{ "cells": [ { "cell_type": "markdown", "id": "b3e1bd53-dc31-489d-8245-33e73a31c1f8", "metadata": { "tags": [ "remove-cell" ] }, "source": [ "# Latex Headers\n", "\n", "$$\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}$$\n", "$$\\newcommand{\\bra}[1]{\\left\\langle{#1}\\right|}$$\n", "$$\\newcommand{\\braket}[2]{\\left\\langle{#1}\\middle|{#2}\\right\\rangle}$$\n", "$$\\newcommand{\\adagger}[0]{\\hat{a}^{\\dagger}}$$\n", "$$\\newcommand{\\ahat}[0]{\\hat{a}}$$" ] }, { "cell_type": "markdown", "id": "6ed56e87-9b66-4ca5-8295-fc5ca3e94e3b", "metadata": { "incorrectly_encoded_metadata": "tags=[\"remove-cell\"] jp-MarkdownHeadingCollapsed=true jp-MarkdownHeadingCollapsed=true tags=[] jp-MarkdownHeadingCollapsed=true", "tags": [ "remove-cell" ] }, "source": [ "# Cell Width Adjust\n", "\n", " - Execute the code below to adjust the width of the cells when editing. \n", " - These cells will not be published to the book and are for editing convenience." ] }, { "cell_type": "code", "execution_count": 1, "id": "d066c0df-aa5c-47f7-997b-1ffce7287a16", "metadata": { "tags": [ "remove-cell" ] }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "width = 70 #Width as a percentage of the screen\n", "\n", "from IPython.display import display, HTML\n", "display(HTML(\"\"))\n", "display(HTML(\"\"))\n", "display(HTML(\"\"))" ] }, { "cell_type": "markdown", "id": "bcdff4e6-8251-4c63-9061-40ac42497a11", "metadata": {}, "source": [ "# BASICS -- Quantum Optics\n", "\n", "This course is about how we can leverage quantum systems as engineers. As such it is not intended to be a course focused purely on the physics of quantum systems. \n", "\n", "In this course we will focus our attention on how to engineer quantum systems to securely transmit information, perform sensitive measurements, and compute among other things. This will require us to develop a proficiency in understanding how quantum signals are generated, transmitted, and received. It will also require us to understand the limitations of measurements, and how to account for noise.\n", "\n", "While we will introduce several quantum engineering platforms in this course, a large number of concepts will be taught through the lens of quantum optics. This chapter overviews basic concepts in quantum optics that will be drawn on throughout the course. It should be used as both review and reference material. For those interested in going deeper than the surface level overview we present here, references are provided at various points." ] }, { "cell_type": "markdown", "id": "9719167f-01df-490a-af61-f7e434583ba8", "metadata": {}, "source": [ "## Optical Modes\n", "\n", "Often we deal with optical signals whose fields oscillate at a single angular frequency $\\omega$. At any given frequency, an optical signal can be written as a summation of modes. These modes are distinguished by a variety of properties, such as their wave-vector $\\mathbf{k}$ or polarization (e.g. linear horizontal, linear vertical, right-hand circular, etc.). \n", "\n", "In most cases, each input or output signal populates a single mode." ] }, { "cell_type": "markdown", "id": "d235d45a-a4ad-45b8-b08a-8575756afba1", "metadata": {}, "source": [ "## The Vacuum State $\\ket{0}$\n", "\n", "The vacuum state represents the condition that no photon populates any mode. This can be expanded as:\n", "\n", "$\\ket{0} = \\ket{0}_a\\ket{0}_b\\ldots\\ket{0}_m\\ket{0}_n\\ldots$,\n", "\n", "where, for example, $\\ket{0}_n$ represents zero photons for mode $n$. \n", "\n", "Here, we have labeled the modes $a$, $b$, $c$, $\\ldots$ for convenience, but it should be noted that there can be infinite number of possible modes." ] }, { "cell_type": "markdown", "id": "932cd127-5cc7-46b1-8bae-9e14548363dc", "metadata": {}, "source": [ "## Photon Number States: $\\ket{N}$\n", "\n", "Number states are those that represent a mode populated with a precise number of photons. Such states are ubiquitous in quantum engineering applications. \n", "\n", "For instance, a single photon in mode $m$ can be written as:\n", "\n", "$\\ket{1}_m = \\ket{0}_a\\ket{0}_b\\ldots\\ket{0}_l\\ket{1}_m\\ket{0}_n\\ldots$.\n", "\n", "Likewise, for N-photons in mode $m$:\n", "\n", "$\\ket{N}_m = \\ket{0}_a\\ket{0}_b\\ldots\\ket{0}_l\\ket{N}_m\\ket{0}_n\\ldots$." ] }, { "cell_type": "markdown", "id": "11166319-1c81-42b5-bc3b-373bcb1f0cb4", "metadata": {}, "source": [ "## The Creation Operator: $\\adagger$\n", "\n", "The creation operator acts to increase the photon number in a particular mode by 1. For instance:\n", "\n", "$\\adagger_m \\ket{0}_m = \\ket{1}_m$\n", "\n", "More generally:\n", "\n", "$\\adagger_m \\ket{N}_m = \\sqrt{N + 1}\\ket{N + 1}$" ] }, { "cell_type": "markdown", "id": "9e421b1c-d08a-4a25-aec6-bc660a32746f", "metadata": {}, "source": [ "## The Annihilation Operator: $\\ahat$\n", "\n", "The annihilation operator acts to decrease the photon number in a particular mode by 1. For instance:\n", "\n", "$$\\ahat_m \\ket{1}_m = \\ket{0}_m.$$\n", "\n", "More generally:\n", "\n", "$$\\ahat_m \\ket{N}_m = \\sqrt{N}\\ket{N - 1}.$$\n", "\n", "Note that:\n", "\n", "$$\\ahat_m \\ket{0}_m = 0.$$" ] }, { "cell_type": "markdown", "id": "8ad483b3-1f3e-4fe9-838a-e82c60f711c7", "metadata": {}, "source": [ "## Commutation Relation\n", "\n", "It's important to note that the annihilation and creation operators **do not** commute. They have the following commutation relation\n", "\n", "$$ [\\ahat_m, \\adagger_n] \\equiv \\ahat_m \\adagger_n - \\adagger_m\\ahat_n = \\delta_{mn}, $$\n", "\n", "where $\\delta_{mn} = 1$ if $m = n$ and $\\delta_{mn} = 0$ if $m \\neq n$.\n", "\n", "This relation can be quite useful, in particular for ensuring operators are in \"normal order\" which we will describe in detail when reviewing the coherent state below." ] }, { "cell_type": "markdown", "id": "b4a9614e-4348-405a-90ec-04fb7e59e460", "metadata": {}, "source": [ "## The Number Operator: $\\hat{N} = \\adagger\\ahat$\n", "\n", "As the name implies, the number operator relates to the number of photons contained within a mode. It is related to the annihilation and creation operators:\n", "\n", "$\\hat{N}_m = \\adagger_m\\ahat_m$. \n", "\n", "Often times we are interested in the time-averaged number of photons in a state. For instance, consider the state $\\ket{\\psi_m}. The time averaged number of photons in this state would then be:\n", "\n", "$\\bra{\\psi}_m\\hat{N}_m\\ket{\\psi}_m$. \n", "\n", "Using the properties of $\\ahat$ and $\\adagger$, you can easily show that:\n", "\n", "$\\bra{N}_m \\hat{N}_m \\ket{N}_m = N$." ] }, { "cell_type": "markdown", "id": "2a84a2c3-0717-4e03-bd96-bfdf5ffefbe9", "metadata": {}, "source": [ "## The Field Operators\n", "\n", "The annihilation and creation operators are also intrinsically related to the electric field of a state. In fact, they arise as a result of quantizing the electric field. \n", "\n", "```{note}\n", "The quantization of the electromagnetic field is discussed in many textbooks. For instance, see the treatment in Ref. {cite:p}`townsendModernApproachQuantum2000`, or the more extensive treatment in Ref. {cite:p}`kongElectromagneticWaveTheory2008`. \n", "```\n", "\n", "The operator relating to the \"in-phase\" component of the electric field is expressed as:\n", "\n", "$$\\hat{A}^{(1)} = \\frac{\\ahat + \\adagger}{2},$$\n", "\n", "and that relating to the \"quadrature\" component of the electric field as:\n", "\n", "$$\\hat{A}^{(2)} = \\frac{\\ahat - \\adagger}{2i}.$$\n", "\n", "Taking the expectation of either $\\hat{A}^{(1)}$ or $\\hat{A}^{(2)}$ provides the time-averaged output of the in-phase and quadrature components of the field respectively. \n", "\n", "Note that it can be useful to define the more general form:\n", "\n", "$$\\hat{A}^{(\\theta)} = \\frac{\\ahat e^{-i\\theta} + \\adagger e^{i\\theta}}{2}$$\n", "\n", "where $\\hat{A}^{(1)} = \\hat{A}^{(\\theta)}(0)$, and $\\hat{A}^{(2)} = \\hat{A}^{(\\theta)}(\\pi/2)$\n", "\n", "### Relating the Field Operators to Classical Electromagnetic Waves\n", "\n", "To get a better sense for these operators, let's consider the electric field of a classical light wave. For a single frequency at one point in space, we can write the field as\n", "\n", "$$ E(t) = |\\alpha|\\cos(\\omega_0 t + \\varphi) \\mathrm{.}$$\n", "\n", "There are three important paramters that describe such a wave:\n", "\n", " 1. The central frequency $\\omega_0$\n", " 2. The amplitude $|\\alpha|$ \n", " 3. The phase offset $\\varphi$\n", " \n", "However, by phasor analysis, we can also write the field as\n", "\n", "$$E(t) = \\mathrm{Re}\\lbrace \\alpha e^{i\\omega_0 t} \\rbrace \\mathrm{,}$$\n", "\n", "where\n", "\n", "$$\\alpha = |\\alpha|e^{i\\varphi} = \\mathrm{Re} \\lbrace \\alpha \\rbrace + i\\mathrm{Im} \\lbrace \\alpha \\rbrace \\mathrm{.}$$\n", "\n", "This means that another set of equally valid parameters to describe the field are:\n", "\n", " 1. The central frequency $\\omega_0$\n", " 2. The in-phase component: $\\mathrm{Re} \\lbrace \\alpha \\rbrace$\n", " 3. The quadrature component: $\\mathrm{Im} \\lbrace \\alpha \\rbrace$\n", " \n", "```{note}\n", "For more on in-phase and quadrature component representation of waves see the [Wikipedia page](https://en.wikipedia.org/wiki/In-phase_and_quadrature_components).\n", "```\n", "\n", "Note that\n", "\n", "$$ \\mathrm{Re} \\lbrace \\alpha \\rbrace = \\frac{\\alpha + \\alpha^*}{2} \\mathrm{,}$$\n", "\n", "and\n", "\n", "$$\\mathrm{Im} \\lbrace \\alpha \\rbrace = \\frac{\\alpha - \\alpha^*}{2i} \\mathrm{.}$$\n", "\n", "To explicitly demonstrate the relation to the field operators, consider the expectation the in-phase and quadrature field operators with a coherent state:\n", "\n", "$$ \\bra{\\alpha} \\frac{\\ahat + \\adagger}{2} \\ket{\\alpha} = \\frac{\\alpha + \\alpha^*}{2}$$\n", "\n", "and\n", "\n", "$$ \\bra{\\alpha} \\frac{\\ahat - \\adagger}{2i} \\ket{\\alpha} = \\frac{\\alpha - \\alpha^*}{2i} \\mathrm{.}$$\n", "\n", "This should now fully connect how the quantum field operators relate directly to the in-phase and quadrature representations of a classical electromagnetic wave of a single frequency. Interferometric measurements using homodyne detection can be performed to directly observe these quantities." ] }, { "cell_type": "markdown", "id": "0a338bef-abc5-4fad-9864-62b28c50f419", "metadata": {}, "source": [ "(basics:mean-and-standard-deviation)=\n", "## Mean and Standard Deviation Observables\n", "\n", "A general concept of note is the determination of mean and standard deviation of an observable, such as photon number or field value. As engineers, we are often just as concerned about noise and its reduction as we are about the signal itself.\n", "\n", "The mean of an observable can be found by taking its expectation given the current state of the system $\\ket{\\psi}$. For example, the mean photon number would be:\n", "\n", "$$ N = \\bra{\\psi}\\hat{N}\\ket{\\psi}.$$\n", "\n", "The standard deviation $\\Delta N$ is found through the relation:\n", "\n", "$$\\Delta N = {\\bigg \\lbrace \\bra{\\psi} \\hat{N}^2 \\ket{\\psi} - N^2 \\bigg \\rbrace }^{1/2}.$$\n", "\n", "Calculation of such quantities are very important as they allow us to determine signal-to-noise ratios in our systems that are critical to their real-world operation.\n", "\n", "```{note}\n", "The approach above follows directly from how such values are obtained for random variables in statistics. For example, see the definitions for [standard deviation](https://en.wikipedia.org/wiki/Standard_deviation) and [variance](https://en.wikipedia.org/wiki/Variance). \n", "```" ] }, { "cell_type": "markdown", "id": "5125da08-cd2b-4d99-b51e-95ac89683fee", "metadata": {}, "source": [ "## Common State Types and Their Properties\n", "\n", "### The number state $\\ket{N}$\n", "\n", "As per its name, the number state contains a well-defined number of photons, such that \n", "\n", "$$N = \\bra{N}\\hat{N}\\ket{N}.$$\n", "\n", "The standard deviation of this photon number $\\Delta N = 0$. \n", "\n", "What can be quite odd about such a state is that despite the fact that the photon number is unrestricted, the average field is always 0. That is:\n", "\n", "$$\\langle \\hat{A}^{(1)} \\rangle = \\langle \\hat{A}^{(2)} \\rangle = 0.$$\n", "\n", "However, the standard deviation of the fields are certainly not zero, with:\n", "\n", "$$\\Delta A^{(\\theta)} = \\sqrt{2N + 1}/2.$$\n", "\n", "So, while these states carry a very well-defined amount of photons, and hence energy ($N\\hbar\\omega$), they carry it in fields of increasing variance having an average value of 0.\n", "\n", "A useful way to visualize quantum fields is to make a two-dimensional plot with $A^{(1)}$ on the $x$-axis, and $A^{(2)}$ on the $y$-axis. In this configuration, $\\theta$ is then the angle going counter-clockwise from the $x$-axis. Then, you mark the region whos center is the mean value of $A^{(1)}$ and $A^{(2)}$ of the state, with a width of $2\\Delta A^{(\\theta)}$ for each value of $\\theta$. This allows a quick visual representation of both the average value and uncertainty of the fields of any given state." ] }, { "cell_type": "code", "execution_count": 11, "id": "8e16ec73-1852-49da-a03f-a745f631099e", "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "application/papermill.record/image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import matplotlib.patches as mpatches\n", "from myst_nb import glue\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot()\n", "\n", "A = 0\n", "phi = 0\n", "delA = np.sqrt(2*4 + 1)/2\n", "\n", "\n", "A1 = A*np.cos(phi)\n", "A2 = A*np.sin(phi)\n", "\n", "\n", "# add a circle\n", "patch = mpatches.Ellipse((A1, A2), \n", " width=delA*2, \n", " height=delA*2, \n", " ec=\"none\", \n", " color='tab:blue',\n", " alpha=0.7)\n", "ax.add_patch(patch)\n", "ax.set_xlim(-5.1, 5.1)\n", "ax.set_ylim(-5.1, 5.1)\n", "\n", "ax.set_xlabel('$A^{(1)}$', fontsize=15)\n", "ax.set_ylabel('$A^{(2)}$', fontsize=15)\n", "\n", "ax.axvline(0, color='black', linestyle='--')\n", "ax.axhline(0, color='black', linestyle='--')\n", "\n", "ax.tick_params(labelsize=13) \n", "\n", "plt.gca().set_aspect('equal')\n", "\n", "fig.set_size_inches(10, 10)\n", "\n", "glue(\"number_state_field_representation\", fig, display=False)" ] }, { "cell_type": "markdown", "id": "3d36b591-3bd7-4f17-8460-d394a1ebcfaa", "metadata": {}, "source": [ "```{glue:figure} number_state_field_representation\n", ":figwidth: 600px\n", ":name: \"fig-number-state-field-representation\"\n", "\n", "Field representations for a number state with $N=4$.\n", "```" ] }, { "cell_type": "markdown", "id": "b2569f26-eaee-4992-82fa-cabb11d36acb", "metadata": { "tags": [] }, "source": [ "### The coherent state $\\ket{\\alpha}$" ] }, { "cell_type": "markdown", "id": "70f14ad9-73de-4b79-a963-b70a30afae67", "metadata": {}, "source": [ "In contrast to number states, classical electromagnetic waves are described as a collection of plane waves that oscillates smothly in time and space. These plane waves have regions of high and low fields that are well defined as a function of phase. There are many applications in quantum optics that use such \"classical\" sources of light (e.g. a continuous-wave laser source), so we need a way to describe it within our quantum framework. For this purpose, we can use *coherent states*. \n", "\n", "We denote a coherent state as $\\ket{\\alpha}$, where $\\alpha$ is a complex number whos amplitude relates to the electric field strength, and whos phase relates to the phase offset of the electromagnetic wave. As with number states, these states can also have other properties, such as polarization and spatial mode. \n", "\n", "An interesting and useful fact is that a coherent state is nothing more than a distribution of number states all added together in a particular way. For instance, a classical state populating the $m^\\text{th}$ mode is represented as:\n", "\n", "$$ \\ket{\\alpha}_m = e^{-|\\alpha|^2/2} \\sum_n \\frac{\\alpha^n}{\\sqrt{n!}} \\ket{n}_m. $$\n", "\n", "We leave it as an exercise to show that\n", "\n", "$$ \\ahat_m \\ket{\\alpha}_m = \\alpha \\ket{\\alpha}_m, $$\n", "\n", "and\n", "\n", "$$ \\bra{\\alpha}_m \\adagger_m = \\alpha^* \\bra{\\alpha}_m. $$\n", "\n", "This makes working with coherent states very easy, so long as you put all expressions in \"normal order\", meaning annihilation operators always come before creation operators when multiplied out.\n", "\n", "```{important}\n", "Remember as we discussed above that quantum operators do not necessarily commute. In particular, the creation and annihilation operators do not commute. This means that we cannot simply move the annihilation operators to the left of creation operators. \n", "\n", "So how do we put things in normal order? We take advantage of the commutation relation\n", "\n", "$$ [\\ahat, \\adagger] = \\ahat\\adagger - \\adagger\\ahat = 1. $$\n", "\n", "For example, take \n", "\n", "$$\\hat{N}^2 = \\adagger\\ahat\\adagger\\ahat = \\adagger\\ahat + \\adagger\\adagger\\ahat\\ahat,$$\n", "\n", "where we have used the commutation relation to achieve the final expression in normal order.\n", "```\n", "\n", "By using the relations above along with normal ordering of the annihilation and creation operators, it is easy to then show that the average photon number of a coherent state is\n", "\n", "$$ N = |\\alpha|^2, $$\n", "\n", "and that the the standard deviation of the photon number is\n", "\n", "$$ \\Delta N = |\\alpha|. $$\n", "\n", "It turns out that the photon number distribution is that of a poisson distribution, which is consistent with such a relation between the mean and standard deviation. \n", "\n", "We can likewise use the above properties to show that\n", "\n", "$$ A^{(\\theta)} = |\\alpha|\\cos(\\varphi - \\theta), $$\n", "\n", "where $\\varphi = \\arg{\\alpha}$. Also,\n", "\n", "$$ \\Delta A^{(\\theta)} = 1/2.$$\n", "\n", "The last part is interesting as it means that no matter how large alpha is, the field fluctuations stay the same, and are the same level as that of a vacuum state. This is due to the fact that phase is very well defined for a coherent state. Thus the photon contribution to the field is very well-defined, leaving only the remaining vacuum field fluctuations. This is in spite of the fact that the number of photons actually varies. Compare this to a number state where there is no fluctuation in the number of photons, but the field fluctuates heavily on top of the ever-present vacuum fluctuations.\n", "\n", "Again, it we can map out the field representation, which we have done below for a coherent state with $|\\alpha| = 4$, and $\\varphi = \\pi/4$.\n", "\n", "[//]: # \"FIXME: Add in a figure that shows the coherent state as a function of $\\theta$ vs. a number state having the same average numer of photons N.\"" ] }, { "cell_type": "code", "execution_count": 8, "id": "9f99c042-bde0-44f3-a62e-cf641976a499", "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "application/papermill.record/image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import matplotlib.patches as mpatches\n", "from myst_nb import glue\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot()\n", "\n", "A = 4\n", "phi = np.pi/4\n", "delA = 1/2\n", "\n", "#Determine projection onto A1 and A2 for center\n", "A1 = A*np.cos(phi)\n", "A2 = A*np.sin(phi)\n", "\n", "# add a circle\n", "patch = mpatches.Ellipse((A1, A2), \n", " width=delA*2, \n", " height=delA*2, \n", " ec=\"none\", \n", " color='tab:blue',\n", " alpha=0.7)\n", "ax.add_patch(patch)\n", "ax.set_xlim(-4.1, 4.1)\n", "ax.set_ylim(-4.1, 4.1)\n", "\n", "ax.set_xlabel('$A^{(1)}$', fontsize=15)\n", "ax.set_ylabel('$A^{(2)}$', fontsize=15)\n", "\n", "ax.axvline(0, color='black', linestyle='--')\n", "ax.axhline(0, color='black', linestyle='--')\n", "\n", "ax.tick_params(labelsize=13) \n", "\n", "plt.gca().set_aspect('equal')\n", "\n", "fig.set_size_inches(10, 10)\n", "\n", "glue(\"coherent_state_field_representation\", fig, display=False)" ] }, { "cell_type": "markdown", "id": "dd82186b-3e9f-452a-9a61-5411cad0064c", "metadata": {}, "source": [ "```{glue:figure} coherent_state_field_representation\n", ":figwidth: 600px\n", ":name: \"fig-coherent-state-field-representation\"\n", "\n", "Field representations for a coherent state with $|\\alpha| = 4$, and $\\varphi = \\pi/4$.\n", "```" ] }, { "cell_type": "markdown", "id": "856111c4-6112-4d6c-8f03-a705edaec4a4", "metadata": { "tags": [] }, "source": [ "(sec:quantum-optics-basics:squeezed-states)=\n", "### Squeezed States" ] }, { "cell_type": "markdown", "id": "19db3978-0553-443c-a0ac-840890f27d30", "metadata": {}, "source": [ "You might have heard of squeezed states. Such states exhibit very interesting noise properties. While there are more rigorous ways to develop notation for generalized squeezed states, lets use a simple example constructured from the vacuum state in addition to a two-photon number state:\n", "\n", "$$ \\ket{\\psi_s} = \\sqrt{1 - s^2}\\ket{0} - s\\ket{2}.$$\n", "\n", "Using the properties of number states, you can show that the mean field is\n", "\n", "$$ A^{(\\theta)} = 0, $$\n", "\n", "and that the standar deviation of the field fluctuations is\n", "\n", "$$ \\Delta A^{(\\theta)} = { \\bigg \\lbrace 1/4 - s \\sqrt{\\frac{(1 - s^2)}{2}} \\cos(2 \\theta) + s^2 \\bigg \\rbrace }^{1/2}.$$\n", "\n", "Note that unlike in past cases, the field fluctions are now a function of $\\theta$. In fact, they are reduced in one quadrature, while increased in the other quadrature in general. \n", "\n", "It can be useful to look at a field represenatation for a couple of values. Let's say $s = 0.25$ and $s=0$." ] }, { "cell_type": "code", "execution_count": 12, "id": "dcec68ff-01b1-45e6-bea1-7e40caf218d0", "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "application/papermill.record/image/png": 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FvkMITGtXr57ZWKeLjp3pOxQgJ5DMAfBm/e4mbT3Q7juMQLzn8k/4DiFQ63c3a+nMcs2fVuo7FCDyaGYF4EVbV6+e2Zg7zavdnR3q7sytfoFPvLk/J2pdAd9I5gB48WSO9av6/m3X6/u3Xe87jEA1d/To+c25k7ADvpDMAQjc2/sY8ZgrXtvRGNmJoIFsQTIHIFBdvX36/Yb9vsNAQJyTnnhjnxIRu9cukE1I5gAEavXWBrV15U7zKqSDbd1at6vJdxhAZIUqmTOzuJl908zqzKzFzB4ys+ph1j3fzJyZtQ54vDBonaPM7AkzazOznWZ2UzBnAuSm5s4evbq9wXcY8GDVlnp19ZLEA5kQqmRO0hckfUjS6ZLmpJbdN8L6fc65sgGPs/oLzCwu6RFJb0qqkXS5pL8zs2syEzqAFzbV5+wtu0696EqdetGVvsPwpr27T6u3ksgDmRC2eeaul/QV59wWSTKz/yVpk5ktcM5tHee+zpU0X9Itzrl2Sa+Y2fck/Y2kB9IYMwBJ+1s69dbeZt9heHPaRVf5DsG7V7c36Pg5laooyvcdChApoUnmzKxS0jxJa/qXOec2m1mzpBMkbR1is7iZ7ZCUn9ruVufca6myEyVtdM4NHFL3iqT/moHwgZz37MYDcjlQKRfr6Va8u0tKJGQu+VDCqa2pQZJTWcUUOTMpFpOz2KG/ewuK5PKjneT09Dm9sKleFx/HnSGAdApNMiepIvXv4F60jQPKBnpL0nJJ6yWVSfo7SU+a2fHOud2SysexL5nZ9UrWDGrevHnjDh7IZVsPtGn7wXDf6SHW3aW8rg7FOzuS/3Z1Km/g310dind1KNY3dL+wW3/+I0nS7R/91LDHSMTz1FdYpN6iYvUWFquvsHjA30XJf4uKlcgvyMg5BuGtvc06eX6VppcX+Q4FiIwwJXMtqX8rBy2vknRY241zbq+kvamnjZJuMbOPSPqApB+m9jemfaX2d4+keySptrY2B+oXgPR5YXO97xDGLtGnwpZGFTYdVGFTg4qaDiq/tVmxROY778f6ehVrb1V++8hz8CXieeour1RXxVR1Vk5VV+UUdZdVSrHs7wbtnPTi5np9aPls36EAkRGaZM4512hm2yWdLGmtJJnZIiVr0taNcTcJSZb6+zVJS8ys1DnXllp2Umo5gDTZtL9F+5o7fYcxtCESt4LWJlkiu29BFevrVVFjvYoa6w/9Ik3E4uquqApFgrelrk17mjp0RGWx71CASAhNMpdyj5IjTn8vqV7SP0r6zVCDH8zsfZK2S9oiqUTSzZJmSPpNapVnJG2TdLuZfUHSUkk3SPrvGT4HIGc45/RiFtXKWW+PSg7sVcmBvSpqrA9F4jZWsUTfsAleZ+U0tdccoY5pM+Tica9x9nthU70+fMqc0VcEMKqwJXPfkDRF0suSCiX9TtK1kmRmn5D0PedcWWrdEyX9SFK1pDYlBze83zm3Q5Kcc31mdpmk7ymZGDZK+qZz7meBnQ0QcRv2tehAa7fXGOKd7Srdv0ul+3apuH5/IM2l2WJggle1baMS8Ty1V89U24zZaps+W4mCQm+xbT/Yrh0H2zV3aom3GICoMJcLw8vSrLa21q1evdp3GEBWSyScfvziVjW09wR+7ILmBpXu26XS/btU2NQgk//PuWc3vC5JOmfpcZ4jSXIydU6pPpTY9ZQNOfYro2ZXFevqU+cGflwgjMxsjXOudqiysNXMAQiJN/Y0B5fIJfpUUr9fpft2qWT/LuV3Zt/I2WxJ4vqZnIob6lTcUKfqt9aqu7Rc7dNnqW36bHVMqQmkr92uxg5tPdCmBdWlGT8WEGUkcwAyIojbduW1t6py+yaV79yivO6ujB9vMupakjMh1ZQPHkSfHQraWlTwzgZVvbNBPUUlap53lJrnLlJfYWYHKazZ1kAyB0wSyRyAtNtW35a5vnLOqaRujyq3v62S/Xuyogl1LP758V9KGnmeuWyR39muaRvXaeqm19U6Y46a5i9W59TpGTnW9oPtOtDapeoyf/33gLAjmQOQdq9ub0z7PmPdXarYuUWV2zeNOg8b0sMSCZXv2a7yPdvVVVappvmL1TJrQdrvVPHq9ka9f9mMtO4TyCUkcwDS6mBbt7bWt42+4hgVNhxQ5fa3VbZnR06NRM02ha1Nmr5+tao3vKaWWQvUNP8odZdXpWXfb+1p1tlHVau4IDumTQHChmQOQFqt3dEw+XuwOqfyXVtVtXWDCpsz3/cOYxfr7VHl9rdVuf1tdUytUeOCo9U2c3LzxfUmnNbtbNTpi6alKUogt5DMAUibzp4+vbmnZfQVR1C6b6emblinwtbBt05Gtik+WKfig3XqrJqm+qUnqmPaxJtK1+1sUu2CqYrHbPSVAbwLyRyAtHl9V5O6eyd2R4Wig3WatuE1FTfUpTmq7HDFKWf5DiFjihrrNXvVk2qrOUL1S09Ud8WUce+jtatXG/e16Jgjgp/vDgg7kjkAaZFIOK3d0Tju7QqaGzVt42sq3b87/UFlkdMWLfUdQsaV1u1RSd1etc6ap/olJ6i3pGz0jQZ4dXsjyRwwASRzANJiU12rWjp7x7x+Xnurpr79R5Xv2haa6UUmY+fBA5KkOVOrPUeSWSan8t3bVLZ3h5rmHqmGo44d81x1+5o7tauxQ7OrMju3HRA1JHMA0mKskwTHuzo1ZdN6Ve7YFJmb3I/FXSsfkRSOeebSwRIJVW17WxU731HjgqVqWHTMmKY0eXV7A8kcME4kcwAmbW9Tp3Y3do68knOq3LZR0zb+UbHe4O/XCj9ifb2aujmZvB84+iS1zFk44vqb97epqaNHlcXpncsOiLLM33wPQOS9MkqtXH5bi2avWqmaN14hkctR8e4uzVj3Bx2x+hnFR7h3bsI5vTaBvpdALiOZAzApLZ09envfMHdkcE6V72zQ3OdWqPhgNEepYnxK9+/SvGdXqHznO8Ou8/ruiY+KBnIRyRyASXlzT4sSQ8wSfKg27s1XFOvjzg34k3hP94i1dF09CW3azy3bgLGizxyASdmwt/ndC/r7xm14jSRugKtPP9d3CFknWUtXpwPHnHxYX7q39jZr2SymKQHGgmQOwITtb+nUgdbuQ8/z21o0/Y+raFIdwvJ5R/oOISv119KV7d2h/cfVqq+oRJK042CH2rp6VVrI1xQwGppZAUzYW/237nJOlVvpGzeSLfv3aMv+Pb7DyFqD+9IlnNOGfZO7NRyQK0jmAEyIc04b97XIenp0xJpnkyNVaVYd1g+eflw/ePpx32Fktf5auunrVkmJvj/9WAAwIuqvAUzIzoYOdRxs1JzVz6iwtcl3OIiQip1blN/WrL0nn62DbTM1tbTAd0hAVqNmDsCEbFy7QXOf/w2JHDKiuOGA5jz/W214Y4vvUICsRzIHYNxaX12rrhWPKt7TPfrKwATld7ar+ZcPq3PjRt+hAFmNZA7AmLm+PrU8+Xvt/M1K9TGpKwLQ3dmt3f/v12p78UW5IeYzBECfOQBjlGhvV/OKx9Wze7fqW6mRG6/r3nOB7xBCq761W+Wr16i3/qDKL3q/YgX0oQMGomYOwKh66+rU8OCD6tm9W72JhBrbSebG65hZ83TMrHm+wwil+rYuOefU/c47avzFL9TXRD9NYCCSOQAj6tq8WY0P/VKJluTtlQ62ditBa9e4vbl7u97cvd13GKHU0+fU2NEjSeqrP6iGBx9U985dnqMCsgfJHIBhdb71lpoff1yup+fQsgOtXR4jCq/7nl+p+55f6TuM0KofcN25zi41P/Kf6t661V9AQBYhmQMwpI7X16vliZUaWA3X1dun5s5ej1EhVx1s61bfgGvR9fap6bHH1LWFqUsAkjkAh+l47TW1PvWUNGj0YEMbfeXgR8JJjR2Drr++hJpXrFDX22/7CQrIEiRzAN6l/ZVX1frMs4clcpIO9VsCfGhsH+L6Szg1//a36nzrreADArIEyRyAQ9pfeVVtzz8/ZFmfc2ommYNHTUMlc5KUcGp5YqU6N2wINiAgSzDPHABJUse6dcMmcpLU3NHDKNZJ+KvzLvYdQuh19yXU1t2r0oIhvrqcU8sTT8jicRUedVTwwQEekcwBUMfr65NNqyNoolZuUhZNP8J3CJHQ1N4zdDInHWpyrYjFVbhoYbCBAR7RzArkuM633hpysMNgTBQ8OWu3b9ba7Zt9hxF6DaNdh30JtfzmcXVv2xZMQEAWIJkDcljXlnfUsnLlqIlcZ0+fOnu4F+tkPLjqGT246hnfYYRea2evehMjX4uut0/NK1aoZ8+egKIC/CKZA3JUb329Wn73O42lIxy1csgWTmNr8nc9vWp+bIX6WlszHxTgGckckIMSHR1q/vWv5brHlqQxJQmyybCjWgdJtLer+dePvesOJkAUkcwBOcYlEmp+/Dfqa2oe0/oJpiRBlhnPj4ve/fvVsvLJDEYD+EcyB+SYtmefVc/OnWNenylJkG26e5NTlIxV19tvq3316gxGBPjF1CRADul4fb061v1xXNvQxJoen73gMt8hRMqIU5QMoe0PqxSfOo0pSxBJ1MwBOaJn1y61PvP0uLdj8EN6zJlarTlTq32HERnjvi6dU8vvfqfegwczExDgEckckAP6mpvV/PjjUt/4phdhSpL0eWnLBr20hdtNpUvLGKYoGcx1d6v50V8r0dmZoagAP0jmgIhz3d1qfuwxJdo7xr0ttXLp86s1L+hXa17wHUZkOGlCA3P6mprU/PjjcuNMBIFsRjIHRFzLypXqrTswoW2bO8feyRwIWnPHxK7Pnh071fbcc2mOBvCHZA6IsM433lDXponfQqqVZA5ZrKVr4tdnx2vruOUXIoNkDoiovtZWtT73/IS37+ztU/c4+9gBQWrv7lXfKLeiG0nLk79XYowTZwPZjGQOiKjWJ5+U6+qa+PbUyiHLOSe1TaJ2LtHaSnMrIoF55oAI6nzjDXVv2z6pfbRO4ksSh/v8xVf5DiGSWjt7VVGUP+HtO9e/ocIjj1TB/PlpjAoIFjVzQMRMtnm1HzVz6VVTXqma8krfYUROOn50tDz5eyUmUYsN+EYyB0TMZJtXpeT9WMdzuySM7tkNr+vZDa/7DiNyWjonf4cSmlsRdiRzQISko3lVStZ2TKJfOYawYt3LWrHuZd9hRE5Pn1Nnb9+k99P5xpuMbkVokcwBEZGu5lVpcp3KgaClq0sAza0Iq1Alc2YWN7NvmlmdmbWY2UNmNuTNDs3sEjN70swOmFmDmT1rZucMWseZWbuZtQ540KkFoZSO5tV+LfSXQ4ika7AOza0Iq1Alc5K+IOlDkk6XNCe17L5h1p0i6TuSjpJUI+k/JK0ws7mD1rvIOVc24NGUgbiBjEpX82o/Bj8gTNJ5vdLcijAKWzJ3vaR/dM5tSSVd/0vSxWa2YPCKzrmfOOceds41Oud6nXN3S+qQVBtsyEBmue5utb34Ytr218VkwQiZtu5eJdLYybP12ee4dytCJTTzzKWaP+dJWtO/zDm32cyaJZ0gaeso258gaZqkwcPJfm5m+ZI2K5ko/jKdcQOZ1v7qWiXaO9K2P+aXy4wvXHq17xAiy7nkdTuZ+eYG6mtoUOebb6r42GPTsj8g08JUM1eR+ndwM2jjgLIhmdl0Sb+Q9E/OubcHFF0oaaGSTbbflvQTM7t4mH1cb2arzWx1XV3dBMIH0i/R3q6OtWvTuk/6y2VGRXGpKopLfYcRWeketNP+0styPZOf9gQIQpiSuZbUv4MHKFRJah5uIzObJen3kn4r6ZaBZc65lc65ztTjAUn3S/rEUPtxzt3jnKt1ztXW1NRM8BSA9Gpfs0YuzfeWpL9cZqxc/6pWrn/VdxiRle4fIYnWVnX88Y9p3SeQKaFJ5pxzjZK2Szq5f5mZLVKyVm7dUNuk+tI9K2mFc+5zzo3aqSIhydIRL5Bpfc3Naf+yYbLgzFn5xlqtfGOt7zAiKxPdA9rXrGGqEoRCaJK5lHsk/Z2ZLTSzCkn/KOk3zrmtg1c0s6MlPSfpp865m4coP87MTjOzAjPLN7MrJF0n6cGMngGQJm2rVklpHqjQ0dPHZMEIpe7ehHrTPGjBdXapY82a0VcEPAtbMvcNSY9IelnSLklxSddKkpl9wsxaB6z7d5JmS7px0Dxy/c2oNZJ+JKlB0n5Jt0n6tHPuP4M5FWDieg8cUNeGjWnfb2fP5GfSB3xp707/9duxbp36WtvSvl8gnUIzmlWSnHN9km5OPQaX/UTSTwY8/5SkT42wr99LYqgSQqntxT8oE1VoHRn4MgSC0tndl7YRrf1cT6/aX35J5e99b1r3C6RT2GrmgJzXs3u3urduzci+SeYQZh0ZqlnufOMN9TY0ZGTfQDqEqmYOgNI6QfBgmfoyhPT3Vww5UB5plLHrN+HUvmqVKi4ecuYqwDtq5oAQ6d62TT2792Rk3845krkMKswvUGF+ge8wIi0Tfeb6dW3arF7mGEWWIpkDQqRj3ZCz8KRFZ2+CkawZ9NhrL+mx117yHUakdfcm1JfI0EXsHPPOIWuRzAEh0dfUpO5t2zO2f/rLZdZzG9fruY3rfYcReZmsXe7auJF555CVSOaAkOh4/fWMjGA9tH+aWBEBHRmc9Nr19KrrzTcztn9gokjmgBBwvZn/EsnklyAQlI6e9E4cfNj+//i6Rr+ZEBAskjkgBLrefluJjs6MHiPTX4JAEDL9o6SvsVE9O3dm9BjAeJHMASGQ6Y7XTo67PyASgugu0MlACGQZ5pkDslzPvv3q3bc/o8foyuQoQEiSbv/osDekQRp19SSUcE4xs8wd45131NfaqnhZWcaOAYwHNXNAlut8PfO1AIxkRVQ4BVA7l3DqfJ2RycgeJHNAFkt0danr7bczfhyaWDPv4TXP6+E1z/sOIycE8eOk84035Pp43yA7kMwBWazzjTfkejI/ypSaucx7ectGvbxlo+8wckIQ/eYSbW3q3rIl48cBxoJkDshinevfCOY4vYxkRXR0BVTT3EFTK7IEyRyQpXrr69XX0BDIsXpI5hAh3X3BDObp2b1LiY6OQI4FjIRkDshS3e+8E9yx+kjmEB3dvQF1G0g4dW/dGsyxgBGQzAFZqiugZK43wbQkQSjIy1dBXr7vMHJCd4A1zUH+6AKGwzxzQBZKtLVlfG65fkF+8eWyL115re8QckbCJX+k5MUyX1/RvX2HXG+vLI+vU/hDzRyQhbq2bpUCuv8jTayIoqB+pLieHm7vBe9I5oAs1P3O1uCORc1cIH626mn9bNXTvsPIGUFe10F1iQCGQzIHZJnkL/0dgR2PZC4Y67Zv0brtzEsWlCBrnLu3bgvsWMBQSOaALNO9Y2cgEwX366GZFREU5I+URGurevYH08cVGArJHJBlurcG22RDzRyiKOjrOsiuEcBgJHNAFnHOBf6l0EUyhwgKemAPU5TAJ8ZSA1mkd98+JdrbAz0mzazBKC8u8R1CTgm6Zq63rk59ra2Kl5UFelxAIpkDskrPjuAGPkhSwjn1BHTro1x3y6XX+A4hp/iYcqdn+3bFly0L/LgAzaxAFgm6EzX95RBVvX1OiYDmajx0zLq6QI8H9COZA7JI0F8GTBgcnH9/7gn9+3NP+A4jpwT9Y4URrfCFZlYgSyTa25VoaQ30mNTMBWfDnmCb0JH8sVKUHw/seH319XKJhCyA24gBA3HFAVnCRxMNgx8QZUH/WHE9veo7eDDQYwISyRyQNXo9NNH0Jhj8gOjq83B9+3gfAyRzQJbw0d/Gx5cdEBQvyRyDIOABfeaALOHjS4BkLjjTyit8h5BzfFzfDIKADyRzQBbwMfhBIpkL0k0Xf9h3CDmnL+CpSSQGQcAPrjYgC/hqmiGZQ5T5uL4ZBAEfSOaALOCr03TQk6rmsu8/tULff2qF7zByiq8fKwyCQNBoZgWyADVz0fdO3V7fIeQcb8kcgyAQMGrmgCzQ29Dg57gkc4gwb8mcp/czchfJHJAFEm3tXo5LzRyizMcACElKtLV5OS5yF8kc4Jnr6ZHr6vJy7ATJHCLM148VXz/OkLvoMwd4lmj3VCvnnEjlgjNryjTfIeQcX8mc6+qS6+2V5fEVi2BwpQGe+WqSoYk1WJ+78HLfIeQcnzXPibY2xSsrvR0fuYVmVsAzkjkgM5x8NrXSbw7BIZkDPPPWzEoyF6j/+8R/6v8+8Z++w8g53gZBeHpfIzeNuZnVzGZLmi2pQ9JG55yfHttAxFAzlxt2N9T7DiEn9SWcFA/+uNTMIUgjJnNmViHpv0n6i9SifZKKJc0xsz9IutM59/vMhghEW5+vZI67PyAH0MyKXDBazdwKSf8u6Qzn3KGflWZmks6Q9GkzW+ycuyeDMQKR5jw1xzAtCXKBt2SOZlYEaLRk7hznXGLwQueck/SipBfNjH53wCT4qplz1MwhB/iagIeaOQRpxETMOZcwsyvN7L+Z2dKBZWb2uf51MhkgEHW+PvRJ5YK1sGamFtbM9B1G7vF0ofv6kYbcNFqfuX+UdLqkdZJuNrNvO+fuTBV/WtL/zWx4QPS5rm5PB/Zz2Fz11+d/wHcIOcnXZe46GSOI4IzWzHqJpJOcc71m9mVJPzez2c65/ynJMh8eEG0ukZA8NXeSywEZRKMVAjRaf7eYc65XklIDIC6WtMDMfjiGbQGMJsEHfq741uMP6VuPP+Q7jJzjq2uo472NAI2WkO0xs5P7nzjnuiVdo+SP+uMyGdhQzCxuZt80szozazGzh8yseoT1Lzaz9WbWYWavm9lFg8qPMrMnzKzNzHaa2U2ZPwvgT3x+4FMzF6z6lmbVtzT7DiMH+eo0RzKH4IyWzH1S0u6BC5xzCefcX0k6J1NBjeALkj6kZD++Oall9w21opktkvRLSV+XVJn692EzW5Aqj0t6RNKbkmokXS7p78zsmgzGD7ybz1/vjGZFDvB2ldPMigDZSNMTmFmJc27EyXLGsk66mNk2SV9xzv0w9fxISZskLXTObR207pclvc85d86AZc9KesI592Uze6+kX0ua7pxrTZV/VdLZzrn3jhRHeXm5O+WUU9617Oqrr9ZnP/tZtbe365JLLjlsm09+8pP65Cc/qQMHDugjH/nIYeWf+cxndM0112jHjh267rrrDiu/6aabdNlll2nDhg264YYbDiu/7bbbdOGFF2rt2rW68cYbDyu//fbbddZZZ+mFF17Qrbfeelj5nXfeqeXLl+uJJ57Q1772tcPKv/e972np0qV65JFH9K1vfeuw8vvuu09z587VAw88oLvvvvuw8l/84heqrq7Wvffeq3vvvfew8scee0wlJSW666679OCDDx5W/tRTT0mS7rjjDj366KPvKisuLtaKFSskSV/96le1cuXKd5VPmzZNDz2UbN665ZZb9OKLL76rfM6cObr//vslSTfeeKPWrl37rvIlS5bonnuSUylef/312rhx47vKly9frjvvvFOSdO2112rnzp3vKj/zzDP19a9/XZL04Q9/WPX1A+4EkEjojPIK3XTxxZKkj919lzp7et61/fuPPU7/9YILJElX/J9/0WCXn3SSPn3OuWrv7tZ/+e7h//cfO/10fez0M1Tf2qq//LcfHlre3ZtQZ0+fPnDCqTpn6XGqa2nSPz/+y8O2v+KUs3TaoqXaefCA7lr5yGHlV59+rpbPO1Jb9u/RD55+/LDy695zgY6ZNU9v7t6u+55feVj5X513sRZNP0Jrt2/Wg6ueOaz8sxdcpjlTq/XSlg361ZoXDiv//MVXqaa8Us9ueF0r1r18WPkXLr1aFcWlWrn+Va18Y+1h5X9/xSdUmF+gx157Sc9tXH9Y+e0f/ZQk6eE1z+vlLe9+7Qvy8vWlK6+VJP1s1dNat33Lu8rLi0t0y6XJ34ef/sG31d7dpUUDRrROK6/QTRd/WJL0/adW6J26ve/aftaUafrchZdLSt4ObPBdJBbWzDw0sOJbjz90WM3f0iPm6i/OvlCS9PVHH1BLx7s/qk+Yt0gfO/08SdKXHr5f3b3vvvZOXbREV57yHknSrT//0WH/N2cvOVaXnHiaunq69eVf/eSw8guWLdcFx56k5o42fePRw9/XQVx7l5+0TJv37dLtjx6+/Vev+rCOnzNHT294S//8m98cVn7HNR/TUTNm6Dd//KPu/v2Th5X/63V/rtlTpuhXr6zRvc89d1j5/3vxRT73NMTnnqQLLrhAX/ziFyVJH/jAB9TR0fGu8ksvvVQ333yzJOn888/XYLn4nfv000+vcc7VHrayRq+Z+62ZfdnMjk9NFCxJMrMqM/uwmT0q6cpR9pEWZlYpaZ6kNf3LnHObJTVLOmGITU4cuG7KK6nl/eUb+xO5IcoHH/96M1ttZqt7Bn3ZAhNG7RiQUbzFkAtGq5mLS7pW0qeUTHJaJRVK6pT0n5K+45zbEECcMrO5krZLWuSce2fA8m2S/j/n3P2D1l8p6Tnn3N8PWPZlSe9xzl1oZl+UdKFz7rwB5e+V9Dvn3IijfGtra93q1avTcl7IbYmODtX/4Iejr5gBe5o6tK2eWeqD8u/PPSFJh2rKEIzFM8o0rbQw+APHY6r57GeDPy4iy8yGrZkbMWlxzvUpeTuvfzezPEnVkjqcc03pD3NULal/Kwctr1Kydm6o9Udad7RyIPNi/gaFM7dQsEji/PB1nZvH9zZyz5ivNudcr3Nur6dETs65RiVr5g6Nrk0NcqhQclLjwV4buG7KSanl/eVLzKx0mHIg4wb0XsipYwPB8XSdc6dLBChsV9s9So44XWhmFZL+UdJvBg9+SPmxpFoz+7iZ5ZvZxyWdomRNoyQ9I2mbpNvNrNjMlku6QdL3Mn0SwCH8es8ZX3/0AX390Qd8h5F7fP1mifFjCcFJ6zeJJR2Vzn0O8g0lpxN5WdIuSf19+mRmnzCzQ4MZUoMjrpJ0m5JNp7dJurI/8Us1IV+m5Hx59ZIek/RN59zPMhg/8G7xuLdD81UTrJaO9sNGkyLz/DWz+ntvI/eMdjuvYZnZfCUToWNTj+MkHS2pSMkkK+1SCdjNqcfgsp9I+smgZY9LOny8+p/KN0m6IM1hAmNmZlI85meCUbI5IGMsj2QOwRlTMmdmf6Z3J23HSCrVn74OnKRVSjaDHj5RE4BhxYpLlGhtHX1FAOPmrWauuNjTkZGLxlozt0LJhG2nksna95W8c8KbkvYoOXHvF5xzh8/4CWBEsVI/yRwVc8gFvgb6xEpLR18JSJOxJnNPSnqfpHZJP3TOHbpbdGoyXwAT5OtDP0YH7UCdMG+R7xBykq9B2yRzCNKYBkA45y6UdKGkJkkPmtkqM6OvGZAGsZISP8dlapJAfez08w7dOgvBiXv60eLrfY3cNJ555p50zp0h6SOSypS81dcTkk7LVHBALvD1C97XlxwQJG/JHDVzCNC4pyZxzj2s5CCIT0tapORoUSepJr2hAbmBZC43fOnh+/Wlh+8ffUWkVdxTDXScZA4BmtA8cy7p3yUtlXSjpP2SfmZm3zWz6WmMD4g8X80xJHPB6u7tUXdvj+8wco6v69xoZkWAJjVpsHOuxzn3HUlHSvqSpGskbUxDXEDO8FUzl0cyh4iLmb++odTMIUhpuQOEc67dOfcPSja7fjcd+wRyha8PfQZAIOq81T7HjJo5BCqtt/NyzjU4576Qzn0CUWclJV7u4xgz4/aRiDRfP1hiJaXe5rdDbprw7bwApIeZJe8C0dYW+LHjMVOizwV+3Fx06qIlvkPIOUxLglxBMgdkgVhZqbdkrodkLhBXnvIe3yHkHG/JXBn95RCstDazApiYvGo/M/swohVR5muQj6/3M3IXyRyQBfJq/Hz4MwgiOLf+/Ee69ec/8h1GTvH1YyVvOskcgkUyB2SBvOl+pmdkehJEma8fK3k1TLeKYJHMAVkgr3qaFA/+7UgzK6LMx/UdKy1VnD5zCBjJHJAFLB5X3tRpgR+XZA5R5uP69tVlArmNZA7IEj6aWknmEGVekjlPXSaQ25iaBMgSPn7R+7oJeS46e8mxvkPIOX6SOWrmEDySOSBL+PhFn+ehn16uuuTE03yHkHN8XN8MfoAPfJIDWSJv2tTAB0EU5PEREJSunm519XT7DiOnFAb8fmLwA3zhkxzIEpaXF/ggiAJq5gLz5V/9RF/+1U98h5FT8gP+scLgB/jCJzmQRYJuaqVmDlFlJuXHg+0zx+AH+MInOZBF8mYE+2WQFzcxBgJRVBCPyRTsxZ0/c0agxwP6kcwBWaRg/gIFmV2ZjKZWRFLQtc6Wn6/82bMDPSbQj09xIIvEy0oDn9qAplZEUdA/UvLnzpHlMUEE/ODKA7JM4cKF6t23P7DjkcwF44Jly32HkFOCvq4LFy4M9HjAQCRzQJYpWLhQbX9YFdzxaGYNxAXHnuQ7hJwSaDJnpoIFC4I7HjAIn+JAlsmrrla8ojyw41EzF4zmjjY1d7T5DiNn5Af4IyV/5gzFSkoCOx4wGJ/iQBYK8lc+yVwwvvHog/rGow/6DiNnBHldF9DECs/4FAeyUJBfDkHWYABBCbL7AMkcfONTHMhC+bNnywoKAjkWNXOIoqCu63hlpfKmTg3kWMBw+BQHspDF4yqYPy+QYzEAAlGTHzfFApqvkVo5ZAM+xYEsFdSXRMws8NseAZkUZNcBkjlkA6YmAbJUwfz5UsykhMv8sfJi6unry/hxctkHTjjVdwg5ozCgJlYrKlT+rCMCORYwEpI5IEvFiopUMH+But95J+PHKojH1CaSuUw6Z+lxvkPIGUH1lytcvFgWo4EL/nEVAlms+PhgEoCi/Hggx8lldS1Nqmtp8h1GTgjqei4+/vhAjgOMhmQOyGL58+YpXlWV8eMUF5DMZdo/P/5L/fPjv/QdRk4oDiCZy581S3nTpmX8OMBYkMwBWczMVHTcsRk/DskcoiSI67kooFpzYCxI5oAsV3TMMbL8zHZvDaImAwhCPGYqzMvs9RwrKVHhkUdm9BjAeJDMAVkuVlSkwsWLM3qMvFiM+eYQCUH0lys6dpkszg8gZA8+vYEQKDou8x2taWpFFGS8ljlmKjo2810fgPFgahIgBPJnTFfejOnq3bc/Y8coLoirqaMnY/vPdVeccpbvEHJCSYZ/lBQsWKB4eXlGjwGMF8kcEBLFxx+vln0rM7d/+s1l1GmLlvoOIScUZTiZYzoSZCOaWYGQKFy8WFZUmLH9M9dcZu08eEA7Dx7wHUbklWTwOo5XVSl/7tyM7R+YKJI5ICQsL09FxyzL2P4z3TyV6+5a+YjuWvmI7zAiLWaZvZVX0XHHyoz7GCP7kMwBIVJ84gmyDE27kB+PKS/OFxXCqyg/nrFky4oKVbQscz+mgMkgmQNCJF5entGRrfSbQ5hlckR2ySm1ihVmrpsDMBkkc0DIlNSeIisoyMy+aWpFiGXqx0isvEzFJzDwAdmLZA4ImVhxsUpOPikj+2YQBMIsUzVzpaedJstj8gdkL65OIISKTzxRHev+qER7e3r3S81cxlx9+rm+Q4i8TNTMxadOUeHRR6d9v0A6UTMHhJAVFKjk1Nq075c+c5mzfN6RWj6P+3lmiikzNculZ54pi/FViewWiivUzErM7N/MrMHMGs3sh2ZWPML6f25mL6TWP2BmK8zs+AHlC8zMmVmbmbWmHjuDORsgPYqOPVbxysq07rMwL658RrRmxJb9e7Rl/x7fYURWSWFcsTSPZM2bOUOFixaldZ9AJoQimZP0L5KOTj2WSDpG0rdHWL9c0t9LmiNptqRXJP12iARwqXOuLPWYk/6wgcyxeFwlp5+e9v2WFdL7IhN+8PTj+sHTj/sOI7Iycd2Wnskt2BAOWZ/MpRKwayV90Tm3zzm3X9IXJf2FmRUNtY1z7l+dc79zzrU557ok3S5pppLJIBAZhUsWK6+mOq37LC/KT+v+gCCUFab3ui1YMF8Fc2andZ9ApmR9MidpqaQiSWsGLHtFUrGStXRjcYGkdkmbBi1fZWZ1ZvaUmZ0/0g7M7HozW21mq+vq6sZ4WCCzzEylZ56Z1n2WUjOHECovSuN1a6bSM85I3/6ADPOazJnZvam+a8M9vqZkk6kkNQ3YtP/vijEcY4mkH0i6yTnXklp8QNKZkhZKWiDpIUkrzOyE4fbjnLvHOVfrnKutqakZ13kCmVQwf77y56Svl0BZUZ7oNYcwyYtbWgc/JGu8+ZxHePiumfucpJoRHrdL6k/ABvb07v+7eaSdm9kySb+XdIdz7rv9y51zrc65PzjnulNNsd+R9Jykj07+lIDglZ1/Xtpu8xU3U0kho1oRHuVprE2OFRep7Oyz07Y/IAhe21Occ62SWkdax8w2SOqUdLKkJ1OLT5LUIWnjCNudLOlxSV9NJWujSUhUSCCc8qZMUcnpZ6jt+efTsr+ywjy1dfWlZV9Iuu49F/gOIbLK0tjPs/TccxUrKUnb/oAg+K6ZG5VzrkPS/ZK+YmbTzWy6pK9I+rFzrnOobczsPZJWSrptqETOzM4ws+PMLM/MiszseknnSXo4c2cCZFbxScuVf8TMtOwr3Z3JIR0za56OmTXPdxiRlK6RrIVHLlLRkrF2xQayR9Yncyn/XclauP7HBkmf7y80s1vNbP2A9b+mZFPstwfMI9dqZuekyhdK+pWSfe92SbpO0mXOuYGDLIBQMTOVXXBBWppb09qZHJKkN3dv15u7t/sOI3JM6UnmYsVFKjv//EnvB/DBnHO+Ywid2tpat3r1at9hAENqf+XVtDS3rtl2UD19fD6ky60//5Ek6faPfspzJNFSUhDXCXOqJr2f8j+7iFo5ZDUzW+OcG/LWP2GpmQMwRulqbmXyYIRBOmqRaV5F2JHMARFzqLk1f3JfcunsVA5kymR/dNC8iiggmQMiKG/KFJWcNrlbfVEzhzCY7I8ORq8iCkjmgIiabHNrWSGTByO75cVMxZOYLJjmVUQFP72BiOpvbm184AG5nt5xbx+PmYoL4mrvZr65dPir8y72HULklE2ivxzNq4gSauaACMubMkVl73vfhLdnipL0WTT9CC2afoTvMCJlwnd+iJnKL76Y5lVEBskcEHFFS5ao5JSTJ7RtZXFBmqPJXWu3b9ba7Zt9hxEplSUTuz7LzjlHBWm8nzHgGz+7gRxQcuaZ6j3YoO533hnXdpXF+TKTmI5y8h5c9Ywkafm8Iz1HEg35cVPpBO4hXHTssSo+4YQMRAT4Q80ckAPMTOUXvV/xqVPGtV08ZipnihJkocrifNk4h+jkz5qlsvPOzVBEgD8kc0COiBUUqPKDH5QVFY5ruyklJHPIPlXjbGKNlZep4gMXy+KTv90dkG1I5oAcEq+qUsXFF0uxsddoVBaTzCH7jOe6tPx8VX7wgwx4QGSRzAE5pmDuXJWdffaY1y8pyFNBHh8VyB5lhXnKj4/xmjRT+YUXKK+mJrNBAR4xAALIQcUnnqje+np1rn9jTOtXFedrf0tXhqOKts9ecJnvECKjahxN/yW1tSo86qgMRgP4x89tIEeVnXee8meNbd6z8fZPwuHmTK3WnKnVvsOIhLFej4VHLlLJ6adlOBrAP5I5IEdZPK6KD3xA8Smjj3CtKM6TcW+vSXlpywa9tGWD7zBCL2+MU5LkzZyh8gsvlHHhIgeQzAE5LFZSosorrlC8snLE9fJiMaYomaRfrXlBv1rzgu8wQq9qDFOS5E2frsrLL5cVUKOM3EAyB+S4eFmpKq/4kGLlZSOuV8WoVmSB0ZpY86qnqfJDlytWOL4peIAwI5kDoHhFhaquuEKx0tJh1xlPp3MgU0aakiQ+ZYoqP/QhxYqKAowI8I9kDoCk5Bx0lVdeMexcXExRAt9GmpIkXlmpyiuGv36BKOOTGcAheVOmqPKqKxUrG7rJlaZW+DRc7XB86hRVXnWV4mXD1ywDUcY8cwDeJW/KFFVddaWafvUr9TW3vKusqqSA+eYm6PMXX+U7hNAbqr9cso/ch6iRQ06jZg7AYeKVlcmajkGjXKtK8hUfx63A8Cc15ZWqKR951DCGV5QfU1nhu+sf8qZPV+WVV5LIIeeRzAEYUry8PJnQTf3TPHQxM00rZbqHiXh2w+t6dsPrvsMIrWll7x6dmjdzRnIUNoMdAJI5AMOLl5Wq6sMfVv7cOYeWDf5SxdisWPeyVqx72XcYoVU94LorXLw4Ofqa6UcASSRzAEYRKypS5eWXq3j5iZKSd4NgVCuCVFqYp+L8uGSm0jNOV8XFfybLZzAO0I9PZACjslhMZeeco/IL3ieLx1VdRlMrglNdViArKFDFJZeo5NRTfYcDZB1GswIYs6JlyxSfMkXtDz+i3Y17fIeDHGCSambVqOpDlylv2jTf4QBZiZo5AOOSf8QRmnPdx5VXU+M7FOSA4vlzNeO/fIxEDhgBNXMAxi1eXq7qqz+it3/5a5Xv2e47nFD4wqVX+w4hdBrnL9aRH7mEEavAKKiZAzAhS+dM0f6T36P6JSfIibnnRlNRXKqKYu5QMBYuFtP+405V0wmn6qiZFb7DAbIeNXMAJqSiKF+zqoq166hj1V1eqenrVine0+07rKy1cv2rkqQLjj3JcyTZrbewWHtPOkudU6draU0ZI6eBMeBdAmDCjknVmrTNmKPt53xAbdNne44oe618Y61WvrHWdxhZrXn2Am0/9xJ1Tp0uSTp6ZrnniIBwIJkDMGGLZ5Qdur1XX1GJ9tSeq30nnKG+fKYuwdj1FhZrd+252n/imUqkrp3igrgWTKNZGhgLmlkBTFhRflwLqku1eX/roWUtcxaqvXqGpr++WqX7d3mMDmHQPHuBDiw75VAS12/JjDLFuA8wMCbUzAGYlGOGaAqjlg6jGao2bqCjGfgAjBk1cwAmZVFNmcqL8tTS2XtY2Z9q6V5W6f7dHqJDNmqevUAHjjlZiYKh7606vaJQs6qKA44KCC+SOQCTEo+ZTphTpec3HRiyPFlLd57Kd76j6jdfydkRr39/xSd8h+Bdb2Gx9h9/qtpHGSizfG5VMAEBEUEyB2DSTphTqZfeqVdPnxt2nf5aumkbXlP5rm0yDb9uFBXmcHOzi8XUNPdIHVx8/LC1cf1KC+M0sQLjRDIHYNKK8pNfwH/c1TTien1FJdp/4plqXHSMpm1Yl1MDJB577SVJ0iUnnuY5kuA4mVpnzVP9khPUW1I2pm2On111aIQ0gLEhmQOQFifNq9Lru5vkxlDh1l1epT2156roYJ2mbXhNxQ11mQ/Qs+c2rpeUO8lcW80Rql96ororpox5m7yY6cS5lRmMCogmkjkAaTGtrFDzppZoW337mLfpnFqjXWdeqJL9uzTtrddU2DpyzR6yX8eUatUvPfHQxL/jsXRmuUoK+FoCxot3DYC0OWnelHElc/3ap89We80sle/aqqlv/1H5HW0ZiA6Z1F1WofolJ6pt5pwJ7+OkeWOvxQPwJyRzANJmwbQSTS0t0MG2CYxYNVPLnIVqmTVPlds2acrm9crr7kp/kEirnqISHVxyvFpmL5Rs4n3d5k4tUU35yIMjAAyNZA5A2piZls+t0pNv7Z/4TmJxNS1cqua5i1S+e5sqt7+twubGtMWI9OiYUq2meYvVesRcKRaf9P5Omlc1+aCAHEUyByCtls2q0Aub69XZ0zep/bi8fDXPO0rN845SUUOdKrdtUuneHYolJrdfX27/6Kd8hzBpiXieWmbNV9P8xeMa2DCaqpJ8LarmPqzARJHMAUir/HhMx8+u1MtbD6Ztn51TatQ5pUbxrpNUvnOLKrdvol9dgLrLKtQ07yg1z14kl5+f9v0vn1slm0QTLZDrSOYApN2Jcyu1ZluDEmOZp2Qc+gqL1HjkMjUuOkYldbtVue1tldTtDcUExA+veV6SdOUp7/Ecydg4M7XNmKOmeYvVUT0jY8cpzI/p2FlMRwJMBskcgLQrL8rX4hll2rC3JTMHMEuOgJ0+W3ntrarcvklle7ZndW3dy1s2Ssr+ZK67tEKts+apae6R6isqyfjxjp1VqYK8WMaPA0QZyRyAjKhdMEUb97WMaRLhyegtKVP90ctVf/RyFTQ3qnT/LpXu26XCpoOhqLHzzZmpc0q12qbPVtuM2eopDe5WWnkx08kMfAAmjWQOQEZMLy/S4unl2rgvQ7VzQ+iuqFJ3RZUajjpW8a4Ole7bpdL9u1Rcv0+xvnAOnMiERF6+2qtnJhO46bNGvV9qphw/p1LlRenvgwfkGpI5ABlz5pHTtGl/a9r7zo1FX2HxodGw1terkrq9Kt2/SyV1u5XX1Rl4PL71FJWoPVX71j5telqmE5mMgryYTls41WsMQFSQzAHImKmlBVo6s1xv7mn2GoeL56lt5pzk3QmcU2FzgwqbDqqw6aCKmg6qoLVJlkhkNIaCvOBqoBLxuLrLq9RZOVVdFVPVVTVV3eVVgR1/LE6cU8Wtu4A0CcU7ycxKJP1fSVdKMkkPSfqcc65jmPU/KenfJA28r9AjzrmPD1inVtJdko6TtEfS3zvn7s/ICQA57MxF07RxX4v6ElnSf81MXZVT1VU5oFYo0afClkYVNqWSvOYGFbY0pjXB+9KV16ZtXwMdlrhVTlV3WYUUy95BBYX5MdUu4NZdQLqEIpmT9C+Sjk49nKRfSfq2pM+MsM0W59xRQxWYWaWkFZLukHSOpHMlPWxmm51zL6YxbiDnVZbk69hZFVq3s8l3KMOLxdVVOU1dldP+tCzRp8KWJhU2HVRBS5Pi3Z3K6+xQXleH4l0dgfbBS8Tz1FdYpN6iYvUWFquvqFhd5VXqqsj+xG0oJ8+boqJ8v828QJRkfTJnZsWSrpV0qXNuX2rZFyU9Ymafd85NpPPLVZI6JP2Tc85J+p2ZPSzpekkkc0Canb5omt7c06yeviypnRuLWPzwGryBxT3dih9K7jqV19WhvM5kohfv7pK5RLJmzzmZS+gXT/9GktNHzvkzKWZyFpeLmWQmZ7FkslZYfChp6ytMJm69hcUZmajXl5KCOLfuAtIs65M5SUslFUlaM2DZK5KKJS2RtG6Y7eaa2V5JPZKel3SLc+6dVNmJkl5JJXID93ndcEGY2fVKJnuaN2/eBE4DyF1lhXk6ed4UrXonfXeF8C2RX6BEfoF6ysc24e3qX/2HJOn0cy/JZFhZ74xF01SYR60ckE5e6+bN7F4zcyM8viapPLX6wDaa/r+HmxDpGUnHS5ol6VRJnUrWvvXf/K980P4kqXGE/ck5d49zrtY5V1tTUzPmcwSQdMqCKSop4Es8l00tLdDxs7nbA5BuvjtafE5SzQiP2yX1T1I18BOg/+8hh8g557Y45zY65xLOub2S/lrJxO6M1Cotg/YnSVXD7Q/A5BXmxXXGommjr4jIOntxtWIx7sEKpJvXZM451+qcOzDCo13SBiVr1k4esOlJSvZ52zjWQ6Ue/Z8ir6X2MdBJqeUAMuT42ZWaWlrgOwx4MGdKsY6sKfMdBhBJvmvmRpWafuR+SV8xs+lmNl3SVyT9eLjBD2b2QTObY0lTJf2rpAOS/pBa5WFJJWb2P82swMwuUHJQxD0ZPyEgh8ViprMXV/sOw4uSiiqVVFT5DsMLM+ncJXRPATIl65O5lP+uZC1c/2ODpM/3F5rZrWa2fsD650t6SVKrpPWSpkl6v3OuVZKcc42SLpH0USX7zn1f0t8wLQmQeUfWlGlBdeZv4J5tPvW/v6NP/e/v+A7Di2VHVGhGRZHvMIDIMufhNjthV1tb61avXu07DCC0mjt7dN+L29Tdm9m7LsC/ssI8XXfmfOaVAybJzNY452qHKgtLzRyACKkoytfZR+VWc+ujP/yWHv3ht3yHEbj3Hj2dRA7IsDDMMwcggk6YU6kN+1q0q2HIu/JFzrY31/oOIXBLZpTrqOkMegAyjZo5AF6Ymd5/zAzlx5mqIoqKC+J679EMegCCQDIHwJsppQXMPRdR5y2pUUkBjT9AEEjmAHh18rwpjHSMmEU1pTrmiGFvqAMgzUjmAHgVi5nev2yG4hG/M0Bl9QxVVs/wHUbGFeTF9L6jp/sOA8gp1IED8K6mvFCnLpiqP2yp9x1Kxlz7hTt8hxCIcxfXqLwo33cYQE6hZg5AVjht4VRVl3GrrzCbO7VEx82meRUIGskcgKwQj5nev2ymYhbN5taH7/4HPXz3P/gOI2Py48nRyRbR1w/IZiRzALLGzMoinXlkNEe37t78lnZvfst3GBnz3qOnq7KE5lXAB5I5AFnltIVTtXgGE82GyfK5VTp2VqXvMICcRTIHIOtctGwm/edCYs6UYp23hMmBAZ9I5gBknYK8mC47cRb39Mxy5UV5+uAJRygW8WllgGxHMgcgK1WVFOgDx81UVPrT18xeoJrZC3yHkTZ5MdNlJ87iLg9AFuBdCCBrLagu1XuOqtZzbx/wHcqkXf35r/oOIa0uOGYGd+4AsgQ1cwCy2qkLpmrJjHLfYWCAk+ZVadks5pMDsgXJHICs9/5lM1RdXug7jEl58J+/qAf/+Yu+w5i0uVNLdO5iBjwA2YRkDkDWK8iL6fITwj0gom7XVtXt2uo7jEmpKM7XB49nwAOQbUjmAIRCZUkykcgjkfCiMD+my044QsUF4U2ogagimQMQGvOmlejSE2eR0AWsMD+mK0+arekMeACyEskcgFBZWF1KQheg/kTuiMpi36EAGAbJHIDQCWNCN+vIozXryKN9hzEuhfkxXXXSHBI5IMuZc853DKFTW1vrVq9e7TsMIOe9c6BNj762W70JPsfSrT+Rm1lJ0yqQDcxsjXOudqgyauYAhFYYa+jCgEQOCBeSOQChtrC6VJeFIKG7/xs36/5v3Ow7jFGRyAHhQzIHIPQWhCChazqwT00H9vkOY0QkckA4kcwBiIQF1aW6fPksFebzsTYRpYVxEjkgpPjUAxAZ86eV6r+cNk81Ib/1V9BmTynWJ06fTyIHhBTJHIBIqSop0DWnztUxR3Aj+LE4Zf4UfeTkOSotzPMdCoAJ4t0LIHLy4zFdfNxMzaoq0tMb6rJi6pL5xyz3HcK7FOTFdNGyGVo8o9x3KAAmiWQOQGSdMKdKMyqK9Oi6PWru6PEay6V/eZPX4w9UXVagS0+YpSmlBb5DAZAGNLMCiLQZFUX6L6fN04LqEt+hZIWjZ5brmlPnkcgBEUIyByDyigviumL5bJ2xaJrM0+wlP/rK3+pHX/lbPweXFI+Z3nv0dH3g+CNUkMdHPxAlNLMCyAlmpjOPnKaF1aV6asN+7WnqDPT47c2NgR5voPnTSnTekhpNK2OULxBFJHMAcsrMyiJdc+pcvbGnWc9vOqC2rj7fIWVMZXG+zl1So6Oml/kOBUAGkcwByDlmpmNnVeqo6WVateWg1u5oVF8WjHhNl/y46dQFU3XK/CnKi9OkCkQdyRyAnFWYF9e5S2p03OxKPbOxTu8caPMd0qSYSUtnlOvsxdUqL8r3HQ6AgJDMAch5U0sLdMVJs7WvuVMvbz2oTftb5dJcUbd4+Rnp3eEA8Zhp6cxynbpgqqYyShXIOebS/YmVA2pra93q1at9hwEgQxraurV6W4Pe2tOcFRMOD6cgL6ZjZ1Xo5PlTVEFNHBBpZrbGOVc7VBk1cwAwyJTSAr1/2Qyds7haG/e16I3dzYGPfh2OmTRnSomOOaJci6eXM80IAJI5ABhOUX5cJ8yp0glzqnSwrVtv7WnWO/VtqmvpGncz7D23/pUk6frbfzDuOMykmRVFWlhdqqOPqFBlMbVwAP6EZA4AxmBqaYHOOqpaZx1VrbauXm2rb9e2+jbtauxQS2fvqNv3dHeN+VhmyWlFZlcVa0F1qeZNLVFRfnwy4QOIMJI5ABin0sI8LZtVoWWzKiRJnT19qmvpUl1rl+pbu9Xa1aO2rj61d/eqozuhxBDVeDEzlRTEVVIYV2lBnsqL8lRdVqjq8kJVlxWoMI/kDcDYkMwBwCQV5cc1d2qJ5k49/P6vzjl19Sb0cFWRJOlvzjtSZlJhXkzm695iACKFZA4AMsjMVJQfVyyVuBUXUOMGIL1I5gAgAJdeeqnvEABEFMkcAATg5ptv9h0CgIhigiIAAIAQI5kDgACcf/75Ov/8832HASCCSOYAAABCjGQOAAAgxEKRzJlZiZn9m5k1mFmjmf3QzIpHWP+7ZtY66OHM7H+kyheknrcNKN8Z3BkBAACkRyiSOUn/Iuno1GOJpGMkfXu4lZ1zf+OcK+t/SLpSUq+knw1ademA9eZkKHYAAICMyfqpSVI1cNdKutQ5ty+17IuSHjGzzzvnOsewmxskPeKc253BUAFgWFdffbXvEABEVNYnc5KWSiqStGbAslckFStZS7dupI3NbKakyyUNNWPnKjMrkLRe0pecc0+lI2AAGOyzn/2s7xAARJTXZlYzuzfVd224x9ckladWbxqwaf/fFWM4zF9K2iHpdwOWHZB0pqSFkhZIekjSCjM7YYRYrzez1Wa2uq6ubmwnCAAp7e3tam9v9x0GgAgy55y/g5uVKVnrNpx2JWvfXpU0xTnXmNpuiqSDkk50zg1bM2dmMUlbJN3tnPvHUWL5naQ/OOe+OFrctbW1bvXq1aOtBgCH9M8x99RTT3mNA0A4mdka51ztUGVem1mdc62SWkdax8w2SOqUdLKkJ1OLT5LUIWnjKIe4WNIRkv5tDOEkJNkY1gMAAMgaWT+a1TnXIel+SV8xs+lmNl3SVyT9eAyDH26Q9Evn3LvaRc3sDDM7zszyzKzIzK6XdJ6khzNxDgAAAJmS9clcyn9Xshau/7FB0uf7C83sVjNbP3ADM5st6YOSvjvE/hZK+pWSfe92SbpO0mXOuTVDrAsAAJC1wjCaVc65dkmfTj2GKr9d0u2Dlu3SMOfnnPuppJ+mOUwAAIDAhSKZA4Cw++QnP+k7BAARRTIHAAEgmQOQKWHpMwcAoXbgwAEdOHDAdxgAIoiaOQAIwEc+8hFJzDMHIP2omQMAAAgxkjkAAIAQI5kDAAAIMZI5AACAEGMABAAE4DOf+YzvEABEFMkcAATgmmuu8R0CgIiimRUAArBjxw7t2LHDdxgAIoiaOQAIwHXXXSeJeeYApB81cwAAACFGMgcAABBiJHMAAAAhRjIHAAAQYgyAAIAA3HTTTb5DABBRJHMAEIDLLrvMdwgAIopmVgAIwIYNG7RhwwbfYQCIIGrmACAAN9xwgyTmmQOQftTMAQAAhBjJHAAAQIiRzAEAAIQYyRwAAECIMQACAAJw2223+Q4BQESRzAFAAC688ELfIQCIKJpZASAAa9eu1dq1a32HASCCqJkDgADceOONkphnDkD6UTMHAAAQYiRzAAAAIUYyBwAAEGIkcwAAACHGAAgACMDtt9/uOwQAEUUyBwABOOuss3yHACCiaGYFgAC88MILeuGFF3yHASCCqJkDgADceuutkphnDkD6UTMHAAAQYiRzAAAAIUYyBwAAEGIkcwAAACHGAAgACMCdd97pOwQAEUUyBwABWL58ue8QAEQUzawAEIAnnnhCTzzxhO8wAEQQNXMAEICvfe1rkqQLL7zQcyQAooaaOQAAgBAjmQMAAAgxkjkAAIAQI5kDAAAIMQZAAEAAvve97/kOAUBEkcwBQACWLl3qOwQAEUUzKwAE4JFHHtEjjzziOwwAEUTNHAAE4Fvf+pYk6bLLLvMcCYCoCUXNnJn9NzNbZWbtZrZpjNv8uZltTm2zysxOGVRea2Yvpco3m9m1mYkeAAAgc0KRzEnaLemfJP3DWFY2s7Ml3S3pM5KmSHpI0mNmVpEqr5S0IrV8iqS/kfRdMzsz/aEDAABkTiiSOefcL5xzD0naNcZN/lrSL51zv3XOdUn6pqQuSVemyq+S1CHpn5xzXc6530l6WNL1aQ4dAAAgo0KRzE3AiZLW9D9xzjlJr6aW95e/klre75UB5Ycxs+vNbLWZra6rq8tAyAAAAOPndQCEmd0r6S9GWOUfnHO3TWDX5ZKaBi1rlFQxxvLDOOfukXSPJNXW1rrh1gOAodx3332+QwAQUb5Hs35O0s0jlLdPcL8tkioHLauStHlA+YIhypsneDwAGNHcuXN9hwAgorwmc865VkmtGdj1a5JO7n9iZiZpuaRfDii/ctA2J6WWA0DaPfDAA5Kka665xnMkAKImFH3mzCzPzIok5SefWlHq+XC+L+kqM7vAzAok3SSpSMlBDkr9W2Jm/9PMCszsAiUHRdyTwdMAkMPuvvtu3X333b7DABBBoUjmJN2m5OjTeyQtSv3d0V9oZrea2fr+58655yR9VsmkrknS1ZIucc41p8obJV0i6aOp8u9L+hvn3ItBnAwAAEC6+O4zNybOuS9J+tII5bdLun3Qsh9L+vEI27ws6bT0RAgAAOBHWGrmAAAAMASSOQAAgBALRTMrAITdL37xC98hAIgokjkACEB1dbXvEABEFM2sABCAe++9V/fee6/vMABEEMkcAASAZA5AppDMAQAAhBjJHAAAQIiRzAEAAIQYyRwAAECIMTUJAATgscce8x0CgIgimQOAAJSUlPgOAUBE0cwKAAG46667dNddd/kOA0AEkcwBQAAefPBBPfjgg77DABBBJHMAAAAhRjIHAAAQYiRzAAAAIUYyBwAAEGLmnPMdQ+iYWZ2kbRk8RLWkAxncf7bivHNLLp53Lp6zxHnnGs47M+Y752qGKiCZy0Jmtto5V+s7jqBx3rklF887F89Z4rx9xxE0zjt4NLMCAACEGMkcAABAiJHMZad7fAfgCeedW3LxvHPxnCXOO9dw3gGjzxwAAECIUTMHAAAQYiRzAAAAIUYyBwAAEGIkcx6Y2X8zs1Vm1m5mm8a4zZ+b2ebUNqvM7JRB5bVm9lKqfLOZXZuZ6CfOzErM7N/MrMHMGs3sh2ZWPML63zWz1kEPZ2b/I1W+IPW8bUD5zuDOaHQTOOdPmlli0Dn/dNA6UXyt/9zMXkitf8DMVpjZ8QPKs/K1NrO4mX3TzOrMrMXMHjKz6hHWv9jM1ptZh5m9bmYXDSo/ysyeSJ3nTjO7KfNnMX7jOW8zu8TMnky9rg1m9qyZnTNoHZe6ngde95XBnM3YjPOcz0+d08DzeWHQOlF8rW8d5jP7/wxYJ+tfa0kys4+lrtVmM+sdw/p+39vOOR4BPyR9RNKHJf1/kjaNYf2zJbVJukhSoaT/JWmfpIpUeaWkOkl/lyp/v6RWSWf6PtdB5/F9SS9ImiFpeurvu8ex/fsl9UialXq+QJKTNMf3uaXrnCV9cqRrIqqvtaT/mjqX0tR5/YOkPZKKs/m1Tr2HN0palHptHpK0Yph1F0lql3StpAJJn0i9rxekyuOS3pT0HUklkk6WtF/SNb7Pc5Ln/QlJV0qqkpQn6TOpa3bugHWcpLN9n1caz/l8Sb0j7CuSr/UQ2y6WlJB0Wphe61Scfybp45I+PdJrmVrX+3vb+39YLj9G++IesN6/S7pvwHOTtF3SX6Sefyr13Aasc5+kH/k+xwHxFEvqkHTBgGUXpN4ARWPcxy8k/XLA8wXKwi/4yZzzaNdEDr3WpanX9qRsfq2VvK3fXw54fmQqzgVDrPtlSc8OWvaspL9P/f3e1P9R2YDyr0r6ve/znMx5D7N9naQrBzzP+i/4cb7W52vkZC4nXmtJd0h6ZdCyrH+tx/Naptbx/t6mmTUcTpS0pv+JS14Jr6aW95e/klre75UB5dlgqaQiDTgPJWMslrRktI3NbKakyyV9d4jiVakmgKfM7PzJh5o2Ez3nuWa218x2mNnPzGzhgLLIv9Yp/cnf4G4IWfNap5qG5und783NkpolnTDEJu96H6cMfO1OlLTROdc6THlWmMB5D97+BEnTJL0+qOjnqabYVWZ2VRpDnrQJnnM89R7ea2a/NrOBr2PkX2szK1Tyx+lQn9lZ+1pPkPf3NslcGpnZvan+AMM9vjbBXZdLahq0rFFSxRjLM2qM512eWn1gnP1/jyXOv5S0Q9LvBiw7IOlMSQuVrLl5SNKK1JdFRmXwnJ+RdLykWZJOldQp6XdmVpoqj/xrbWZLJP1A0k3OuZbUYm+v9Qj6z2Wsr0dWv4/HYbznfYiZTVeyhv2fnHNvDyi6UMnXdo6kb0v6iZldnJZo02O85/yWpOVKntPRktZJetLMZqXKI/9aK9mdqEDSfwxanu2v9UR4f2/npWtHkCR9TtLNI5S3T3C/LUr2VRioStLmAeULhihvnuDxxmss591fI1Op5EXc/7c0SpxmFpP010r2uTpUI5X6lfOH1NNuSd8xs8slfVTJD89Mysg5O+e2DHi618z+WskPgTMkrVT0X+tlSibsdzjnDv2i9/xaD6c/0RzqvTnUeQ73Pm4eY3m2GO95S5JSiczvJP1W0i0Dy5xzKwc8fcDMLlSy39Hjkw02TcZ1zs65vZL2pp42SrrFzD4i6QOSfqiIv9YpN0j6yaDaqDC81hPh/b1NzVwaOedanXMHRnhMNJl7TckOk5IkMzMlf/W9NqD8pEHbnDSgPKPGeN4blKxlOnnApicp2bdq4yiHuFjSEZL+bQzhJJTsU5hRAZzzoUOlHv3nFNnX2sxOlvSUpG845/5pDOEE8loPxznXqGT/xYHvzUVK/toeKsF81/s4ZeBr95qkJQNqYQeXZ4UJnLfMbIGSfYhWOOc+N6ibwFC8vraDTeSchzDwnCL7WqfWWSbpHA3dxDpYVr3WE+T/vR1UJ0Ie7+oYmadkn6K/VrJ2rUgjdAxXcjRrq5L9iAqUrBkZOJq1SskOxf8zVX6BsneE43NKjm6cnvr7u2PY7v9J+ukQy8+QdNyA/8/rlUwiTvF9rhM9Z0kfVLL5wSRNlfQ9JTsgl0X5tZb0HkkNkq4fpjwrX2slR/ptULLZqELSzyU9Psy6RypZc/lxSfmpf4ca8fYvSvYvXJ56n3/M9+s5yfM+WtJOSV8bpvw4Saelrud8SVek/p8u932ekzjn90k6SskKkzJJX1Kyhm5ulF/rAdv8i6QXw/paD3iNipScRaI39XeRBgw+G7Cu9/e29/+wXHyk3thu8GNA+a2S1g/a5s8lbVGyduMlDfoSU7J/1Uup8i2SrvV9nkOcd4mStWuNqccPlZp6YoTznp16I503xP4+rmQH+TZJ9Ur+8n+/7/OczDlL+qak3alz2qNk/6IlUX+tJf1eyV/orYMe52Tza536kL5DyT59LZJ+Kak6VfYJSa2D1r9Y0vrUa7de0kWDyo9Ssjm9PXUd3Oz7HCd73pJ+lPqMG/zafiJV/t7U/0Wbkgn9amVnUjOec/68kj/C2pScguJxSadG/bVOLSuWdFCp2RYGlYXitU7F+kkN8T2tZDeXrHtvW+ogAAAACCH6zAEAAIQYyRwAAECIkcwBAACEGMkcAABAiJHMAQAAhBjJHAAAQIiRzAFAQMwsz8yeN7Oy1PO7zWyXmbkB68TN7AUzq/IWKIBQIZkDgOBcK+lJ96f7Vf5Ug24D5Jzrk/RjSX8bcGwAQopkDgDSxMyeMDNnZh8YZpVPKXlXD0mSc+4Z59y+Idb7haS/yESMAKKHZA4A0sDM3qfkvXIl6dghyvOVvCfj66Ptyzl3ILmJzU1njACiiWQOANLj65I2KnlT+cOSOUnVSt7PsW+M+9ur5L2JAWBEJHMAMElmdqWk0yTdpmTN23FDrNYhqXAcuy1ObQMAIyKZA4BJMLOYpK9JWqNkX7c3JR1jZjZwPedco6ROM5s6xn3OVbKmDwBGRDIHAJNznaRlkm51zjklk7lSSQuGWPc/9ad+dTKzH5jZztTfO83sB6mi0yX9wTlHzRyAUVnyswcAMF5mViBpg6Stzrn3ppadLelZSZc75x4ZtP7Rkr7tnLtklP3+QNJPnXMrMxM5gCihZg4AJu4GJWvgvmFmVamJfnenyg4bBOGce0vST/snDR6KmcUlrSaRAzBW1MwBwASYWamkzZJmDLPK/c656wIMCUCOyvMdAACE1I2SaiRdI2n/oLKva+gRrQCQdtTMAcA4mdkUSe9I+rlz7q+HKL9TySbYsnHMKwcAE0KfOQAYvy9Iikv64jDl6yUVSToysIgA5Cxq5gAAAEKMmjkAAIAQI5kDAAAIMZI5AACAECOZAwAACDGSOQAAgBAjmQMAAAgxkjkAAIAQI5kDAAAIMZI5AACAECOZAwAACLH/H8XTPjW3RqrIAAAAAElFTkSuQmCC\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import matplotlib.patches as mpatches\n", "from myst_nb import glue\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot()\n", "\n", "\n", "s = 0.25\n", "delA1 = np.sqrt(1/4 - s*np.sqrt((1 - s**2)/2) + s**2)\n", "delA2 = np.sqrt(1/4 + s*np.sqrt((1 + s**2)/2) + s**2)\n", "\n", "A1 = 0\n", "A2 = 0\n", "\n", "# add a circle\n", "patch = mpatches.Ellipse((A1, A2), \n", " width=delA1*2, \n", " height=delA2*2, \n", " ec=\"none\", \n", " color='tab:blue', \n", " alpha=0.5)\n", "ax.add_patch(patch)\n", "\n", "\n", "s = 0.0\n", "delA1 = np.sqrt(1/4 - s*np.sqrt((1 - s**2)/2) + s**2)\n", "delA2 = np.sqrt(1/4 + s*np.sqrt((1 + s**2)/2) + s**2)\n", "\n", "A1 = 0\n", "A2 = 0\n", "\n", "# add a circle\n", "patch = mpatches.Ellipse((A1, A2), width=delA1*2, height=delA2*2, ec=\"none\", color='tab:red', alpha=0.5)\n", "ax.add_patch(patch)\n", "\n", "\n", "ax.set_xlim(-1.1, 1.1)\n", "ax.set_ylim(-1.1, 1.1)\n", "\n", "ax.set_xlabel('$A^{(1)}$', fontsize=15)\n", "ax.set_ylabel('$A^{(2)}$', fontsize=15)\n", "\n", "ax.axvline(0, color='black', linestyle='--')\n", "ax.axhline(0, color='black', linestyle='--')\n", "\n", "ax.tick_params(labelsize=13) \n", "\n", "plt.gca().set_aspect('equal')\n", "\n", "fig.set_size_inches(10, 10)\n", "\n", "glue(\"squeezed_state_vs_vac_state_field_representation\", fig, display=False)" ] }, { "cell_type": "markdown", "id": "0d3d37a2-5fb0-4a4e-82ad-24ea3a81832e", "metadata": {}, "source": [ "```{glue:figure} squeezed_state_vs_vac_state_field_representation\n", ":figwidth: 600px\n", ":name: \"fig-squeezed-state-vs-vac-field-fluctuations\"\n", "\n", "Field representations for a vacuum state (red circle) and squeezed state $\\ket{\\psi_s} = \\sqrt{1 - s^2}\\ket{0} - s\\ket{2}$ (blue circle) for $s=0.25$.\n", "\n", "```" ] }, { "cell_type": "markdown", "id": "b155f866-3513-4d68-860c-4e992445edd0", "metadata": {}, "source": [ "For $s = 0$ (the red circle), the state is nothing more than the vacuum state. However, when $s = 0.25$ we arrive at the blue ellipse, where the fluctuations along $A^{(1)}$ have been reduced, while those along $A^{(2)}$ have been increased. **As engineers, we can design systems that are only sensitive to the fields in one of the two quadratures (using [Homodyne detection](https://en.wikipedia.org/wiki/Homodyne_detection ) for example), thus enabling measurements below the noise floor set by the standard quantum limit (SQL, which is represented by the vacuum state here with $s = 0$). We will discuss such measurements in detail.**\n", "\n", "One final question of interest for $\\ket{\\psi_s}$ is what happens to the noise along the two quadratures $A^{(1)}$ and $A^{(2)}$ and how does this noise compare to the standard quantum limit (SQL) as we let $s$ vary from 0 to 1." ] }, { "cell_type": "code", "execution_count": 13, "id": "51979760-5b7c-4910-9b91-494a99fe17d6", "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "application/papermill.record/image/png": 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\n", 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QYcOGMX36dJo2bcqhQ5rAQ8SV4qM910IlnfIMNS9Q2ulEPqEh6AHio48+YtCgQbz22mtnbuvQoQMvvvjimX9ba+nduzeFCxdm2bJlFCjg+Svspptu4s4776RevXr84x//YOrUqT7PLyKXkJIEU/vAke3QezqUrO10Ip/RnlSAiI6OplSpUhfcbs46ofrzzz+zbt06hg8ffqagTitTpgxDhgxhxowZ7Nu37/ynERGnWAtz/wG7foaOH0HlVk4n8imVVIBo2LAhH374IePGjePo0aMZbvPzzz8D0LFjxwzv79SpE2lpaSxdujTbcopIFv3wKvwxGW4eDtf1cDqNz6mkAsR///tf8uXLR//+/SlevDi1a9fmhRdeICYm5sw2+/fvp1ChQhQsWDDD56hQoQKA9qRE3GL1OPj5Lc+6UDc+5XQaR+ic1CW0atXqgtu6devGww8/TFxcHO3bt7/g/v79+9O/f3+OHDlCly4XroY5ePBgunfvzt69e+nTp88F9z/55JN06NAhy1nr1avH5s2bWbhwIQsWLGDJkiWMGDGCyZMns2bNGvLly3fZ5zh9aNAE8DUXIn5j+/cw73Go2iYg1oW6UtqTCiBhYWF06NCBjz76iE2bNvH555+zfft2Ro8eDXjOO0VHR5+zd3W2yMhIAK655hpfRRaRjPy9Hqb1g5LXQtexAX8t1KVoT+oSfvzxx4velydPnkveX6xYsUveX65cuUve7w0DBgzgmWeeYcuWLYBnFB/A3Llz6d279wXbnx6u3qxZs2zNJSKXEL3HM9Q8vDDcO82zPlQQ055UgDh8+PAFt0VFRXHixAlKliwJQMuWLalfvz4jRozg5MmT52z7999/8/7773PTTTdRuXJln2QWkfOcvhYqOSH9Wigd1dCeVICoW7cuHTt2pG3btpQoUYLdu3fz9ttvkydPHvr16wd4zjWNHz+em2++mWbNmvHMM89QsWJFtmzZwquvvkpKSsqZQ4Nn+/XXX0lISDjntooVKxIREeGTr00kKKQkwpTecHQn9JkJJWo5ncgVVFIB4oUXXmDOnDkMGTKEY8eOUapUKZo3b86UKVOoVKnSme3q1KnD6tWrefnll3n22Wc5dOgQaWlp1KhRg59++omKFSte8Nyvv/76Bbf169ePsWPHZuNXJBJErIU5j0DkUrj7M6h0o9OJXEMlFSAeeeQRHnnkkUxtW758+XP2mIYPH86bb75JZGTkOSVVsWJFrLXejioi51syAv6cBq1fgHrdnE7jKjonJYwYMYI77riDu+++m61btzodRyS4rBoDS9+BRv3hhgsnhA522pMSjDHMmjXL6RgiwWfbQvjmCajWFtq/E7TXQl2K9qRERJxwYC1M6w+l6kKXMRCifYaMqKRERHzt+G74qhvkKZp+LdTlZ4QJVqpuERFfijsGX3WB1ETo9zXkL+l0IldTSaWz1mrOOh/QaEEJasnxMKknHI+EPrOgRE2nE7meDvcBoaGhxMfHOx0jKMTHxxMaGrzzkEkQS0uFmQ/C3hXQeSRUvMHpRH5BJQWUKFGC/fv3ExcXp7/0s4m1lri4OPbv30+JEiWcjiPiW9bCd8/C5q/httegzt1OJ/IbOtwHZ1apPXDgAMnJyQ6nCVyhoaGULFnyglWBRQLer+/DylHQ7FFo9rDTafyKSipdgQIF9MtTRLzvj2nw/YtQ+264dYTTafyODveJiGSXv36E2YOhYkvo/Cnk0K/crNI7JiKSHQ7+CVP6QLFq0H0C5AxzOpFfUkmJiHhb9F7PulC58nnWhQov5HQiv6VzUiIi3hR/HCbcA0lxcP98KFjW6UR+TSUlIuItyQkw6V44vgt6z4SStZ1O5PdUUiIi3pCWBrMGwp7f4J7RUKml04kCgs5JiYhcLWthwT9h0xxo+yrU7eJ0ooChkhIRuVrLPoIVn0DTh6H5o06nCSgqKRGRq/HndFg4HK7t5NmLEq9SSYmIXKldP8Osh6BCC8+ksbpY1+v0joqIXIlDG2FyLyhaFXp8BaG5nU4UkFRSIiJZdWIfTOgCufJC7+kQXtjpRAFLQ9BFRLIiPtpTUEmxcJ8u1s1uKikRkcxKSfQc4ju6A3rPgFJ1nE4U8FRSIiKZkZYGswbB7l88F+tWvsnpREFB56RERDJj0fOwcRbc+i9drOtDKikRkctZ9l/PBbtNHoLmQ5xOE1RUUiIil7JhpmfKo1p3wW2vgTFOJwoqKikRkYuJ/MVzHqp8M7j7M8gR4nSioKOSEhHJyMENMKknFK4EPSbqYl2HqKRERM4XvQe+6uJZWbf3DMhTxOlEQUtD0EVEzhZ3DMbfDclxcN93UKic04mCmkpKROS0pDiY2M2zJ9V3NpS81ulEQU8lJSICkJoC0++D/auh25dQobnTiQSVlIiIZ2XdeY/Btu/gjnehVgenE0k6DZwQEVnyCqydADf9H1w/wOk0chaVlIgEt5WfwdK3oWE/aDXM6TRyHpWUiASvjbPh26ehRnvPYT7NJuE6KikRCU67lsLMB6FcY8+s5iE6Re9GKikRCT4HN8Dkez2zSfScDLnyOJ1ILsLRkjLG9DDGLDXGxBhjUi6zbXtjzBJjzBFjzPH0x7X0VVYRCRBnzybRZ6Zmk3A5p/ekjgMfA0MzsW1h4EOgKlAcmAjMN8bocnARyZyzZ5PoM1NLv/sBRw/CWmsXABhjWmVi26/Ou+kTY8y/gAhgr9fDiUhgSTp17mwSJWo5nUgywW/PFBpj6gFFgQ1OZxERl0tNgWmaTcIfOX2474oYY0oA04E3rbXbL7HdQGPMKmPMqqioKN8FFBH3OD2bxPYF0P5tzSbhZ/yupIwxpYEfgIXAJa+8s9aOstZGWGsjihcv7pN8IuIymk3Cr/lVSRljKgJLgfnW2kettdbhSCLiZitGaTYJP+f0EPQQY0xuIFf6v3Onf1xw2bcxpibwCzDJWvuUj6OKiL/ZOBvmP6PZJPyc03tSfYB4YAEQkv7f8UAFY0wvY0zsWdv+H1AGGGqMiT3ro5fPU4uIu509m0SXLzSbhB8zwXLELCIiwq5atcrpGCKS3Q5ugDG3Q4HScN98XazrIGPMamttxNU8h9N7UiIi3hO9Bybc45lNovcMFVQA0D6wiASGU0c9s0mkxMP9CzSbRIBQSYmI/0uMhYld4cRe6DNLs0kEEJWUiPi3lCSY2gcOrIPuEzSbRIBRSYmI/0pLg9kPwc4l0PG/ULO904nEyzRwQkT8k7Xw3f/BhhnQ5mVo0NvpRJINVFIi4p9+fhtWjoJmj0KLx5xOI9lEJSUi/mfVGPjhFajXA24dodkkAphKSkT8y6Y58M0TUK0tdPwIcujXWCDT/10R8R+7foYZD0DZ66HrOAgJdTqRZDOVlIj4hwPrYNK9UKQK9JwMufI4nUh8QCUlIu53dKdnuqPwQtBnpqY7CiIqKRFxt5i/YXwnwHpmkyhQ2ulE4kO6mFdE3Cs+2rMHdeoo9P8ailVzOpH4mEpKRNwpOR4m9YAj26DXVCjTyOlE4gCVlIi4T2oKTLsP9iz3LFpY5RanE4lDVFIi4i7WwtePwbb50P5tqHO304nEQRo4ISLu8v1LsG4C3PQsNH7Q6TTiMJWUiLjHbx/Cr+9BxABo9azTacQFVFIi4g7rJsHC4XBtJ2j/lubjE0AlJSJusG0BzHkEKt0Ed4+CHCFOJxKXUEmJiLP2LIep/aBUXejxFeQMczqReEFcUopXnkclJSLOObQJJnbzzCLRazqE5Xc6kXjJpz/u9MrzqKRExBnHI2HC3ZAz3DPdUb7iTicSLzoRn+yV59F1UiLieycPwZedPLNK3PctFK7gdCLxMpWUiPin+GjPHlTsIeg7B0rWdjqRZAOVlIj4n6Q4mNgdorbCvVOgXGOnE0k2UUmJiH9JSYKpfWHvCug6Bqq2djqRZCOVlIj4j7RUmP0Q7FgEHd6H2p2dTiTZKC3NciA6wSvPpdF9IpK9rIVvn4YNM6DNS9Cov9OJJJvtj44nPjnVK8+lkhKR7LXkFVg1Glo8Bjc87nQa8YEdUbFeey6VlIhkn98+gqVvQ8O+0OZlp9OIj+w4pJISEbdbOwEWPge17oI739OEsUFk88EYiuf3zvRWKikR8b7N82DuP6ByK7jnc00YG2TW7ommfrlCXnkulZSIeNdfP8H0+6B0Q+iuCWODzfFTSew6coqG5Qt75flUUiLiPftXw+R7oUgV6DUNwvI5nUh8bNXu4wA0LF/IK8+nkhIR74jaChO6QJ4inglj8xRxOpE44NcdR8gdmoP6KikRcY3oPZ4JY3PkhD6zocA1TicSh/y64wiNKxUlLKd3zkOqpETk6sRGeQoq6ZRnD6poFacTiUMOxSSw/XAsN1Qt6rXn1LRIInLlEk7AhM4QcwD6zoZSdZxOJA76aVsUAC2qFvPac6qkROTKJMfDxB5weDP0nALlmzqdSBy2aNMhShfMzbXXFPDac+pwn4hkXWoyTO0He5ZB55FQrY3TicRh8UmpLN0eRdvapTBevHBbe1IikjVpaTD7Ydi+AO54F+p2cTqRuMDP26NISE6j7bUlvfq82pMSkcyzFuY/A39OhVuGw/UDnE4kLrFw4yEKhodyfSXvXnqgkhKRzFv8L/j9M2j2KLR8yuk04hIJyaks3HiQW68tSWiId2tFJSUimfPLf+CXd6FhP2j7iiaMlTMWbz7MycQUOjco4/XnVkmJyOWt/Ay+fwnq3AN3/kcFJeeYtXY/JQuE0bSy966POk0lJSKXtn4KfPsUVG/nGcmnGc3lLMdOJfHj1sN0rF+GkBze/+NFJSUiF7d5HsweDBVbQtexEBLqdCJxmW/+/JuUNEun+t4/1AcqKRG5mJ1L0pfcaAA9J0FouNOJxIVmrdlHjZL5qXVN/mx5fpWUiFxozwqY3AuKVktfciN7fgGJf9tyMIY1e6Lp0qisVy/gPZtKSkTO9fcf8FVXyF9KS27IJU1csYdcOXPQpVHZbHsNlZSI/E/UNhjf2bPn1HcO5Pfu7AESOOKSUpi1Zj931L2GwnlzZdvrqKRExOP4bhjfyTO8vO8cKFTe6UTiYl+vP8DJxBTubZK93yeau09E4ORB+LIjJMVC/2+gWFWnE4nLTVyxh+ol8xFRoXC2vo72pESCXdwxzyG+2MPQawaUqut0InG5P/edYP2+E9zbuHy2DZg4TXtSIsEs8SRMuAeO7oReU6Hc9U4nEj8w5tdd5M0VQueG2Tdg4jTtSYkEq9OLFv693nOhbuVWTicSP3DwRAJz1x+g2/XlKBie/Rd3a09KJBilJHkWLdz9K9z9GdRs73Qi8RNfLoskzVrua17JJ6+nkhIJNmmpMGugZ9HCO9+Del2dTiR+Ii4pha9W7KHttaUoXzSPT17T0cN9xpgexpilxpgYY0xKJrZvZ4zZaIyJN8ZsMMa09UVOkYBhLXz9GGycBbeOgIj7nE4kfmTGmv2ciE/mgZa+2YsC589JHQc+BoZebkNjTGVgJvBvoGD651nGmIrZmE8kcFgLC56DtePhxqehxRCnE4kfSUuzfPHLLq4rV4hG2Tzs/GyOlpS1doG1dhLwVyY27westtZOsNYmWWu/Atak3y4il/Pj67D8v9B4ENz8nNNpxM8s2HiQXUdO8cANlbJ92PnZnN6TyorrgNXn3bYm/XYRuZRf/gM/vQ71e0O717VooWSJtZaPfthBpWJ5aV/3Gp++tj+VVH7gxHm3RQMFLvYAY8xAY8wqY8yqqKio7Mwm4l4rRv5vVd27PoAc/vRjL27w47YoNh6IYfBNVbJlYcNL8afv1pN4zkWdrRAQc7EHWGtHWWsjrLURxYsXz85sIu605kuY/wzUvFOr6soVsdby3yU7KF0wN50aZM/ChpfiTyW1Hmh43m0N0m8XkfP9MQ3mDoGqbaDLF1pVV67Iyl3HWLX7OANvrEyunL6vDKeHoIcYY3IDudL/nTv9I6P9yS+BCGNMT2NMqDGmJ9AIGOfDyCL+YfPXMGsQVLwBuo2HnGFOJxI/9dEPOyiWLxc9GjszK77Te1J9gHhgARCS/t/xQAVjTC9jTOzpDa21O4G7geF4DvENBzpbayN9HVrE1bYvgmn3QZlGnmXfc/nmoksJPOv2RrN0+xEG3FCZ3KHOHCp2dMYJa+1YYOxF7o4Evjpv+++A77I1lIg/++snmNIbSl6rZd/lqr27aBuF84TSp1kFxzI4vSclIt6yZwVM6gmFK0HvWRBeyOlE4sd+jzzGz9uieOimKuQLc25/RiUlEggOrIWvukD+Up5VdfMWdTqR+Ll3Fm6lWL4w+jar6GgOlZSIvzu00bNoYXgh6DcX8pd0OpH4ud92HGH5X8d45OYqhOdy9rIFlZSIPzuy3bPse85w6DsXCmb/InQS2Ky1vL1wK9cUzE1Ph0b0nU0lJeKvjkfCuLs8/913DhTx3czUErh+3BrFmj3RPHpLVcdG9J1N60mJ+KMT+2FcB0iJh37zoHh1pxNJALDW8u6ibZQtHE7XRuWcjgNoT0rE/5w8BF/eBfHR0HsmlKrjdCIJEN/+eZA/95/gsdbVHJldIiPakxLxJ3HHYHwniDkAfWZBmfNnChO5Mkkpaby5YAs1Subn7obuObfpjqoUkcuLj/YU1NGd0HMylG/qdCIJIBNX7Gb30TiebV/T5zOdX4r2pET8QWIsfNUVDm2CHhOh8k1OJ5IAEpOQzAdLdtC8SlFaVXfXihEqKRG3SzoFE7vB/tXQdQxUb+t0IgkwI3/aybFTSQy7vZZPV93NDJWUiJslx3umOtqzDO7+DK7t6HQiCTB/n4jn86W76Fi/NHXLnr9kn/N0TkrErZITYHIv2PUzdPwY6nZxOpEEoP8s2oa18FTbGk5HyZBKSsSNUpJgWj/YuRju+hDq93Q6kQSgLQdjmLZ6H32bVaBcEXcu6aKSEnGb1GSYfh9s+w7u/A807ON0IglA1lpe+3YL+cNy8ugtVZ2Oc1EqKRE3SU2BGQ/Alnlw+5sQcb/TiSRALdlymJ+3RTGkdTUK5cnldJyLUkmJuEVaKsx+CDbNhravQpNBTieSAJWUksaIeZuoUjwv/ZpXdDrOJamkRNwgLQ3mPAp/ToPWL0LzR51OJAFs7G+7iDwax/N3XktoiLtrwN3pRIJBWhrMewzWT4RW/4SWTzidSAJY1MlEPli8g1tqlqBVjRJOx7kslZSIk6yF+U/Dmi+h5VNw0zNOJ5IA99aCLSSmpDL8jlpOR8kUlZSIU6yF74bB759D8yFwy3Bw2dX+Elj+2BfNtNX7uK9FJSoXz+d0nExRSYk4wVpY9AKs+ASaDIZb/6WCkmxlreXlrzdRNG8uVw85P59KSsTXrIUlr8BvH8D1D0C7f6ugJNvNXX+A1buP88xtNSmQO9TpOJmmkhLxtZ/ehKVvQ8N+cPtbKijJdicTknn1m83ULVOQLo3cs1ZUZmiCWRFfWvoO/Pga1O8Fd74HOfR3omS//yzaTlRsIp/1jSCHi9aKygz9hIj4ym8fwuJ/Qd2unvn4VFDiAxsPnGDsb7vo1aQ815Ur5HScLNNPiYgvLP8UFg6HaztBp08hR4jTiSQIpKVZnp+9gcJ5cvF025pOx7kiKimR7Lb8U/ju/6DmnXDP5xCio+ziG9NW72XNnmj+2b4WBfP4z2CJs6mkRLLTipH/K6iuYyHEP39RiP85diqJf8/fQuOKRbi7YRmn41wxlZRIdlkxCuY/4ymoLmNUUOJTb363hZMJKYzoVMd1S8JnhUpKJDus/Mwz3VGNOzwFldO9SyFI4Fm9+ziTf9/LgBsqUaNUfqfjXBWVlIi3rfwMvn3KU1Bdx6qgxKdSUtMYPnsDpQrk5rHW1ZyOc9VUUiLe9Pvn6QXVXgUljhjzaySb/47hxQ7XkjfM/wfpqKREvOX30fDNk1D9dug6TgUlPrfnaBzvLNpKm1olaFenlNNxvEIlJeINq76Ab56A6u2gmwpKfM9ay3Oz/yRnjhx+P1jibCopkau1agzMexyq3QbdvoScYU4nkiA0a+1+lm4/wjPtanBNwXCn43iNSkrkaqwaA/OGegqq+3gVlDjiaGwiI+ZtomH5QvRuUsHpOF6lkhK5UqvHphdUWxWUOGrEvE3EJqbw+j31/G4C2ctRSYlcidXj4OvHoOqt0E0FJc75aVsUs9cdYHCrqlQv6d/XRGVEJSWSVWu+hK+HQNU20H0ChOZ2OpEEqbikFJ6b9SdViuflkZurOB0nW/j/IHoRX1ozHuaeLqivVFDiqHcXbmPf8XimPdSMsJyBObO+9qREMmvtBJj7D6hyiwpKHLdubzRf/OpZJ+r6ikWcjpNtVFIimbF6LMx5BKrcDD0mqqDEUQnJqTw1bT0lC+Tm/273z3WiMkslJXI5v4/+3yCJHpNUUOK49xdvZ8fhWF6/px4Fcgf27PoqKZFLWTHqfzNJ9NAhPnHeur3RjPxpJ90jynFT9eJOx8l2KimRi1n28f+W29Awc3GBsw/zPXdnLafj+IRG94lk5NcPYNHzUOsu6PKFFiwUVzh9mG/c/Y0D/jDfadqTEjnf0nc9BVW7swpKXCPYDvOdpj0pkbP99Bb88ArU7QqdPoUQ/YiI8xKSU3k6yA7znaafQBEAa+HH1+Gn16FeD+j0MeQIzIsjxf+8v3g72w/HMva+64PmMN9pKikRa2HJK7D0bajfG+76QAUlrnH6MF+3iLK0qlHC6Tg+p5KS4GYtfP8S/PoeNOwLd74POXSqVtzh7NF8w++81uk4jlBJSfCyFhYOh2UfQcQAaP+2Ckpc5c3vtgbdaL7zqaQkOFkL3w2DFZ9A40Fw+xsQIMttS2D4dccRvvh1F/2aVQiq0XznU0lJ8ElL81yk+/vn0PRhuO01FZS4yon4ZJ6atp7KxfPy7O3BNZrvfCopCS5paZ5pjlaPgeb/gFtHqKDEdV6cs4HDJxOZObg54bmCexBPpkvKGFMGKAPEA9ustYnZlkokO6SleiaKXTsebngCWr+gghLX+Xr9AWavO8DjbapzXblCTsdx3CVLyhhTABgC9Eu/6RAQDpQ1xiwH3rPW/pC9EUW8IDUFZg+GP6fCjc/Azf9UQYnrHDyRwPDZG7iuXKGAXWk3qy63JzUfGAc0tdYePX2jMcYATYABxphq1tpR2ZhR5OqkJMGMAbB5LtzyPNz4lNOJRC5greXp6etJSknjP92uI2eIRprC5UuqpbU27fwbrbUWWA4sN8bonRT3Sk6Aaf1g23dw27+h2cNOJxLJ0Pjlu1m6/QgjOtWhcvF8TsdxjUsWTEYFdSXbXIoxJsQY85YxJsoYc9IYM8MYU+wS2z9ljNmZvu12Y4x+60jGkk7BpO6egrrjXRWUuNbOqFhe+3YzN1UvTu8m5Z2O4yqZ2gsyxvzTGHPAGPOHMeZLY8wTxphbvJThWaAjnsOHZdNvG3+RHHcBLwO9rLX5gb7AW8aYW72URQJF4kmY0AV2/QydPoHrBzidSCRDSSlpPD5lHblDQ3irSz2MzpWeI7OH6v4B1AduAyYBuYGHvJRhIPCGtfYva+0J4BmgnTGmYgbbVgXWW2uXA1hrlwF/ANd5KYsEgvjj8GUn2LsC7vkc6t/rdCKRi3p30Tb+2HeC1++uS4kCWvn5fJkdgr7BWns4/b//xjOg4qoZYwoC5YHVp2+z1u40xsQA9YDI8x4yGbjfGNMCWAa0AKoD33kjjwSAU0dgfCeI2grdx0PNO5xOJHJRv+44wsifd9KzcXna1bnG6TiulNk9qbXGmHeNMeFefv0C6Z9PnHd79Fn3ne0wMB34AUhK//yitXZDRk9ujBlojFlljFkVFRXlncTiXicPwtg74Mh26DFJBSWuduxUEo9PWUflYnl5PsjWiMqKzJZUYeAGYJ8xZpkx5mNjzEAvvP7J9M8Fz7u9EBCTwfbPA/fiOfQYiucw3+PGmAxPOFhrR1lrI6y1EcWLB+/cV0HhxD4Y0x6i90KvaVCtjdOJRC7KWssz09cTHZfMhz0bkieXJv+5mEyVlLX2QWttY6A4cD/wM1Dpal/cWhsN7AEanr7NGFMZz17UHxk8pBEwy1q7yXpsBGYDd15tFvFjxyNhzO1wKgr6zIJKNzqdSOSSxi/fzfebD/Ps7TW5tnRGB43ktEuWlDEmz9n/ttamWWs3W2snW2uHZbTNFRgF/J8xplL6DBdvAAustZEZbPsr0MkYUy39tWsBnYA1V5lB/NWRHfDF7Z7RfP3mQvkmTicSuaStB0/yyjebaVWjOPe1qOh0HNe73J7UQmPMy8aYuuascZHGmELGmHuMMfOAzleZ4XXga+B3YD8QAvROf51expjYs7Z9C5gFLEq/fQGePanXrzKD+KNDmzx7UGnJ0G8elG7gdCKRS0pITuUfk9ZQIHcob3e9TsPNM8F4Jo+4yJ3GnC6M+/Cc/4kFwoAEYC7wobV2qw9yXrWIiAi7atUqp2OItxxYB+M7Q84w6DsXild3OpHIZT0/ewPjl+/my/sbc2MQrBFljFltrY24mue45Nk6a20qnrn7xhljcgLFgPj065lEnLF3pedC3dwFPIf4ilR2OpHIZS3adIjxy3fzYMtKQVFQ3pLpISXW2hTgYDZmEbm8nT/A5F6Qv6RnD6pQOacTiVzWwRMJPDN9PbVLF+Cp22o4HceveHVyWONR1ZvPKXLGlm9gYjcoXBHu+04FJX4hJTWNIZPWkpiSxgc9GxCWM7gXMcyqKx6cb4ypANQBaqd/1AFq4pkySf8XxLvWT/GsB1W6gec6qDxFnE4kkin/+X4bKyOP8V73+lTR7OZZlqmSMsbcxrllVAvIC5wemmKBFXiGk2/0fkwJais/g2+f8lz/1GMihOV3OpFIpvy0LYqPf9xJj+vL0alBGafj+KXM7knNx1NE+/CU0GfA5vSPv4EdwLPW2p+zI6QEsaXvwuKXofrt0HUshGoCTvEPB08k8PiUdVQvkZ8XO9R2Oo7fymxJLQFuAeKA0dbaGafvSJ8kVsS7rIXvX4Jf34O6XT3LbYSEOp1KJFNSUtMYMnktCcmp/LdXQ8Jz6QzIlcrstEhtgDZ4JoKdaoxZYYxpna3JJHilpcE3T3oKKuJ+6DxKBSV+5b3vt7Ny1zFe7VyHqiV0HupqZHp0n7V2ibW2KdAFyIdnNorvgcbZFU6CUGoyzBoEq0ZDi8c8K+rm8OogVJFs9fO2KP774w66RZSlc4Oyl3+AXFKWf/qttbPwDJ64H6iMZy0ni2fyWZErl5wAU/vBn1Oh9Qtw679A08aIHzkU4zkPVa1EPl6+q47TcQLCFf2Jmj4D+TigBjAUzzpPk40xnxpjSngxnwSLxFjPNVBbv4H2b0PLJ51OJJIlp6+HiktK5WOdh/KaqzqOYq1NttZ+CFQBXgK6A395IZcEk/jjntV0I3+BziOh8YNOJxLJsvcXb2fFrmO80qkOVUvoMglv8dbB/ng8y7nPABK99JwSDGIPw9gO8Pd66DYOruvhdCKRLPthy2E+XLKDro3Kck8jnYfypqtaDtIY0wToCXQDSuJZ0j2XF3JJMIje45nJPOYA3DsFqtzidCKRLNt7LI6hU9ZRs1R+/tVR56G8LcslZYypg6eYegAVgeN41niajGfZ96neiycB6/BmGH83JJ+CPrO1WKH4pYTkVAZ/tZo0axnZp5HOQ2WDzE6LVBlPKfXEMzVSDDAHeBRYlD5DOsaYjtmUUwLJ3t/hqy6QMzfcNx9K6mp88U8vztnIhv0xfN43ggpF8zodJyBldk9qB5AGTAeeB7611iZlWyoJXDu+hyl9IF9J6DvbM6O5iB+a8vsepqzayyM3V6HNtSWdjhOwMjtwYnf6ti2AG4H62RVIAtif02FiDyhaBQYsVEGJ3/pz3wmen7ORG6oW44lbtT5UdsrstEiV8BTULDyH/JYZY3YZY143xjTMzoASIFZ+BjMegHKNof83kE+X04l/io5LYvBXqymaNxfv96hPSA5dcJ6dsjIt0jJr7RCgDNAO+AEYCPxujNlujBkBXJs9McVvWQs//Nuz1EaN26H3DMitOYnFP6WlWR6fso5DMQl83KshRfOFOR0p4GV5dJ+1Ng1YBCwyxjwEtMezd/U4kAfPFEkinoli5z8Dv38G9XtBhw8g5KquehBx1IdLdvDD1ihGdKxNg/KFnY4TFK7qN0b64InZwGxjTF6gE55RgBLsUpJg9kOwYQY0/wfcOkLz8Ilf+2lbFO8t3kbnBmXo3bSC03GChtf+rLXWngK+Sv+QYJZ0yjOCb+diaPMy3DDU6UQiV2X30VMMmbSWGiXz81rnuhj9weUzOvYi3hV3zDNR7P7VcNeH0LCv04lErsqpxBQGfrkaQBfsOkAlJd4Tc8AzzdGxXdDtS6jVwelEIlfFWstT09az/fBJxt7XWBfsOkAlJd5xZLtnmqP449B7OlS60elEIlft4x93Mn/DQf7ZviY3VteSeU5QScnV27cKvuoKJgf0nwel6zudSOSqLdlyiLcXbuWu60rzYMvKTscJWlqXW67O1u9g7J2ea58GLFRBSUDYGRXLY5PWce01BXjjnnoaKOEglZRcuTXjYfK9ULyGp6CKVnE6kchVO5mQzMAvVxGaM4cGSriADvdJ1lkLP78NP7ziWQOq23gIy+d0KpGr5plRYj2RR+OYMKAJZQvncTpS0FNJSdakpXqmOFr1BdTr4RlmnlPrXEpgeH/xdr7ffIiXOlxLsypFnY4jqKQkK5LjPZPEbpkHLYZCm5c0i4QEjAUbD/L+4u10aVSWfs0rOh1H0qmkJHPijsGknrB3BbR7A5o+5HQiEa/Z/HcMj09Zx3VlC/JKpzoaKOEiKim5vBP7YMI9cOwv6PIF1Lnb6UQiXhN1MpEHxq0if+6cjOobQe5QDZRwE5WUXNqhTZ6CSor1LLOhi3QlgCSmpPLQhNUcPZXItEHNKVkgt9OR5DwqKbm4yF9hck/IGQ73zYdSdZxOJOI11lqGzfyT1buP8997G1K3rNY5cyNdJyUZ2zTXMw9f3hLwwCIVlAScT3/6i5lr9vN4m+rcUe8ap+PIRaik5ELLP4GpfeGa6zwX6RYq73QiEa9atOkQby7YQofrSjOkdVWn48gl6HCf/E9aKiwcDss/hpp3wt2fQS5dzCiBZfPfMTw2eS31yhTkrS6a8sjtVFLikRwPMx+EzV9Dk8Fw26uQQ6OcJLCcHslXIHeoRvL5CZWUwKkjMKmHZzbzdq9D08FOJxLxuoTk/43km/6QRvL5C5VUsDu60zPE/OTf0H28FiqUgGSt5Z/pI/k+6dWQOmU0ks9fqKSC2Z4Vnj0oY6DfPCh3vdOJRLLF+4u3M3Ptfp68tTq319VIPn+i0X3BauNsGNcBwgvDgEUqKAlYM1bv473vPXPyPXqLRvL5G5VUsLEWfvsIpvX3LFA4YJHWgZKAtWznUZ6d+QfNqxTltc51NZLPD+lwXzBJS4XvnoWVo6DWXXD3KAgNdzqVSLbYcfgkg8avomLRvHzSuxG5cupvcn+kkgoWSXGeZTa2fgPNHoVbR0AO/dBKYIo6mUj/Mb+TK2cIY+67noLhoU5HkiukkgoGsYc9AyT2r4Hb34Qmg5xOJJJt4pNSeeDLVRyJTWTKwGZaXdfPqaQC3aFNMLE7nIqCHl9BzTucTiSSbVLTLEOnrOWPfdGM7N2I68oVcjqSXCWVVCDb/r1ngESuvHDft1CmodOJRLLVv7/dzIKNh3jhzmtpW7uU03HEC3RSIlCt/AwmdoXCFeHBxSooCXhfLovk81920b95Re6/oZLTccRLtCcVaNJSYcFzsOITqN4O7hkNYfmcTiWSrb7bcJCX5m6kTa0SPH/ntU7HES9SSQWSxJMwfQBsXwBNH4G2IzRJrAS83yOPMWTyWq4rV4gPezYkJIeuhQokKqlAEb3XM4Lv8Ga44124foDTiUSy3bZDJxkw9nfKFg5ndL/rCc+lP8oCjUoqEOxfDZN6epbb6DUNqrZ2OpFItjsQHU+/L1aSOzSEcfc1pkjeXE5HkmygkvJ3m+bAzEGQrzj0nQslajqdSCTbnYhLpv+YlcQmpDBlUDPKFdG1UIFKo/v8lbWw9F3PMu+l6sIDS1RQEhQSklN58MtVRB6JY2TfRlxbuoDTkSQbaU/KH6UkwTePw9oJUKcLdPwvhGoBNwl8qWmWxyav5ffdx/iwZwOaVynmdCTJZiopf3PqCEzpA3t+g5v+D1oN86wHJRLgrLW8MGcDCzYe4sUO13JnvdJORxIfUEn5k4MbPAMkTh2GLl9AnXucTiTiMx8t2cFXK/bw0E1VuK+FLtYNFo6fkzLGhBhj3jLGRBljThpjZhhjLroPb4wpYYwZZ4w5aoyJMcasM8YE/p9Um7+G0W0hLQXu/04FJUFl/PLdvLNoG3c3KMP/tavhdBzxIcdLCngW6Ag0Acqm3zY+ow2NMbmBxUASUAMoBPQCYrM9pVOshZ/egim9PQMjBv4ApRs4nUrEZ+as288LczbQplYJ3uhSTwsXBhk3HO4bCPzLWvsXgDHmGWCHMaaitTbyvG374Smmh621yem3bfRVUJ9LioM5j8DGmVCvO3T4QAMkJKgs2XKIJ6eup3HFInx0b0NCQ9zwd7X4kqP/x40xBYHywOrTt1lrdwIxQL0MHnIzsAkYmX64b4sx5gmfhPW1E/thzO2wcRa0eRk6j1RBSVBZ8ddRBk9YQ61rCvB5vwhyh2o2iWDk9J8lpy9wOHHe7dFn3Xe2YkBbYD1wDdAb+KcxpldGT26MGWiMWWWMWRUVFeWdxL6w93f47GY4ugN6ToYbhmoEnwSVDftP8MC4VZQtHM7Y+64nf26trBusnC6pk+mfC553eyE8e1MZbb/fWvu+tTbJWrsKmIDnnNYFrLWjrLUR1tqI4sWLeytz9lo/GcbeAaHh8MD3UKOd04lEfGrH4Vj6frGSAuGhjB/QhKL5wpyOJA5ytKSstdHAHuDMYkfGmMp49qL+yOAh6wCb0VNlQzzfSkuFRS/ArEFQrjE8+AOUqOV0KhGf2h8dT9/RK8hhYPyAxpQuFO50JHGY03tSAKOA/zPGVDLGFADeABZkMGgCYCxQ1BjzSPrQ9evwjO6b6bO02SE+2nP906/vQ8QA6DML8hRxOpWITx2JTaTP5ys4mZjCuPsbU7m41kETd5TU68DXwO/AfiAEz7kmjDG9jDFnhpdba3cD7YEH8BwOnA68ZK2d4uvQXnN4C3x2C+xcDHe8A3e+CyE6/i7BJTouiT6jV3LgRDxf9L+e2qXPPwMgwcpY6/9HyjIjIiLCrlq1yukY59r8Ncx6CELzQLcvoUIzpxOJ+FxMQjK9P1/Blr9P8lm/CG6q7ifnj+WyjDGrrbURV/McbrhOKvikpcGPr8HPb0GZRtBtPBQs43QqEZ+LTUyh/xcr2XQghk97N1JByQVUUr4WHw0zH4TtC6FBH88hvpwavSTBJz4plQFjf2f9vhN81LMBba4t6XQkcSGVlC8d3gKT74Xo3Z5yihig658kKCUkpzJw/CpWRh7jve71ub3uNU5HEpdSSfnK2eef+s3T+ScJWkkpaTz81RqWbj/CW13q0bG+DnXLxamksts5558ioPt4KBD4k7aLZCQ5NY1/TFrDki2HebVzHbpGlHM6kricSio76fyTyBmpaZbHp6w7s2hhryYVnI4kfkAllV0OboCpfSB6L9zxLkTcr/NPErRSUtN4atp65v3xN8Nur6lFCyXTVFLZYd0kmPc4hBeC/t9A+SZOJxJxTEpqGo9PXc/X6w/w9G01GHRTFacjiR9RSXlTcgJ89yysHgMVW0KXMZBP131I8EpOTWPolHV888ffPHt7TR5SQUkWqaS85fhumNYPDqyFGx6Hm4dDiN5eCV7JqWk8Nnkt3/55kH+2r8nAG1VQknX6LeoN27+HmQ94RvL1mAg173A6kYijklLSGDJpLd9tPMjwO2rxQMvKTkcSP6WSuhppqfDTm/DTG1Cytmf+vaL6a1GCW1JKGo9MXMOiTYd44c5ruf8GDZKQK6eSulJxx2DGA57Zy6+71zO8PFcep1OJOCoxJZVHvlrD95sP8/JdtenXvKLTkcTPqaSuxP7VMLUfxB6CO9+DRv01vFyCXkJyKoMnrOaHrVGM6FibPs0qOh1JAoBKKiushZWfwcLnIF8puH8BlGl4+ceJBLjYxBQeHLeK5buO8lrnutzbpLzTkSRAqKQyK+EEzHkUNs+Fam2h80itnisCnIhLpt+Ylfy5/wT/6VafTg00F594j0oqM/avgWn94cQ+uHUENHsUcrhhUWMRZ0WdTKTP6BX8FXWKj3s15LbapZyOJAFGJXUp1sKKkbBwOOQrCfd/B+UaO51KxBUORMfT+/MV/H0igdH9I2hZTReui/eppC4m/rjn8N6WeVD9duj0sQ7viaTbffQU9362gpj4ZL4c0JjrK+pnQ7KHSioj+1bD9P4QcwDavgrNHtHoPZF02w6dpPfnK0hOTWPig02pW7ag05EkgKmkzmYtLP8EFr0A+a/xjN4rG+F0KhHXWLPnOPeP/Z1cITmYMqgZ1UvmdzqSBDiV1GlxxzyH97Z+AzXugE7/hfDCTqcScY0lWw7x8FdrKFkgN+Pvb0L5orp4XbKfSgog8heYORBiD8Nt/4amg3V4T+Qs01fv4/9m/EGta/Izpn9jiufX4p3iG8FdUqnJnnn3fn4bilSGAQt1ca7IWay1jPz5L16fv4UWVYsysk8E+cKC+9eG+Fbwfrcdj/TMvbfvd6jfG25/A8LyOZ1KxDXS0iyvfruZ0b/s4s561/BOt+sIyxnidCwJMsFZUn9Mg2+e8Pz3PaOhbhdn84i4TFJKGk9PX8+cdQfo37wiL9x5LTly6BC4+F5wlVTiSfj2aVg/Cco1gbs/g8IVnE4l4ionE5J5+Ks1LN1+hKdvq8HDrapgdI5WHBI8JZUcB5+2hOjdcNOzcOPTWjlX5DwHouO5f+zv7Dgcy5v31KPb9eWcjiRBzlhrnc7gE/nDjG1ULg8UqwG5CwDQrVs3Hn74YeLi4mjfvv0Fj+nfvz/9+/fnyJEjdOly4SHBwYMH0717d/bu3UufPn0uuP/JJ5+kQ4cObN26lUGDBl1w//Dhw2nTpg3r1q1j6NChF9z/2muv0bx5c3777Tf++c9/XnD/e++9R/369fn+++955ZVXLrh/5MiR1KhRg6+//pp33nnngvvHjx9PuXLlmDJlCp988skF90+fPp1ixYoxduxYxo4de8H93377LXny5OHjjz9m6tSpF9z/448/AvD2228zb968c+4LDw9n/vz5AIwYMYLFixefc3/RokWZMWMGAMOGDWPZsmXn3F+2bFkmTJgAwNChQ1m3bt0591evXp1Ro0YBMHDgQLZt23bO/fXr1+e9994DoHfv3uzbt++c+5s1a8a///1vAO655x6OHj16zv2tW7fm+eefB+D2228nPj7+nPvvvPNOnnrqKQBatWrF+dz4vXcqMYWtB0+Sai1vv/E6g7u31/eevvcuuD8r33s1a9Zcba29qotNg2ZXIpUQEorXI3eYhs6KnO94XBI7DseSM0cOal9TgOvKFXI6kggQRHtSeUpXtxUGfMBzd9SiV5PyOsYukm7cb5G8/PVGapcuyOh+EZQokNvpSBIgjDFXvScVNOtNVCuZn4iKhRk+ewP3jf2dwzEJTkcScVRqmuVfX2/ixbkbaV2rJFMGNVVBiesETUmFhhi+vL8x/+pYm+V/HaXtez/zzR9/Ox1LxBEnE5IZNH4VX/y6i/tbVOLT3o3Ikytojv6LHwmakgIwxtC3WUW+GdKSCkXy8MjENTw+ZR0n4pOdjibiM7uPnuLuj3/jh61RjOhYmxc6XEuIroESlwqqkjqtSvF8TB/cnKFtqjF3/QFuf+9nfttxxOlYItnu1x1HuOujX4mKTWT8gMb0aVbR6UgilxSUJQUQGpKDoW2qM2Nwc3KHhnDv5yt4ae5G4pJSnI4m4nXWWsb+uou+X6ykZIEw5j5yA82rFHM6lshlBW1JnVa/XCG+GdKSfs0qMPa3SG5/fynL/zp6+QeK+ImklDSGzfyTl77exM01SjDz4RZaZkP8RtCXFEB4rhBe7liHSQ82xVroMWo5L87ZwKlE7VWJfzsUk8C9ny1n8u97efTmqozq00izmItfUUmdpVmVonw3tCX9m1fky+W7afe+zlWJ/1r+11Hu+OAXNh6I4YOeDXjqthqaJFb8jkrqPHly5eSlu2ozdVAzcubIwb2fr+C5WX8Sq70q8RPWWkb9vJNen6+gQO6czH6kBXddV9rpWCJXRCV1EddXLMK3Q1rywA2VmLhyD7f952d+2a69KnG30zOYv/btFm6tVZI5j7agRqn8TscSuWIqqUsIzxXC8DuvZfpDzQgLzUHv0St4Zvp6ouOSnI4mcoFth07S8aNfWbjpEM+1r8UnvRuSP3eo07FEropKKhMaVfDsVT10UxVmrNlP63d+Yvba/QTLvIfibtZapq3aS8ePfiUmIYWvHmjCgzdW1vyUEhBUUpmUOzSEZ2+vydeP3kDZInkYOmUdfb9Yye6jp5yOJkHsZEIyQ6es4+npf1CvbEG+GXIDTSsXdTqWiNcEzSzoERERdtWqVV55rtQ0y4Tlu3lrwVaSU9N4rE01HmxZmdAQdb74zvq90QyZvJa9x+IY2qY6j9xcVdMbiatoFnSHhOQw9Gteke+fuIlWNYrz5ndb6fDhL6zZc9zpaBIE0tI8o/fu+eQ3klPSmDKoGUNaV1NBSUBSSV2FUgVzM7JPBKP6NOJEfDL3fPIbz836UwMrJNscjkngvrG/89q3W7ilZgm+fawl11cs4nQskWyjS8+9oG3tUjSvWox3Fm7ly2W7+fbPv3n6tpp0v76c/roVr/nmj795bvafxCel8q+OtenTtIIGR0jA0zkpL9v8dwwvzt3Iyl3HqFumIC93rE3D8oWz/XUlcJ2IS+aFuRuYs+4A9coW5N1u9alaIp/TsUQuyxvnpFRS2cBay9z1B3jt280cikmkW0RZnmlXk2L5wnzy+hI4ftoWxTPT13M0Nol/3FKNh2+uogE64je8UVI63JcNjDF0rF+G1rVK8uHi7Yz+ZRfzNxzkiVur07tpBf2SkcuKTUzh9fmbmbB8D9VK5OPzvtdTt2xBp2OJ+Jz2pHxgx+FYXpq7kV92HKFy8bwMu70WbWqV0PkEydDizYcYPnsDB2MSGNCiEk/dVoPcoSFOxxLJMh3uywInSwo8hwAXbz7Ma/M381fUKZpWLsLwO66lThn9dSweUScTefnrjcz742+ql8zH6/fU0/lM8WsqqSxwuqROS05NY9LKPbz3/XaOxyXRuUEZnr6tBtcUDHc6mjjEWsu01ft49ZvNxCel8o9bqjLopirkyqnDwuLfVFJZ4JaSOi0mIZn//rCDMb9EkiMHPHBDZQbeVJkCmhA0qGw9eJIX525g+V/HaFyxCK/dXVcj9yRgqKSywG0lddreY3G8uWArX68/QMHwUB66qQr9mlcgTy6NaQlkMQnJvLdoO+OWRZI/d06evq0GPa8vr0UJJaCopLLArSV12ob9J3h74VZ+3BpFsXxhPHpzFXo2KU9YTp0wDyRpaZYZa/bxxndbOHoqiXsbl+eptjUonDeX09FEvE4llQVuL6nTfo88xlsLtrJy1zHKFArnsdbVuLthGXJq2LrfW7PnOCPmbWLtnmgali/EvzrW0cAZCWgqqSzwl5ICz4n0pduP8PbCrfyx7wQViuZh8E1VuLthWZ1M90N/RcXy5ndb+W7jQYrlC2PY7TXp3KCMDu1JwFNJZYE/ldRp1loWbTrEh0t28Of+E1xTMDcDb6xMj+vLE55LhwHdLupkIu8v3saklXvJnTMHA2+swgMtK5E3TOcbJTiopLLAH0vqNGstP28/wn+X7GBl5DGK5s3FgJaV6NO0gpYHd6HouCRG/7KL0b/sIikljXublOcft1SjeH5NiyXBJSBKyhgTArwO9AdyAwuBQdbaI5d53GDgY+B5a+0rl3sdfy6ps63cdYyPftjBz9uiyJ87Jz2uL0e/5hUpWziP09GC3vFTSXz+y1+M+203sYkp3FH3Gp66rQaViuV1OpqIIwKlpJ4D+gHtgKPAF0Aea+3tl3hMBWAxEAdMDaaSOu2PfdGM+vkv5m84CEC72qW4/4aKNCxfWNMt+dixU0l8vvQvxv0WSVxyKu3rXMM/WlelZqkCTkcTcVSgTDA7EPiXtfYvAGPMM8AOY0xFa23kRR4zGngOGOybiO5Tr2whPrq3Ifuj4/lyWSSTVuzhmz//5rpyhbi/RUXa1Sml4evZLPLIKUb/sovpq/eRkJLKHXWvYUjralQvmd/paCIBw9GSMsYUBMoDq0/fZq3daYyJAeoBkRk8ZhAQZ62dkn7IL6iVKRTOsNtrMeSWasxYs48xv0by2OR1FM4TSpdGZenRuDxVimsGA2+x1vJ75HE+X/oXizYfIjRHDjrWL83AGytTTeUk4nVO70mdPh5y4rzbo8+67wxjTHlgONA0M09ujBmIZ0+N8uXLX3FIf5A3LCd9m1Wkd5MK/LrzCJNW7mHMr5F8tnQXTSoV4d4m5bmtdinNpn2FTiWmMHf9ASau2MOf+09QKE8oj7SqSt/mFSiRP7fT8UQCltMldTL98/lXNBYCYjLY/nPgFWvt/sw8ubV2FDAKPOekrjCjX8mRw9CyWnFaVitO1MlEpq3ey+SVe3ls8jryh+WkXZ1SdGpQhqaVi2pp+0zYsP8EE1fuYc7a/ZxKSqV6yXyM6FibexqV1dRVIj7ghoETu4GXrbVfpP+7MrATqHT+OSljjAWOAadDFwSSgDXW2paXep1AGziRFWlplmV/HWXmmv0s2HiQ2MQUShYIo0O90nRqUIbapQtosMVZDp5I4Ov1B5i9bj8bD8QQljMHd9S7hl5NymtgikgWBNLovr78b3TfaCC/tbZdBtuWPe+macBS4B1r7aFLvU4wl9TZEpJT+X7zIeasO8CPWw+TnGopUyictrVLcuu1JWlcsUhQTsF0/FQSCzYeZPa6/azYdQxr4bqyBenUoAx3NyhLwTy6Hk0kqwJldN/rQGHgdyAMWAT0BjDG9AJGWmvzAVhr9539QGNMIhBzuYKS/8kdGsKd9UpzZ73SRMd5fjEv2nSIr1Z4zmEVyhPKLTVKcFON4rSoWoxi+QL3AtSdUbF8v+kQizcfZtXuY6RZqFwsL4+1rsZd15WmsgaciDjO8T0pX9Ge1KWdSkxh6fYoFm46xJIth4mOSwag1jUFaFGlKC2qFaNxxSJ+PaXP8VNJrNh1lGU7j/Lz9iPsOnIK8HyNt9Yqwa3XlqJOGR36FPGWgDjc5ysqqcxLTbNs2H+CX3Yc4dcdR1gVeZyk1DRyGKhRqgANyheiQblCNChfmMrF8rpyotS0NEvk0VP8uf8E6/ZGs/yvY2w5GIO1EB4aQuNKRWhdqwSta5WkTCGtiiySHVRSWaCSunLxSams2n2M3yOPs3bPcdbtjeZkQgoAeXOFUK1kfmqUzE/1UvmpWSo/FYvlpVSB3D4bPXj8VBI7omLZeTiWHYdj2Xwwhj/2nTiTMSxnDhpVKEyzykVpVqUo9coW0mzyIj6gksoClZT3pKVZdkbFsnZPNJv+jmHrwZNsPXSSY6eSzmyTM4ehdKFwyhYOp1zhPBTPH0bhvLkokjeUInnDKBgeSu7QHOTOGUJYaA7CcoZggJQ0S5q1pKRZUlLTOJmQQkx8MjEJycTEpxAVm8jBEwn8fSKBgzHx7D8ez/H0Q5PgKaRqJfNRr2wh6pUpSL2yhaheMl9QDgYRcVqgDJwQP5Mjh6FayfznzLBgreVIbBLbDp1k99E49h2PY+/xePYdj2PJ1sMcO5VEapp3/iAqlCeUUgVyc03B3NQrW4jKxfJSpUQ+qhbPR5lC4a48/CgiV0YlJV5hjKF4/jCK5w+jRdUL709Ls8QkJHPsVBLHTiVxIj6ZxJQ0ElNSSUhOIzE5FYCQHIaQHDkIyQE5c+Qgf+6cFAgPpUDuUAqE56RI3ly6iFYkiOinXXwiRw5DoTy5KJQnF5WLO51GRPyFDtSLiIhrqaRERMS1VFIiIuJaKikREXEtlZSIiLiWSkpERFxLJSUiIq6lkhIREddSSYmIiGuppERExLVUUiIi4loqKRERcS2VlIiIuJZKSkREXEslJSIirqWSEhER11JJiYiIa6mkRETEtVRSIiLiWiopERFxLZWUiIi4lkpKRERcSyUlIiKupZISERHXUkmJiIhrqaRERMS1VFIiIuJaKikREXEtlZSIiLiWSkpERFxLJSUiIq6lkhIREddSSYmIiGuppERExLVUUiIi4loqKRERcS2VlIiIuJZKSkREXEslJSIirqWSEhER11JJiYiIa6mkRETEtVRSIiLiWiopERFxLZWUiIi4lkpKRERcSyUlIiKupZISERHXUkmJiIhrqaRERMS1VFIiIuJaKikREXEtlZSIiLiWSkpERFzL8ZIyxoQYY94yxkQZY04aY2YYY4pdZNv2xpglxpgjxpjjxpilxpiWvs4sIiK+4XhJAc8CHYEmQNn028ZfZNvCwIdAVaA4MBGYb4wpl90hRUTE99xQUgOBN6y1f1lrTwDPAO2MMRXP39Ba+5W1dpa1Ntpam2Kt/QSIByJ8G1lERHzB0ZIyxhQEygOrT99mrd0JxAD1MvH4ekBRYEN2ZRQREec4vSdVIP3zifNujz7rvgwZY0oA04E3rbXbL7LNQGPMKmPMqqioqKvNKiIiPuZ0SZ1M/1zwvNsL4dmbypAxpjTwA7AQGHax7ay1o6y1EdbaiOLFi19lVBER8TVHS8paGw3sARqevs0YUxnPXtQfGT0m/VzVUmC+tfZRa63N/qQiIuIEp/ekAEYB/2eMqWSMKQC8ASyw1kaev6ExpibwCzDJWvuUb2OKiIivuaGkXge+Bn4H9gMhQG8AY0wvY0zsWdv+H1AGGGqMiT3ro5evQ4uISPYzwXK0LCIiwq5atcrpGCIiQcMYs9pae1WXCLlhT0pERCRDKikREXEtlZSIiLiWSkpERFxLJSUiIq6lkhIREddSSYmIiGuppERExLVUUiIi4loqKRERcS2VlIiIuJZKSkREXEslJSIirqWSEhER11JJiYiIa6mkRETEtVRSIiLiWiopERFxLZWUiIi4lkpKRERcSyUlIiKupZISERHXUkmJiIhrqaRERMS1VFIiIuJaKikREXEtlZSIiLiWSkpERFxLJSUiIq6lkhIREddSSYmIiGuppERExLVUUiIi4loqKRERcS2VlIiIuJZKSkREXEslJSIirqWSEhER11JJiYiIa6mkRETEtVRSIiLiWiopERFxLZWUiIi4lkpKRERcSyUlIiKupZISERHXUkmJiIhrqaRERMS1VFIiIuJaKikREXEtlZSIiLiWSkpERFxLJSUiIq6lkhIREddSSYmIiGuppERExLVUUiIi4loqKRERcS2VlIiIuJZKSkREXMvxkjLGhBhj3jLGRBljThpjZhhjil1i+3bGmI3GmHhjzAZjTFtf5hUREd9xvKSAZ4GOQBOgbPpt4zPa0BhTGZgJ/BsomP55ljGmYvbHFBERX3NDSQ0E3rDW/mWtPQE8A7S7SPH0A1ZbaydYa5OstV8Ba9JvFxGRAONoSRljCgLlgdWnb7PW7gRigHoZPOS6s7dNtyb9dhERCTA5HX79AumfT5x3e/RZ950t/0W2rZ3RkxtjBuLZUwNINMZsuKKUga0YcMTpEC6k9yVjel8ypvclYzWu9gmcLqmT6Z8Lnnd7ITx7Uxltn9ltsdaOAkYBGGNWWWsjrjRooNL7kjG9LxnT+5IxvS8ZM8asutrncPRwn7U2GtgDNDx9W/rgiALAHxk8ZP3Z26ZrkH67iIgEGDcMnBgF/J8xppIxpgDwBrDAWhuZwbZfAhHGmJ7GmFBjTE+gETDOd3FFRMRX3FBSrwNfA78D+4EQoDeAMaaXMSb29IbpgyruBobjOcQ3HOh8kUI73yjvxg4Yel8ypvclY3pfMqb3JWNX/b4Ya603goiIiHidG/akREREMqSSEhER1wqIktL8fxnLyvtijGlvjFlijDlijDlujFlqjGnp68y+kNXvl7MeN9gYY40xw32R0wlX8LNUwhgzzhhz1BgTY4xZZ4wp7cvMvnAF78tTxpid6dtuN8Y87Mu8vmCM6ZH+eyLGGJOSie2v6PduQJQUmv/vYjL9vgCFgQ+BqkBxYCIw3xhTLrtDOiAr7wsAxpgKwJPAn9kbzXFZ+VnKDSwGkvBctFkI6AXEZrS9n8vK+3IX8DLQy1qbH+gLvGWMudUXQX3oOPAxMPRyG17V711rrd9/ALuBAWf9uwpggYoZbPsysPS825YCLzr9dTj5vlzk8VF4Rk86/rU4/b4A3wPdgR+B4U5/DW54b4BBwF4g1OncLntfngB+O++2ZcBTTn8d2fTetAJSLrPNFf/e9fs9Kc3/l7EreF/Of3w9oCgQUFNJXcn7YowZBMRZa6f4JKRDruC9uRnYBIxMP9y3xRjzhE/C+tAVvC+TgQLGmBbGmBzph82rA9/5Iq9LXfHvXaenRfKGbJ3/z49l9X05wxhTApgOvGmt3e79aI7K0vtijCmP53q8ptkbyxWy+j1TDGiN53DPQ3h+YX9njDlkPSsUBIqsvi+H8fz8/MD/TqkMtdYG1B98WXTFv3f9fk+KbJ7/z49l9X0BIP2k9w/AQmBYtiRzVlbfl8+BV6y1+7MzlEtcyc/Sfmvt+9azdM4qYAKeczeBJKvvy/PAvUB9IBTP3sLjxpgB2ZTPH1zx712/Lymr+f8ydAXvC+knMZcC8621j9r0A8eB5Arel1uB19JHPR4BWgDDjDFLfRDXp67gvVmH57zMBU+VDfEccwXvSyNglrV2k/XYCMwG7sz+tK515b93nT7p5qUTd88BW4FKeL5xpgHfXWTbKkAc0BPPXzk9gVNkcjCBP31k8X2pCezDs9fgeHYXvS9lz/tYBrwJlHT663DBe1Mh/WfpETzTmV2HZ7BNd6e/Doffl2Hp21ZL/3ctYCfwvNNfh5ffkxAgN9AWSEn/79ykz2R03rZX/HvX8S/Ui2/W23jWczmJZ6hjsfT7egGx523fDtgIxKd/buv01+D0+wKMwfMXcOx5H72c/jqc/n4577E/Etij+7L6s9QKWJv+C2c78IjTX4PT7wuec/2vA5HpP0N7gHcIsFGQQP/03xnnf1T05u9dzd0nIiKu5ffnpEREJHCppERExLVUUiIi4loqKRERcS2VlIiIuJZKSkREXEslJSIirqWSEhER11JJiYiIa6mkRFwqfbntX4wx0elLdK8KwNVdRS5JJSXiQsaYVnhmzl4E3I1n6Yfv8UzkKRI0NHefiAsZYz4Dilhr73E6i4iTtCcl4k7xwG3GmKHGmFJOhxFxivakRFzIGFMQeBXPYb6CeA71PWE9C+iJBA2VlIiLGWNCgNbAp8Bha21ThyOJ+JQO94m4mLU21Vq7EFiAZ+E9kaCS0+kAInIuY8xIPKP4fgCOAi2BAcBAJ3OJOEElJeI+W4EeeJbgzoFnqe2u1to5jqYScYDOSYmIiGvpnJSIiLiWSkpERFxLJSUiIq6lkhIREddSSYmIiGuppERExLVUUiIi4loqKRERcS2VlIiIuNb/A6DACIUqL4TWAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import matplotlib.patches as mpatches\n", "from myst_nb import glue\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot()\n", "\n", "\n", "s = np.linspace(0, 1, 1000)\n", "delA1 = np.sqrt(1/4 - s*np.sqrt((1 - s**2)/2) + s**2)\n", "delA2 = np.sqrt(1/4 + s*np.sqrt((1 + s**2)/2) + s**2)\n", "\n", "\n", "ax.plot(s, delA1, label=\"$\\Delta A^{(1)}$\")\n", "ax.plot(s, delA2, label=\"$\\Delta A^{(2)}$\")\n", "ax.axhline(0.5, color=\"black\", linestyle=\"--\", label='SQL')\n", " \n", "ax.set_xlim(0, 1.0)\n", "ax.set_ylim(0, 1.55)\n", "ax.set_xlabel('$s$', fontsize=15)\n", "ax.set_ylabel('$\\Delta A^{(n)}$', fontsize=15)\n", "ax.tick_params(labelsize=13) \n", "ax.legend(fontsize=15)\n", " \n", "plt.gca().set_aspect('equal')\n", "\n", "fig.set_size_inches(10, 10)\n", "\n", "glue(\"squeezed_field_fluctuations\", fig, display=False)" ] }, { "cell_type": "markdown", "id": "a9642913-0dd7-4e6f-becb-0dc872f7292d", "metadata": {}, "source": [ "```{glue:figure} squeezed_field_fluctuations\n", ":figwidth: 600px\n", ":name: \"fig-squeezed-field-fluctuations\"\n", "\n", "Field fluctuations in each quadrature compared to the SQL. \n", "```" ] }, { "cell_type": "markdown", "id": "4d6726ca-39d3-4512-8416-14c1503328cd", "metadata": {}, "source": [ "### The thermal state\n", "\n", "Another state is the termals state, produced by radiation with random intensity and phase.\n", "\n", "The thermal state is a statistical mixture of number states without specific phase relations between the number states.\n", "\n", "The density operator in terms of the number state are given as\n", "\n", "$$\\hat{\\rho} = \\left[1 - \\exp\\left(-\\frac{\\hbar\\omega}{k_BT} \\right)\\right ]\\sum_n \\exp\\left( -\\frac{n\\hbar\\omega}{k_BT} \\right )|n\\rangle\\langle n|$$\n", "\n", "The mean photon number is given by\n", "\n", "$$\\langle n\\rangle = Tr \\{ \\hat{\\rho}\\hat{n} \\} $$\n", "\n", "And the probability of finding the mean photon number n is given by the distribution\n", "\n", "$$P(n) = \\frac{\\langle n \\rangle^n}{\\left (1 + \\langle n \\rangle \\right ) ^{1+n}}$$\n", "\n", "The photon number variance is given as\n", "\n", "$$ \\left ( \\Delta n\\right )^2 = \\langle n \\rangle ^2 + \\langle n \\rangle$$" ] }, { "cell_type": "markdown", "id": "4b0f15fe-ebf7-450c-9552-681447d9bedd", "metadata": {}, "source": [ "## References\n", "\n", "```{bibliography}\n", ":filter: docname in docnames\n", "```" ] }, { "cell_type": "markdown", "id": "c90cc152-5793-4bdc-b14d-936559623fe1", "metadata": {}, "source": [ "[//]: # \"FIXME: Add in a short note on a generalized squeezer and how you represent it's creation and annihilation operators. Also provide a schematic of the system.\"" ] }, { "cell_type": "markdown", "id": "f0585087-867f-4437-acb8-bad3d20b1427", "metadata": {}, "source": [ "[//]: # \"FIXME: Flesh out a simple section getting to the essence of entanglement and a simple demonstration of entangled states.\"" ] } ], "metadata": { "jupytext": { "formats": "ipynb,markdown//md:myst" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.15" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }