQxhG9Ge/lNkSEREJbwq2QhDKMKJ/xqL6bImIiIQ3BVshCGkY0aVhRBEREVGwFRJ/ZiuUYUT/DEYREREJTwq2QhAZ4ZAQExnUMGK+P9hSzZaIiEhYU7AVIrsYtQrkRUREJDgKtkKUHBsVWs2WCuRFRETCmoKtECXFRQU1jFjgm42YHBvd1IckIiIiLZiCrRAlBTmMWOAqI8KBuGi9xCIiIuFMkUCIEoMeRvSQGBuF4zh74KhERESkpVKwFaLk2KjypXhqU+Byk6zieBERkbCnYCtESXFRFARZIK+ZiCIiIqJgK0TBtn4oULAlIiIiKNgKWVJsFGUeQ0mZp9b9Clzu8oWrRUREJHwp2ApRSlxwS/YUutxaF1FEREQUbIXKv9ZhXTMSC0o0jCgiIiIKtkLmb1JaV5G8hhFFREQEFGyFbHdmq6zGfYwxFJZ6tFSPiIiIKNgKlT9blV9LzZbL7cXjNRpGFBEREQVbofIPI9ZWs+W/LUnBloiISNhTsBUif2aroJZhRP9C1Qq2RERERMFWiIKZjehvC6FhRBEREVGwFaLoyAjioiNq7bOlzJaIiIj4Kdiqh6TYaPKCyGwp2BIREREFW/WQEhdVa+sHDSOKiIiIn4KtekiKq30x6kKXXTdRmS0RERFRsFUPyXFRdRTI26xXkjrIi4iIhD0FW/WQFBtV63I9Bb7MVkK0OsiLiIiEOwVb9ZAcF11rzVahy01iTCQREc4ePCoRERFpiRRs1UNSbFSty/UUutwqjhcRERFAwVa9pPgK5L1eE/D2vJIyUuKj9/BRiYiISEukYKsekuKiMAaKyjwBb88vcZOi4ngRERFBwVa9JMf5F6MOXLeVV6zMloiIiFgKturB3z+rphmJeSXu8oBMREREwpuCrXpI9g0R1rRkT15xmYYRRUREBFCwVS/+YCtQF3ljjArkRUREpJyCrXqorWbL5fZS5jGkaBhRREREULBVL7XVbOUV2wAsWcOIIiIigoKtevEHUoHWR8zzZbs0jCgiIiKgYKteEmOicBwCdpHPLbbbVCAvIiIioGCrXiIiHJJiogLWbOUrsyUiIiIVKNiqp6S4qMA1WyXKbImIiMhuCrbqKSUumtzi6pktf4G8ZiOKiIgIKNiqt1YJ0eQECrY0jCgiIiIVKNiqp9SEaHKLAmW23MRERhAbpZdWREREFGzVW+v4GLKLSqttzy8pIyU+CsdxmuGoREREpKVRsFVPrRPtMKIxptL2nOIy1WuJiIhIOQVb9dQ6PoZSt5fiMk+l7TlFpaQmxjTTUYmIiEhLo2CrnlITbPYqu0rdVlZhGakJCrZERETEUrBVT619AVVOlbqtnKLS8kBMRERERMFWPbX2BVQ51TJbpaRpGFFERER8FGzVU2p5Zmt3sFVc6sHl9pZnvUREREQUbNVT6/Kard3DiFm+n9MSNYwoIiIiloKtemoV7x9G3B1sZRfan5XZEhERET8FW/UUFx1JfHRkpWHE7PLMloItERERsRRsNUBqQnSl1g9ZvsyWWj+IiIiIn4KtBkhLimFXoav8+q4CG2y1UWZLREREfBRsNUD75Dh25O0Otnbku4iJjCgvnhcRERFRsNUA7VLi2JFfUn59R14JbZNjtQi1iIiIlFOw1QDtU2LZWVBKmccL2MxWu5TYZj4qERERaUkaFGw5jpPmOM63juOs8l2m1rJviuM4GY7jPN2Q52xJ2qfEAZCZb4cSt+eV0D45rjkPSURERFqYhma2bgG+N8b0Bb73Xa/JPcDPDXy+FqW9L4u1Pc8OJSqzJSIiIlU1NNg6BXjd9/PrwKmBdnIcZyTQHvimgc/XorTzZbG257koLvWQW1xWnu0SERERgYYHW+2NMVt9P2/DBlSVOI4TATwK3FTXgzmOc4XjOHMcx5mTmZnZwENrev7AanteCRuzigDompbQnIckIiIiLUxUXTs4jvMd0CHATbdXvGKMMY7jmAD7XQNMMcZk1DVLzxjzIvAiwKhRowI9VouSnhRDQkwk63cV0rGVDby6K9gSERGRCuoMtowxR9V0m+M42x3H6WiM2eo4TkdgR4DdxgGHOI5zDZAExDiOU2CMqa2+a6/gOA490xNZt7OQTq3iAejeRsGWiIiI7FZnsFWHz4ELgQd8l59V3cEYc57/Z8dxLgJG7QuBll/P9EQWZuTSLjmWtMQYLUItIiIilTS0ZusB4GjHcVYBR/mu4zjOKMdxXm7owe0NBnVKYWNWEdNWZLJfp5TmPhwRERFpYRqU2TLG7AKODLB9DnBZgO2TgEkNec6W5sDe6cAKduS7OH9s9+Y+HBEREWlh1EG+gYZ0bkWfdknEREVwyv6dm/twREREpIVpaM1W2IuMcPj4mgPJLSpT2wcRERGpRsFWI0iJiyYlLrq5D0NERERaIA0jioiIiDQhBVsiIiIiTUjBloiIiEgTUrAlIiIi0oQUbImIiIg0IQVbIiIiIk1IwZaIiIhIE1KwJSIiItKEFGyJiIiINCEFWyIiIiJNSMGWiIiISBNSsCUiIiLShBRsiYiIiDQhBVsiIiIiTUjBloiIiEgTcowxzX0MATmOkwls2ANPlQ7s3APP0xKF87lDeJ+/zj18hfP5h/O5Q3if/5449+7GmLaBbmixwdae4jjOHGPMqOY+juYQzucO4X3+OvfwPHcI7/MP53OH8D7/5j53DSOKiIiINCEFWyIiIiJNSMEWvNjcB9CMwvncIbzPX+cevsL5/MP53CG8z79Zzz3sa7ZEREREmpIyWyIiIiJNSMGWiIiISBMK22DLcZzjHMdZ4TjOasdxbmnu42kqjuOsdxxnkeM4fziOM8e3Lc1xnG8dx1nlu0z1bXccx3nS95osdBxnRPMefWgcx3nVcZwdjuMsrrAt5HN1HOdC3/6rHMe5sDnOpT5qOP87HcfZ7Hv//3AcZ0KF2271nf8Kx3GOrbB9r/vdcBynq+M4PzqOs9RxnCWO4/zFt32ff/9rOfdwee/jHMeZ5TjOAt/53+Xb3tNxnJm+c3nPcZwY3/ZY3/XVvtt7VHisgK9LS1XLuU9yHGddhfd+f9/2feb/vZ/jOJGO48x3HGey73rLfN+NMWH3D4gE1gC9gBhgATCouY+ric51PZBeZdtDwC2+n28BHvT9PAH4CnCAscDM5j7+EM/1UGAEsLi+5wqkAWt9l6m+n1Ob+9wacP53AjcF2HeQ7/99LNDT9/sQubf+bgAdgRG+n5OBlb5z3Off/1rOPVzeewdI8v0cDcz0vafvA+f4tj8PXO37+Rrged/P5wDv1fa6NPf51fPcJwFnBth/n/l/X+GcbgTeBib7rrfI9z1cM1tjgNXGmLXGmFLgXeCUZj6mPekU4HXfz68Dp1bY/oaxZgCtHcfp2AzHVy/GmJ+BrCqbQz3XY4FvjTFZxphs4FvguCY/+EZQw/nX5BTgXWOMyxizDliN/b3YK383jDFbjTHzfD/nA8uAzoTB+1/LuddkX3vvjTGmwHc12vfPAOOBD33bq773/v8THwJHOo7jUPPr0mLVcu412Wf+3wM4jtMFOAF42XfdoYW+7+EabHUGNlW4nkHtH057MwN84zjOXMdxrvBta2+M2er7eRvQ3vfzvvi6hHqu++JrcJ1vyOBV/zAa+/D5+4YHhmO/5YfV+1/l3CFM3nvfUNIfwA5soLAGyDHGuH27VDyX8vP03Z4LtGEvPf+q526M8b/39/ne+8cdx4n1bdvX3vv/Av8EvL7rbWih73u4Blvh5GBjzAjgeOBax3EOrXijsXnUsOj/EU7nWsFzQG9gf2Ar8GizHk0TcxwnCfgI+KsxJq/ibfv6+x/g3MPmvTfGeIwx+wNdsFmJAc17RHtO1XN3HGcwcCv2NRiNHRq8ufmOsGk4jnMisMMYM7e5jyUY4RpsbQa6Vrjexbdtn2OM2ey73AF8gv0g2u4fHvRd7vDtvi++LqGe6z71Ghhjtvs+jL3AS+xOj+9z5+84TjQ22HjLGPOxb3NYvP+Bzj2c3ns/Y0wO8CMwDjtEFuW7qeK5lJ+n7/ZWwC728vOvcO7H+YaWjTHGBbzGvvneHwSc7DjOeuyQ93jgCVro+x6uwdZsoK9v1kIMtlju82Y+pkbnOE6i4zjJ/p+BY4DF2HP1zza5EPjM9/PnwAW+GStjgdwKQzB7q1DPdSpwjOM4qb5hl2N82/ZKVWruTsO+/2DP/xzfDJ2eQF9gFnvp74av9uIVYJkx5rEKN+3z739N5x5G731bx3Fa+36OB47G1q39CJzp263qe+//P3Em8IMv61nT69Ji1XDuyyt8wXCwNUsV3/t94v+9MeZWY0wXY0wP7P/VH4wx59FS3/eGVtjvrf+wszJWYsf2b2/u42mic+yFnWWxAFjiP0/sOPX3wCrgOyDNt90BnvG9JouAUc19DiGe7zvY4ZIy7Lj7pfU5V+ASbJHkauDi5j6vBp7/m77zW4j9UOlYYf/bfee/Aji+wva97ncDOBg7RLgQ+MP3b0I4vP+1nHu4vPdDgfm+81wM3OHb3gv7R3M18AEQ69se57u+2nd7r7pel5b6r5Zz/8H33i8G/sfuGYv7zP/7Kq/D4eyejdgi33ct1yMiIiLShMJ1GFFERERkj1CwJSIiItKEFGyJiIiINCEFWyIiIiJNSMGWiIiISBNSsCUiIiLShBRsiYiIiDSh/wcFlnwjdUhXLQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,7))\n", "plt.plot(time,uprime_global[0],label=\"u'1\")\n", "plt.plot(time,uprime_global[1],label=\"u'2\")\n", "plt.plot(time,0.5*(1-uprime_global[2]),label=\"carriers\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The emergence of the Free Induction Decay (FID) mechanism is clearly visible." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Echo mechanism in the $\\pi/2$ - $\\pi$ configuration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We add a second $\\pi$ pulse to realize the echo mechanism." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time unit: fs\n", "the width parameter of the pulse is 42.466090014400955 fs\n", "Rabi coupling (fs^-1): (0.020869049285023034+0.020869049285023034j)\n", "Rabi coupling (module) (fs^-1): 0.029513292532712117\n", "field amplitude (V/m): 259577656.98568386\n", "field intensity (kW/cm^2) : 17885622.0699653\n" ] }, { "data": { "text/plain": [ "{'Omega0': (0.020869049285023034+0.020869049285023034j),\n", " 'Omega0_abs': 0.029513292532712117,\n", " 'field_amplitude': 259577656.98568386,\n", " 'intensity': 17885622.0699653}" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta2= np.pi # set the area of the pulse\n", "pars2 = TLS.pulseParametersFromTheta(dipole,theta2,fwhm=fwhm)\n", "pars2" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "Omega = lambda t : G.doubleGaussianPulse(t,energy=energy,amplitude1=pars1['Omega0_abs'],amplitude2=pars2['Omega0_abs'],\n", " fwhm1=fwhm,fwhm2=fwhm,t_start2=800,envelope_only=True,verbose=False)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(time,Omega(time))" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "uprime0 = np.array([0.,0.,1.]) # set the system in the GS before the pulse" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "uprime = np.zeros([3,len(time),numk])\n", "for k in range(numk):\n", " delta_fsm1 = 1e-3*deltas[k]/h_red\n", " uprime[:,:,k] = TLS.solveBlochEq(uprime0,time,Omega,mu12=dipole,delta=delta_fsm1)\n", "uprime_global = np.mean(uprime,axis=2)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "k = 0\n", "plt.plot(time,uprime[0,:,k],label=\"u'1\")\n", "plt.plot(time,uprime[1,:,k],label=\"u'2\")\n", "plt.plot(time,0.5*(1-uprime[2,:,k]),label=\"carriers\")\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,7))\n", "plt.plot(time,uprime_global[0],label=\"u'1\")\n", "plt.plot(time,uprime_global[1],label=\"u'2\")\n", "plt.plot(time,0.5*(1-uprime_global[2]),label=\"carriers\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The echo signal emerges." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }