{ "cells": [ { "cell_type": "markdown", "id": "bb162714", "metadata": {}, "source": [ "# Physical benchmarks: radiation pressure\n", "\n", "In this notebook we benchmark ``atomsmltr`` simulations on simple physical examples. We focus on the effect of radiation pressure." ] }, { "cell_type": "markdown", "id": "0b8b3519", "metadata": {}, "source": [ "## Formulaes and orders of magnitude\n", "\n", "### Radiation pressure\n", "\n", "We consider radiation pressure for an atom of mass $m$, a laser of wavenumber $k$ and a transition of natural linewidth $\\Gamma$. It takes the form: \n", "\n", "$$\n", "F = \\hbar k \\frac{\\Gamma}{2} \\frac{s}{1+s},\n", "$$\n", "\n", "with $s$ the saturation parameter, given by:\n", "\n", "$$\n", "s = \\frac{I}{I_\\mathrm{sat}} \\frac{1}{1 + (2\\delta/\\Gamma)^2}\n", "$$\n", "\n", "where $I_\\mathrm{sat}$ is the transition saturation intensity, and $\\delta$ the laser detuning with respect to the atomic transition. We consider the limit $s\\ll 1$ so that the radiation pressures of independent lasers can be summed up. \n", "\n", "### Acceleration of an atom at rest\n", "\n", "We introduce the typical acceleration due to radiation pressure $\\alpha$, defined as:\n", "\n", "$$\n", "\\alpha = \\frac{\\hbar k}{m}\\frac{\\Gamma}{2}\n", "$$\n", "\n", "We consider a laser propagating along $+x$ and an atom initially at rest at $x=0$. In the limit where $s\\ll 1$, applying Newton's law of motion we obtain the following trajectory:\n", "\n", "$$ \n", "\\left\\{\n", "\\begin{array}{lr}\n", "\\ddot{x}(t) = \\alpha s\\\\\n", "\\dot{x}(t) = \\alpha s t\\\\\n", "x(t) = \\frac{1}{2} \\alpha s t^2\n", "\\end{array}\n", "\\right. \n", "$$\n", "\n", "This is valid for short times, that is when the effect of Doppler detuning due to the speed of the atom is negligible. Formally, this means that $\\Delta_\\mathrm{Doppler} \\equiv k\\dot{x} \\ll \\Gamma$. This yields:\n", "\n", "$$\n", "t \\ll \\frac{2m s}{\\hbar k^2}\n", "$$\n", "\n", "We introduce a typical time $\\tau$:\n", "\n", "$$\n", "\\tau = \\frac{2m}{\\hbar k^2}\n", "$$" ] }, { "cell_type": "markdown", "id": "45b1f4d0", "metadata": {}, "source": [ "### Doppler friction in a 1D Molasse\n", "\n", "Now if we consider two counter-propagating beams, in the limit where $kv \\ll \\Gamma$, the radiation pressure can be approximated by a friction force :\n", "\n", "$$\n", "F_\\mathrm{rad} = -m\\gamma v\n", "$$\n", "\n", "with\n", "\n", "$$\n", "\\gamma = -\\frac{\\hbar k^2 }{m} s_0 \\frac{2 \\delta \\Gamma}{\\delta^2 + \\Gamma^2 / 4} \n", "$$\n", "\n", "where $s_0 = I / I_\\mathrm{sat}$. In this case, an atom with an initial speed $v_0$ is slowed as $v(t) = v_0 \\exp(-\\gamma t)$" ] }, { "cell_type": "markdown", "id": "456bde78", "metadata": {}, "source": [ "### Order of magnitude for the main transition of ytterbium\n", "\n", "Let's give the values of $\\alpha$ and $\\tau$ for the main transition (399nm) of Ytterbium :" ] }, { "cell_type": "code", "execution_count": 1, "id": "05955e81", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+ atom mass : 2.89e-25 kg\n", "+ transition Γ : 2π x 28.90 MHz\n", "+ transition λ : 398.91 nm\n", "+ transition k : 0.016 nm^-1\n", "\n", "> acceleration α : 5.22e+05 m/s^2\n", "> recoil speed : 5.75 mm/s\n", "> typc. time τ : 22.1 µs\n", "> typc. speed v : 11.5 m/s\n" ] } ], "source": [ "# imports\n", "from atomsmltr.atoms import Ytterbium\n", "import scipy.constants as csts\n", "\n", "# parameters\n", "atom = Ytterbium()\n", "transition = atom.trans[\"main\"]\n", "\n", "# compute\n", "alpha = csts.hbar * transition.k * transition.Gamma / 2 / atom.mass\n", "tau = 2 * atom.mass / csts.hbar / transition.k ** 2\n", "v_friction = transition.Gamma / transition.k\n", "\n", "# display\n", "print(f\"+ atom mass : {atom.mass:.3g} kg\")\n", "print(f\"+ transition Γ : 2π x {transition.Gamma / 2 / csts.pi * 1e-6:.2f} MHz\")\n", "print(f\"+ transition λ : {transition.wavelength * 1e9:.2f} nm\")\n", "print(f\"+ transition k : {transition.k * 1e-9:.3f} nm^-1\")\n", "print(\"\")\n", "print(f\"> acceleration α : {alpha:.2e} m/s^2\")\n", "print(f\"> recoil speed : {csts.hbar * transition.k / atom.mass * 1e3:.2f} mm/s\")\n", "print(f\"> typc. time τ : {tau * 1e6:.1f} µs\")\n", "print(f\"> typc. speed v : {v_friction:.1f} m/s\")\n" ] }, { "cell_type": "markdown", "id": "66fc61ce", "metadata": {}, "source": [ "## Test #1 : initial acceleration of an atom at rest\n", "\n", "We consider the case of an atom initially at rest, at short times - _i.e_, when the change of detuning due to the Doppler effect is still negligible. We check that the initial acceleration is consistent with the analytical formula." ] }, { "cell_type": "code", "execution_count": 2, "id": "74acc835", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────\n", "| main |\n", "────────\n", ". Parameters :\n", " ├── λ : 398.91 nm\n", " ├── Γ : 2π × 2.89e+07 Hz\n", " ├── Isat : 59.51 mw/cm²\n", " ├── Doppler temp. : 6.93e-04 K\n", " └── lande factor g : 1.035\n", "\n", "\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# - import packages\n", "from atomsmltr.atoms import Ytterbium\n", "from atomsmltr.environment.lasers import PlaneWaveLaserBeam\n", "from atomsmltr.simulation import Configuration, RK4\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# - init config\n", "# atom\n", "atom = Ytterbium()\n", "transition = atom.trans[\"main\"]\n", "transition.print_info()\n", "# laser\n", "s = 0.1\n", "laser = PlaneWaveLaserBeam(\n", " wavelength=transition.wavelength, direction=(1, 0, 0), tag=\"399\"\n", ")\n", "laser.set_power_from_I(s * transition.Isat)\n", "# config\n", "config = Configuration(atom=atom) + laser\n", "config.add_atomlight_coupling(\"399\", \"main\", detuning=0) # resonant laser\n", "# simulator\n", "sim = RK4(config)\n", "\n", "# - simulate\n", "# physical parameters\n", "alpha = csts.hbar * transition.k * transition.Gamma / 2 / atom.mass\n", "tau = 2 * atom.mass / csts.hbar / transition.k**2\n", "# simulation parameters\n", "t = np.linspace(0, s * tau, 1_000)\n", "u0 = np.zeros(6)\n", "# run\n", "res = sim.integrate(u0, t)\n", "\n", "# - plot results\n", "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n", "ax[0].plot(res.t * 1e6, res.y[0, :] * 1e6, label=\"sim\")\n", "ax[0].plot(res.t * 1e6, 0.5 * s * alpha * res.t**2 * 1e6, \"--k\", label=\"theory\")\n", "ax[0].set_ylabel(\"position (µm)\")\n", "ax[0].legend()\n", "ax[1].plot(res.t * 1e6, res.y[3, :] * 1e3)\n", "ax[1].plot(res.t * 1e6, s * alpha * res.t * 1e3, \"--k\")\n", "ax[1].set_ylabel(\"speed (mm/s)\")\n", "\n", "for cax in ax:\n", " cax.grid()\n", " cax.set_xlabel(\"time (µs)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "da81c342", "metadata": {}, "source": [ "Let's vary the saturation parameter" ] }, { "cell_type": "code", "execution_count": 3, "id": "b1bc7e00", "metadata": {}, "outputs": [], "source": [ "s_list = np.logspace(-5, -1, 50)\n", "v0_sim = []\n", "\n", "for s in s_list:\n", " # update laser power\n", " laser.set_power_from_I(s * transition.Isat)\n", " config.update_objects(laser)\n", " sim.config = config\n", " # run simulation\n", " t = np.linspace(0, 0.01 * s * tau, 1_000)\n", " u0 = np.zeros(6)\n", " res = sim.integrate(u0, t)\n", " # fit\n", " p = np.polyfit(res.t, res.y[3,:],deg=1)\n", " v0_sim.append(p[0])" ] }, { "cell_type": "code", "execution_count": 4, "id": "e6cc85f4", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v0_sim = np.asanyarray(v0_sim)\n", "v0_th = alpha * s_list\n", "\n", "plt.figure()\n", "plt.plot(s_list, v0_sim)\n", "plt.plot(s_list, v0_th, '+k')\n", "plt.loglog()\n", "plt.grid(which='both', alpha=0.5)\n", "plt.xlabel(\"saturation parameter s\")\n", "plt.ylabel(\"initial speed (m/s)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f70dfc91", "metadata": {}, "source": [ "And now let's change the detuning" ] }, { "cell_type": "code", "execution_count": 5, "id": "30f1d114", "metadata": {}, "outputs": [], "source": [ "s = 0.01\n", "laser.set_power_from_I(s * transition.Isat)\n", "config.update_objects(laser)\n", "\n", "delta_list = np.linspace(0, 5, 100) # in units of Gamma\n", "v0_sim = []\n", "\n", "for delta in delta_list:\n", " # update laser power\n", " config.reset_atomlight_coupling()\n", " config.add_atomlight_coupling(\"399\", \"main\", detuning=delta*transition.Gamma) \n", " sim.config = config\n", " # run simulation\n", " t = np.linspace(0, 0.01 * s * tau, 1_000)\n", " u0 = np.zeros(6)\n", " res = sim.integrate(u0, t)\n", " # fit\n", " p = np.polyfit(res.t, res.y[3,:],deg=1)\n", " v0_sim.append(p[0])\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "54eed2c7", "metadata": {}, "outputs": [ { "data": { "image/png": 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xeFDAt7CIiEgaHHRIJ1oOfR9vWs/DB4+GYfpvl6SOQ0REVRQHHdIJc1NTjB4yBHKZgJ3n07HrQrrUkYiIqArioEM6E+Bhj/HtasMGRVBsfhMP7yZLHYmIiKoYDjqkUxM7+GGp7RoMVu9Gxo+vA1xIkIiIRMRBh3TK3EQOtz7/Q5LKA7Nyu2DXxQypIxERURXCQYd0rl7DYGxvuRGnVP74cMsFZOU/ljoSERFVERx0SBSTOtaDv5sdHhaV4n+/noBaWSZ1JCIiqgI46JAozExkWDgoCB1MLuDD26NwfuMcqSMREVEVwEGHRFO/hh1eaWgKVyEX5pc34s4DhdSRiIjIyHHQIVG1GfgmlttOQu/iWXhn02WoVPwUFhER6Q4HHRKVXC5DlxHvQ2ZqiZM3HmD1iVtSRyIiIiPGQYdE5+NkjQ+6NwAAnN/7PVLPH5U4ERERGSsOOiSJl8O9MMMtFovkiyHfOhYlRbxeh4iItI+DDklCEAT0GDIed+GMjSXNsOhQqtSRiIjICHHQIck4u9TApT4x+LJsAL4+dhunbjyQOhIRERkZDjokqc7BtTCoiSfUauCtDQnIy8uVOhIRERkRDjokuek9/RHkWIJZRZ/izspB3PiTiIi0hoMOSc7a3ARzI93QWnYRfgXxOHj0sNSRiIjISHDQIb3gH9QMB+t+jN4ln2LKwRKk5RRJHYmIiIwABx3SG50GT4KNVxDyi8swef05lCpVUkciIiIDx0GH9IaJXIZFg4Nha2GCrNTrOLruf1JHIiIiA8dBh/SKRzUrfNHdAzvNP0DHWwtw9fAGqSMREZEB46BDeicyrCESnXrgrMoP7x9X4mFhidSRiIjIQHHQIb0U9uoiTLOdh3P59nh303mo+ZFzIiJ6Dhx0SC9ZWVrhy6FhMJPLEHM5E+sPn5M6EhERGSAOOqS3GtW0x/td62GYfD96H+6CG6f3SB2JiIgMjIkmd75y5QrWr1+P33//Hbdv30ZRURGcnZ3RuHFjREZGol+/fjA3N9dVVqqCRrashZOxd2GVX4xLe7+BU2BH2FmYSh2LiIgMRKXO6Jw9exYRERFo3Lgxjh07hvDwcEydOhWffvopXn75ZajVanz44Ydwd3fHvHnzUFxcrOvcVEUIgoCGY1biM5M3MKlwJN7fdIHX6xARUaVV6oxOv3798M4772Djxo1wcHD4z/udPHkSixcvxoIFC/DBBx9oKyNVcfYODogcPg3fLD+JnRfS0Ty2Ol5u5i11LCIiMgCVGnSSkpJgavrstwuaN2+O5s2bo7S09IWDEf1dY69qmNalPubuuoSHu2bhhtlQ+IZESB2LiIj0XKXeunrWkJObm6vR/Ymex6uta+HzGgcxSbYJttvHQqF4KHUkIiLScxp/6mrevHnYsOGv1WoHDhyI6tWro2bNmkhMTNRqOKK/EwQBHUd+jCuCHz4tHoy3t6bweh0iInoqjQed5cuXw9PTEwAQExODmJgY7N69G127dsU777yj9YBEf+fg4IiSUTHYI7TGvsuZ+Pb4LakjERGRHtN40MnIyCgfdHbs2IGBAweic+fOePfddxEXF6f1gM+Sm5uLJk2aIDg4GI0aNcKqVatEz0DiCvJyxMc9/QEAS/ZewJ3k8xInIiIifaXxoFOtWjWkpaUBAPbs2YOIiD8uCFWr1VAqldpNVwm2trY4evQoEhISEBsbizlz5uDBgwei5yBxvRzuheENTbHR5GM0OfMmcu4lSx2JiIj0kMaDTt++fTF06FB06tQJDx48QNeuXQEA586dg5+fn9YDPotcLoeVlRUAoLi4GGq1mtdtVAGCIOC9fi0hMzFHqVqGxduOo0ypkjoWERHpGY0HnS+//BITJ06Ev78/YmJiYGNjAwBIT0/H+PHjNQ5w9OhR9OzZE+7u7hAEAVu3bn3iPtHR0fDx8YGFhQXCw8Nx+vTpCt/Pzc1FUFAQPDw88M4778DJyUnjHGR4rKysYTpkHfop5+KHO674fO81qSMREZGeqfQWENOnT0fv3r0RGhqKt99++4nvv/nmm88VoLCwEEFBQRg9ejT69u37xPc3bNiAqKgoLF++HOHh4Vi0aBEiIyNx7do1uLi4AAAcHByQmJiIzMxM9O3bF/3794erq+sTxyouLq6warNCoQAAKJVKrb/tplQqoVKpJHk7ryrx8PbDsBaFmHs0CyuO3kCjGhboFuQldSyjw9ezeNi1ONizOHTVsybHE9SVfJ9n9OjR2LFjB8zMzNCzZ0/07t0bHTp0gJmZ2XMHfSKMIGDLli3o06dP+W3h4eEICwvD0qVLAQAqlQqenp6YNGkS3nvvvSeOMX78eHTo0AH9+/d/4nszZ87ErFmznrg9Li6u/MyUtqhUKuTk5MDR0REyGfdO1ZU/e956E0i5fAaLzaJxt9knqFarsdTRjApfz+Jh1+Jgz+LQVc8FBQUICwtDXl4e7OzsnnrfSg86wB+Bjx8/ju3bt2Pbtm1IT09Hp06d0Lt3b/To0QOOjo4vFPyfg05JSQmsrKywcePGCsPPiBEjkJubi23btiEzMxNWVlawtbVFXl4eWrZsiZ9//hkBAQFPHP/fzuh4enoiJyfnmUVpSqlUIjk5GX5+fpDL5Vo9Nv3lz559avni/JIBaPboKOJkQfCL2gc7Sy5cqS18PYuHXYuDPYtDVz0rFAo4OjpWatDRaPdymUyG1q1bo3Xr1pg/fz6uXLmC7du3Y8WKFRg7diyaNm2KXr16YciQIahZs+YL/RAAcP/+fSiVyifehnJ1dcXVq1cBALdv38bYsWPLL0KeNGnSvw45AGBubv6vu6vL5XKdvNBlMpnOjk1/kclkMDczRd3XVmND9BR8UtgHzTZewKrhTSCTCVLHMxp8PYuHXYuDPYtDFz1rciyNBp1/atCgARo0aIB3330XWVlZ2L59O3777TcA+NfreHShadOmSEhIEOW5SL85OlZHw9HRKPv6BA5czcKiA9cR1amu1LGIiEhCWnvDzMXFBWPGjMG2bdu0NuQ4OTlBLpcjMzOzwu2ZmZmoUaOGVp6DjEujmvaY/dIfZ/SSDv2IxJ0rJE5ERERS0viMzuPHj/HVV1/h0KFDyMrKgkpVce2Ss2fPai2cmZkZQkNDceDAgfJrdFQqFQ4cOICJEydq7XnIuPQP9UDRtUMYnrQIJadNcMM7GL6NwqWORUREEtB40BkzZgz27duH/v37o2nTphCEF7sGoqCgAMnJf61qe/PmTSQkJMDR0RFeXl6IiorCiBEj0KRJEzRt2hSLFi1CYWEhRo0a9ULPS8Zt6MAhOLPgJyTm22PtDgW21CqBo7X2PiFIRESGQeNBZ8eOHdi1axdatmyplQBnzpxB+/bty7+OiooC8Mcnq1avXo1BgwYhOzsb06dPR0ZGBoKDg7Fnz55/XSfneXEdHcP1Xz0LgoBa435B1IozSM0pwhs/xGPNqCYwlfNjpM+Dr2fxsGtxsGdxGNQ6On/y9/fH+vXrERgYqHEwfREdHY3o6GgolUokJSVxHR0D9qyeb+eWYOqOO3hUpsJ7Xklo174r8IJnIasivp7Fw67FwZ7FYXDr6ADA7t27sWTJEixfvhze3t4vFFRqCoUC9vb2XEfHgFWm5/2XM6H45XUMkB9FfJ0pCB48Q+SUho+vZ/Gwa3GwZ3EY3Do6ANCkSRM8fvwYvr6+sLKygqlpxUXZcnJyND2k5LiOjmF7Vs+RAe44mtgMZdePYeuVfDy68RCt6nA/NE3x9Swedi0O9iwOg1tHZ8iQIbh79y7mzJkDV1fXF74YmUgMrYe+j3k/NsS6S6bY+mM8toxvCT8X7b5dSURE+kfjQefEiRM4efIkgoKCdJGHSCcEmQxvDumJM6ticeb2Q4xbfQIbRwXAwdlN6mhERKRDGl8ZVL9+fTx69EgXWYh0ytxEjhWvhKKhQylmF3yM7JW9UfKoUOpYRESkQxoPOp999hneeustHD58GA8ePIBCoajwPyJ9Vt3GHEv7+qKecAeuJalY9utOaHg9PhERGRCN37rq0qULAKBjx44Vbler1RAEwSDXJOA6OobreXr2qt0Q5zqswPt77+H6ZWvIDlzHhPa1dZjS8PH1LB52LQ72LA59WEdH40Hn0KFDmj5E7/x9HR0ASElJ0dk6OsnJyVyjQYeet2cbVz90buqM66fuY+H+6zB//ABt/arpMKlh4+tZPOxaHOxZHLrquaCgoNL31XgdHWPCdXQM34v2PGf3VRw+fhyrzBbiccfZqNeyj/ZDGgG+nsXDrsXBnsVhMOvopKamwsvLq9IB7t69i5o1a1b6/lLjOjqG7UV6/rCbP9pcnwffvHRcPfgJbtXvhNou2h16jQVfz+Jh1+Jgz+KQeh2dSp1HCgsLw+uvv464uLj/vE9eXh5WrVqFRo0aYdOmTZUOQCQlmUxA+Bsr8JtlHwx9/B5GrY7H/YJiqWMREZGWVOqMzuXLlzF79mx06tQJFhYWCA0Nhbu7OywsLPDw4UNcvnwZly5dQkhICObPn49u3brpOjeR1lhYWKLFhJWwWXYCqTlFGLM6Dj+91gzW5hpfwkZERHqmUmd0qlevjoULFyI9PR1Lly5FnTp1cP/+fVy/fh0AMGzYMMTHx+PkyZMccsggOdmYY/WoMFSzMoXNvWO4tqgnSou5XhQRkaHT6J+slpaW6N+/P/r376+rPESS8XW2wffDGsB77WhUe5SP3d9+jC5vfM5tToiIDBg/U0f0N8G1PXGz3RJsVrbClNRW+DImSepIRET0AjjoEP1DSPu+KO75NUpgiiUHk/HDqdtSRyIioufEqy3BlZENma56HhhaE+m5RVhyMAXXty9AQnZ9BHR7XavPYUj4ehYPuxYHexaHQa6MbAy4MrLx0GXPXT3VMPG8jsnZa1B2RoZ9cEGtOo20+hyGgq9n8bBrcbBncXBlZIlxZWTDp+uelUol4pcMxcmH9vhW3h8/jAlHoIe91p9H3/H1LB52LQ72LA6DWRn5t99+q/ST9+rVq9L31RdcGdmw6bJnuVyOkCnr8dXqMyhMeYAxa+Px67jmqO2s3TOAhoCvZ/Gwa3GwZ3FIvTJypQadPn36VPhaEAT8/UTQ3z9+y/c7ydiYm5pg5fAmGLLyFC7dfYgTyyfBdvg0uHjXlzoaERE9Q6XeMFOpVOX/27dvH4KDg7F7927k5uYiNzcXu3btQkhICPbs2aPrvESSsDE3wepRYfif7Ra8otyMktV9cD8vX+pYRET0DBpfjDx16lQsX74crVq1Kr8tMjISVlZWGDt2LK5cuaLVgET6orqNOdqPnI4b35zG/OJ+SF2dgJ/HNoO9panU0YiI6D9ofAl0SkoKHBwcnrjd3t4et27d0kIkIv3lVtMHGHcMZ6xa43K6AqO+P43C4jKpYxER0X/QeNAJCwtDVFQUMjMzy2/LzMzEO++8g6ZNm2o1HJE+8nV1wLoxTWFvaYqk1Hs4+tWreFyokDoWERH9C40Hne+++w7p6enw8vKCn58f/Pz84OXlhbt37+Lbb7/VRUYivdPAzQ6rR4VhpflidC3YggvLXkapUiV1LCIi+geNr9Hx8/PD+fPnERMTg6tXrwIAGjRogIiICG5+SFVKY69quNB1Bu7sHoeZOZHwXn8OSwY3homci48REemL51oZWRAEdO7cGW3atIG5ubnBDzjcAsJwSd2zf1gHHLE+hOvrL+LShQyYyBLwRf9AyGWG/d/EP0ndc1XCrsXBnsWhD1tAaLwyskqlwuzZs7F8+XJkZmYiKSkJvr6++Pjjj+Hj44MxY8ZoHFhsf98CIikpCXFxcTrbAsLR0ZHLi+uQvvR8MrUQ/zuUAQ9k4OPqh+HedRpkcuPZYUVfeq4K2LU42LM4dNVzQUEBwsLCKrUyssaDzieffII1a9bgk08+wWuvvYaLFy/C19cXGzZswKJFi3Dy5MkXCi8mbgFh+PSp572JqQjY1gmeQjYOuQxH67FfGvzZzj/pU8/Gjl2Lgz2Lw2C2gPi7tWvXYuXKlejYsSPGjRtXfntQUFD5NTuGhltAGDZ96blbSC2czvgIilML8U5qc3TfeRUzezU0mmFHX3quCti1ONizOKTeAkLj80h3796Fn5/fE7erVCqUlpZqejgio9K020hc7vkbHgj2WHPyNmZtv4wqvG8uEZHkNB50/P398fvvvz9x+8aNG9G4cWOthCIyZAPCfDCvbyAEAUg6tQNxy8ZAreIFj0REUtD4ravp06djxIgRuHv3LlQqFTZv3oxr165h7dq12LFjhy4yEhmcgWGeMCt5iIh9o2GT/Rg7v/dBt9EfG83bWEREhkLjMzq9e/fG9u3bsX//flhbW2P69Om4cuUKtm/fjk6dOukiI5FB6tMyEBcbz8I+ZSjevB7It7GIiCTwXJ9/bd26NWJiYrSdhcjoNOszDr+4d0PplgtYfeIWylQqfNKzIWRcVJCISBTP9bdtbm4uvvnmG3zwwQfIyckBAJw9exZ3797VajgiYzCwqRfm9/vjmh153CokLhkAZRkv3CciEoPGZ3TOnz+PiIiI8t3KX331VTg6OmLz5s1ITU3F2rVrdZGTyKANaOIJ++J0tNv3A8zylFj73RIMHfMmt4sgItIxjf+WjYqKwsiRI3H9+nVYWFiU396tWzccPXpUq+GIjEnnlk2R2PwrLFP2wfQb9TBlQwI3AiUi0jGNB524uDi8/vrrT9xes2ZNZGRkaCUUkbEK6zIMtQfPg6lchp3n0zHhhzg8LiqQOhYRkdHSeNAxNzeHQqF44vakpCQ4OztrJRSRMYtsWAMrXgmFmYmA9tfn4tbiLijKz5E6FhGRUdL4Gp1evXrhk08+wS+//ALgj53MU1NTMW3aNPTr10/rAcXA3csNl6H23LaOE358yRn1fzsFq8ePMefbHzDptbGwtTCVOtq/MtSeDRG7Fgd7FodB7l6el5eH/v3748yZM8jPz4e7uzsyMjLQvHlz7Nq1C9bW1hoHFht3Lzceht7zvZTz2BebgPUlLeFX3QyzO7nD3kL/9t0x9J4NCbsWB3sWh0HuXv6nY8eO4fz58ygoKEBISAgiIiKeK6yUuHu54TOGni/fU2DE6jPIKSxBkLOAFf1rw9njyf3kpGQMPRsKdi0O9iwOg9y9/E+tWrVCq1atnvfheoW7lxs2Q+85wLMafnm9OV795ig+yJsF2ffZSB+6CR519WvvOEPv2ZCwa3GwZ3EY3O7lAHDgwAH06NEDtWvXRu3atdGjRw/s37//eQ5FRAD8XGzw03B/uJoUwkJdhHc3xOHi3TypYxERGTyNB51ly5ahS5cusLW1xZQpUzBlyhTY2dmhW7duiI6O1kVGoirB3cMHtm/EYLr9bJworIkhK08h9sYDqWMRERk0jd+6mjNnDr788ktMnDix/LbJkyejZcuWmDNnDiZMmKDVgERVSXVnN3wyfjjurTmD0zdz8NF3v+HzNiYI7vyK1NGIiAySxmd0cnNz0aVLlydu79y5M/LyeKqd6EXZWZhi7eim6FPXHN/JZiPw+CQc37pS6lhERAZJ40GnV69e2LJlyxO3b9u2DT169NBKKKKqzsJUji9eaYs71VsgVe2Cyads8NWB63jOD0kSEVVZGr915e/vj9mzZ+Pw4cNo3rw5AODUqVM4fvw43nrrLSxZsqT8vpMnT9ZeUqIqxsTUFM0mrUb0rjN4cCwbC2KSkJn/GLN6NYJcJkgdj4jIIGg86Hz77beoVq0aLl++jMuXL5ff7uDggG+//bb8a0EQOOgQvSBBJsPEHk1h63gLM7dfwo3Tu3D++ntoMP5nWFhrd+0nIiJjpPGgc/PmTV3kIKKnGNHCB66WKjTZ+gacCvPwy7L30Gn8IlSzNpM6GhGRXnvh9ZiVSiUSEhLw8OFDbeQhov/QpbEvMrp+gxiE46MHndHv6xNIfVAkdSwiIr2m8aAzderU8reolEol2rRpg5CQEHh6euLw4cPazkdEf9OoWWd4v7EJzg52uHG/EC8tO45LVy5JHYuISG9pPOhs3LgRQUFBAIDt27fj1q1buHr1Kt588018+OGHWg9IRBXVdbXF5vEt4O9mhy6Pd6H2+rZI3LtG6lhERHpJ40Hn/v37qFGjBgBg165dGDBgAOrWrYvRo0fjwoULWg9IRE9ytbPAL683Qx+7JFgIpdj/++/4/jivnyMi+ieNL0Z2dXXF5cuX4ebmhj179uDrr78GABQVFRnsxmhKpRJKpVLrx1SpVFo/LlVUlXu2NJUhYMomrP/hK3yV3ADYfhk3sgvwUbf6MJG/8OV3FVTlnsXGrsXBnsWhq541OZ7Gg86oUaMwcOBAuLm5QRAEREREAABiY2NRv359TQ8niejoaERHR5cXlZKSAhsbG60+h0qlQk5ODpKTkyGTafeXDv2FPQNBLXtgjEMuvj2Tgx9P3UKjpGjUixgNCyvtffycPYuHXYuDPYtDVz0XFBRU+r6C+jmWWt24cSPS0tIwYMAAeHh4AADWrFkDBwcH9O7dW9PDSUahUMDe3h45OTmws9PumiRKpRLJycnw8/Mz2DNdhoA9/2XvpQzc3TgNr8m2I0nuB8s3DsG9mrVWjs2excOuxcGexaGrnhUKBRwdHZGXl/fM398an9EBgP79+z9x24gRI57nUHpBLpfr5IUuk8l0dmz6C3v+Q7fAmkhSjkPGthNY/KgbYpefxqrhoWjsVU0rx2fP4mHX4mDP4tBFz5oci+friIxI3catoBx/GikunXC/oBiDVp7CjjPJUsciIpIMBx0iI1PTxQmb3miBiAauMC0rRO3fXkLcyglQlZVJHY2ISHQcdIiMkLW5CVa8Eoo5De+igSwVPne34/0fDqGohMMOEVUtHHSIjJRcJqD3K1NwqvF8vKF8GxuulqDvshNIy+G2EURUdVTqYmSFQlHpA2r700tE9GKa9X4d7wXlYNwP8biakY+Pln6P9zrURINWfaSORkSkc5UadBwcHCAIwlPvo1arIQgCF18i0kNNfBzx28RWeH/NPnyeMx/VY/JwKGcx2vcy3E9LEhFVRqUGnUOHDuk6BxHpmLuDJVaMjUDi8mbIeXgJE07YoHfZeczs1RDmJvx4LREZp0oNOm3bttV1DiISgYWlNZpO+RnfHzyPRwfu4ufTabiakY8VA+rCxdlZ6nhERFr3XAsGAn/sbZWamoqSkpIKtwcGBr5wKCLSHUEmw+iIYPh6umPyz+fgdmcPTKIH42rkctRv3l3qeEREWqXxoJOdnY1Ro0Zh9+7d//p9XqNDZBja1XPB9oktkff1LDgqFfh11884jYZ4pZn3M6/JIyIyFBp/vHzq1KnIzc1FbGwsLC0tsWfPHqxZswZ16tTBb7/9pouMRKQj3k428Ivaiy1Or2N+6UBM33YJb/2SiEcl/AcLERkHjQedgwcPYuHChWjSpAlkMhm8vb3x8ssvY/78+Zg7d64uMhKRDllZ26LPhHmY1q0h5DIBm8/dwfYFr+Hu9QSpoxERvTCNB53CwkK4uLgAAKpVq4bs7GwAQEBAAM6ePavddEQkCkEQMLZNbfz4ajjesDqIgcWbYPVjDxxMTJE6GhHRC9F40KlXrx6uXbsGAAgKCsKKFStw9+5dLF++HG5ubloPSETiaeZbHaNfm4qLpgFYUNofo3++ivl7rqJMqZI6GhHRc9H4YuQpU6YgPT0dADBjxgx06dIFP/74I8zMzLB69Wpt5yMikTm7ecH+nYMw2Z0EnLyNZYdTcONGEsYE2QJ16kgdj4hIIxoPOi+//HL5n0NDQ3H79m1cvXoVXl5ecHJy0mo4IpKGmZkZZvZuhFAfR3y06SxezfgUtbPScQkrEdiym9TxiIgq7bnX0fmTlZUVQkJCtJGFiPRMzyB3BNg/RtnaUsiVZZi8IwMDSpLxRtvakMn4EXQi0n+VGnSioqLw6aefwtraGlFRUU+978KFC7USTExKpVLr6/8olUqoVCquK6Rj7Fn3PD29UTD5EBb/uAm30lzx+d5rOJVyH1/0bQAnexup4xkdvqbFwZ7FoaueNTlepQadc+fOobS0tPzPhi46OhrR0dHlRaWkpMDGRrt/YatUKuTk5CA5ORkymcbXfFMlsWdxqFQqtA+qD1sPU3x9+gEyUxJQtuRl/B44DTX8W0sdz6jwNS0O9iwOXfVcUFBQ6fsKarVarbVnNjAKhQL29vbIycmBnZ2dVo+tVCqRnJwMPz8/yOXcMFFX2LM4/t5z8v0iZH83FG3LjuOQMhgJrVZgQgc/yPlWllbwNS0O9iwOXfWsUCjg6OiIvLy8Z/7+1vgandGjR2Px4sWwtbWtcHthYSEmTZqE7777TtNDSk4ul+vkhS6TyXR2bPoLexbHnz37uzug6M0NOPTdO3jrblvkHErB6du5+HJQMGrYW0gd0yjwNS0O9iwOXfSsybE0Po+0Zs0aPHr06InbHz16hLVr12p6OCIyQFbWtmg/aTk+GtgaVmZynLzxAD8uegfnY9ZJHY2IqIJKn9FRKBRQq9VQq9XIz8+HhcVf/3JTKpXYtWtX+YrJRFQ19A3xQLCnA5as24CpeesgP74Wq+5b4JX+fWFhyn8lE5H0Kj3oODg4QBAECIKAunXrPvF9QRAwa9YsrYYjIv3n62yDeROGIva7eNy9m4bZiVbYnHUCXw0Jhp+L7bMPQESkQ5UedA4dOgS1Wo0OHTpg06ZNcHR0LP+emZkZvL294e7urpOQRKTfzM0t0eKNZTh4JR2OGy/iSroC/b46iK+Db6P5SxMh8FMtRCSRSg86bdu2BQDcvHkTXl5eEAR+woKIKurQwA17plTDW78mouPNL9Diwj4cu3kc/m+sg6O1mdTxiKgKqtSgc/78eTRq1AgymQx5eXm4cOHCf943MDBQa+GIyPC42FlgzaimOLW+MR5fO4SVOUG4sugoFgwIQpu6zlLHI6IqplKDTnBwMDIyMuDi4oLg4GAIgoB/W35HEASuMklEkMkEtBj6Aa4mD8S93+4iO6sAw787jbcbA6/2aA0La+2uW0VE9F8qNejcvHkTzs7O5X8mIqqM+n5+2D6xFubuvoItJ6+gz+X3kH3NHI/6/Yi6DRtLHY+IqoBKDTre3t7/+mciomexNJPjk96N0NP1Acz2qPCorBQDf7qBsZ1s8Xqb2lxRmYh06rl2L79+/ToOHTqErKwsqFSqCt+bPn26VoIRkXEJa9YWD/1OYfnW35GbbIH5e67h4JUsLOzuDi8vH6njEZGR0njQWbVqFd544w04OTmhRo0aFT59JQgCBx0i+k/VnFzx8Zh+aBB/B7O2X4Zd2gE4f7sEp/3fQtjAafw0JxFpncaDzv/+9z/Mnj0b06ZN00UeIjJygiBgQBNPNK9dHTdWroDloxIkXkjEVwWnMb9/INzsLaWOSERGRONVvB4+fIgBAwboIgsRVSEe1azQ6u2NOOr/KZZgMH6/fh+dvzyKzaeTof7HW+JERM9L40FnwIAB2Ldvny6yEFEVI5PL0GbgZGyZ3BFBng7If1wGs+0TcPHzzsi+e0PqeERkBDR+68rPzw8ff/wxTp06hYCAAJiamlb4/uTJk7UWjoiqBj8XG2wa1xzr9x5Bp9h4yIuUeHnVXgzu3Qu9g9157Q4RPTeNB52VK1fCxsYGR44cwZEjRyp8TxAEDjpE9FxM5DK83K09btaKwfYdm3HqgRdObUjAjvPpmN2rHlyrcYNQItKcxoMOFwwkIl2q1aAx3qgbBOFwCpYcvI7EK1dRdnMwzgRMQOhLU7hBKBFphH9jEJHeMZXLMKljHeyY1BrvVjuCmsiGeeJqjPo+FndzH0kdj4gMSKXO6ERFReHTTz+FtbU1oqKinnrfhQsXaiUYEVG9GraoHbUMJ9Z7YO41V1y4noPOC49gWpe6eLmpF2Qmz7XmKRFVIZX6W+LcuXMoLS0t//N/4QWDRKRtJqamaPHKDCzKLsC7G88j/vZDXN4ZjeuHjsGi39fwrh8idUQi0mOVGnQOHTr0r38mIhJLbWcb/Pp6c/xwIhmdYibBrfQB5vz4HWzb2WJcu9owlfOdeCJ6Ev9mICKDIZMJGN6qDvBqDHbZDcQ3pZFYEJOEnl8dw9lbWVLHIyI9xEGHiAyOm2dtdH1zJb4cHAJHazNcy8hD6Xc9Ebd0BPJzH0gdj4j0CAcdIjJIgiCgd3BN7I9qi7fr5SBcdhX+2bvxcnQM9l7KkDoeEekJDjpEZNAcrc0wYdQIXIj4EYvMxyEx3xavr4vHa2vPID3rvtTxiEhi/GwmAKVSCaVSqfVjqlQqrR+XKmLP4jCEnv2bd4Vvk84wOZSCVb/fxI0rZ2GV0gun/F5F44EfwsRAPopuCF0bA/YsDl31rMnxDOO/fC2Ljo5GdHR0eVEpKSmwsbHR6nOoVCrk5OQgOTkZMq7kqjPsWRyG1HPvWgKCHGqi8NDPsC8pRGHSUXRb1AqTWrigvrOF1PGeyZC6NmTsWRy66rmgoKDS9xXUarVaa89sYBQKBezt7ZGTkwM7OzutHlupVCI5ORl+fn6Qy+VaPTb9hT2LwxB7VilViN/+NWZdcMSVx9UgCMDLIS54s40b7J3cpI73nwyxa0PEnsWhq54VCgUcHR2Rl5f3zN/fVfKMzj/J5XKdvNBlMpnOjk1/Yc/iMLSe5XI5mvWbjB8iizFn11VsOnsHjglfQ7i0D6dDpiO8x2uQyfRzkVND69pQsWdx6KJnTY7F83VEZNSq25hjwcAgbHg1DF0tLqAa8vHDqTQMWnkSV9IVUscjIh3joENEVUK4nwtqv3cc+xt+hkMmLRB36yF6fHUM0Ru2I+9httTxiEhHOOgQUZVhamqGiAFvYH9UO3QPcINMVYrOl6ZBuTgEh2J2oApfskhktDjoEFGV4+5giehhIfhpkDdMTWRQqoEpB4rQf/lJXLybJ3U8ItIiDjpEVGWFNQ6G+7R4HGz6DcrM7BB/+yF6Lj2Gjd/MxcOsu1LHIyIt4KBDRFWambk5BnWPxMG32qF3sDsaIwn973wG2bIwrD+cgDKlSuqIRPQCOOgQEQGoYW+BxYMb45N+obgur409ZWF4b89ddF9yDMeTuZUEkaHioENE9DeNmrSB7/unoYqcCwcrU1zLzMf4bw4g9ou+uJdyUep4RKQhDjpERP8gNzHBkNb+OPx2O4xs4YMo000ILziAB2tewbzdV5D/uFTqiERUSRx0iIj+g4OVGWb2aog2w95HokUTzC0bjK+P3ED7L45gfewtKMs48BDpOw46RETPUKt+YwRO24/RL4+Er5M17hcU4+S2FUibE4JLv2+TOh4RPQUHHSKiShAEARH+rtgztQ0+7t4Ab5jthI8qFTv37MCra+KQkl353ZSJSDzc1JOISANmJjKMae2L3AYxOLJxLlantkPRlSwcupaN8Y3NMKpNfTi6ekgdk4j+H8/oEBE9BwcnV7Qdtwjb34xARANXKFVqhJz/BGbLmmDPxm/wuFQpdUQiAgcdIqIXUtvZBt+MaIINI/zhYVYIc5Tgs3ig44Ij2Hz2DlQq7p9FJCW+dUVEpAXhDWpB9cFpHDocg5LTpriX+whRvyTizv6v0SE8FI3a9pU6IlGVxDM6RERaIpPL0bFjFxx8ux2mdakPX3MFXi1chUaHRmH2slW4dI8bhhKJjYMOEZGWWZjK8Ua72tg0uSMSXV/CSZU/VqW6ofuSY5i6/hzSsjnwEImFgw4RkY5Uq+6C5uNXwH3yPvQKqgkA2J6QhqKlLREbPQY59zMlTkhk/DjoEBHpmLeTLZYMaYwdk1phgscN1BPS4Je1F5FLTmDR/iQUFJdJHZHIaPFiZCIikTSqaY9GE6fiwu+1sDP2MrLvm2HR/utYe/I25jdMQ+tug2BiaiF1TCKjwkGHiEhkAa17o2HLXgi4mIEv9l2D3YNERJyfjvTzc3C883Y0cJA6IZHx4KBDRCQBmUxA90A3dG7oiuN77iEzrjqOKxvg7d9uwMPOFO92s0WPwJqQyQSpoxIZNF6jQ0QkIVO5DO26D4X9tAsoajcL1axMcUdRihnrf8flOS2QuP9HqFUqqWMSGSwOOkREesDC0hrDO4bg0Ftt8UpwNUww341GZZchPzofLy07gd+vZ0Ot5irLRJriW1dERHrE1sIEw4Id4dzhM5zYWg3fpbkh4U4eXvn2NMJ97DE9qAANm3eROiaRweCgQ0Skhxyqu6LF2MXwy38Mz8Mp+PFUKtxSd6JhxjKcPtoK8sHrEOrtKHVMIr3Ht66IiPSYi60FZvRsiCPvtkNXLyVK1CY4rKiJfl+fxPDvTuNc6kOpIxLpNZ7RISIyAG72lnAbNx/pqa+hMPYBTM7l4GhSNh5cj8Nn9ptgFvEB6jWJkDomkd7hGR0iIgPi5lUHswY0w8G32mFAqAcmm25BwON4XN62ECO+O42zPMNDVAHP6BARGSCv6lb4fEAQ7oZ+hdjfPsWyrPa4npSNI0nZ6FbbHFMCy1AvnBctE/GMDhGRAavp2wDhU3/CN28NxYBQD8hlAurfXod6uwch5vOXEXvjgdQRiSTFQYeIyAh4V7fG5wOCcOitdgiqYYkStRwbH/ph0MpTGLjiJI4lZXHhQaqS+NYVEZER8apuBa+Jy5Ge+jZc4gthduYeTt/MwS+3d8DVah8KWkxDcPt+EARuLUFVA8/oEBEZITcvP3z6UhCOvNsOI1v44FXT3ahTloQDB/ag+5Jj2Hk+HUoVV1om48czOkRERszN3hIzezXE/fDfcHzb59h4pw0y0hWY8NNZdHTMxji/PAT3eB2mZhZSRyXSCQ46RERVgJOrB5zGLsbuwhJ8f+IWVh+/iZfyf0LY+VhsunQChRHzMLCJJyxM5VJHJdIqvnVFRFSFVLM2Q1Snujj+Xgc41muJLDhiZVE7TN92CS0/O4hVMeeQ9zBb6phEWsNBh4ioCrK1MEWLl2fA7v2reLlXV9R0sMSDwhIUHlkCk0WNsHf1p8hSPJY6JtEL46BDRFSFWZib45XmPjj8Tjt8OTAQ7cyvw1p4jK1JpWg17xDe33weN7ILpI5J9Nx4jQ4REcFULsNLIZ5QBR3F2SNbkH3FGSVp+fj5dBry43/Bqw5nYdlxGuqFtJU6KpFGeEaHiIjKyeQyhHToh40T2uDXcc3RsZ4zxsm3I7jwOHZsWotBK07i4NVMqPjRdDIQPKNDRET/KszHEWGjmuLW1e9xcs9C/JQViQc3cxB7Mwedq2fjtdq5COw2FuYWVlJHJfpPBn9GJy0tDe3atYO/vz8CAwPx66+/Sh2JiMio+NQPQfOpP2D7uz3xWutasDE3QQ/FeoSdn4Ht80di2eFk5BWVSh2T6F8Z/BkdExMTLFq0CMHBwcjIyEBoaCi6desGa2trqaMRERkVdwdLfNjdH5M61sGFjaeRmZyE7x61xeU917D0YDJGBNvjlWB7uPv6Sx2VqJzBn9Fxc3NDcHAwAKBGjRpwcnJCTk6OtKGIiIyYnYUpWr78Map9cBVj+vdG/Rq2KCpRwjT+G7iuaYHdSybibOpDqWMSAdCDQefo0aPo2bMn3N3dIQgCtm7d+sR9oqOj4ePjAwsLC4SHh+P06dP/eqz4+HgolUp4enrqODUREZmZmaFfqAd2T2mNdWOaoql9LuSCGjszHNB32Qn0XXYcOxPvoKy0ROqoVIVJ/tZVYWEhgoKCMHr0aPTt2/eJ72/YsAFRUVFYvnw5wsPDsWjRIkRGRuLatWtwcXEpv19OTg6GDx+OVatW/edzFRcXo7i4uPxrhUIBAFAqlVAqlVr8qf44pkql0vpxqSL2LA72LB5D7bqFryPw1i9IuRwP6ysymCVm4WxqLmre2YVQs/VIqvc6AntNhq2FqdRRARhuz4ZGVz1rcjxBrVbrzWcEBUHAli1b0KdPn/LbwsPDERYWhqVLlwIAVCoVPD09MWnSJLz33nsA/hhgOnXqhNdeew2vvPLKfx5/5syZmDVr1hO3x8XFwcbGRqs/i0qlQk5ODhwdHSGTSX7izGixZ3GwZ/EYS9cPH5Vhx1UFulx9H62FBHxZ2g8rhf7oVMcOfRrYw91O2oHHWHrWd7rquaCgAGFhYcjLy4Odnd1T76vXg05JSQmsrKywcePGCsPPiBEjkJubi23btkGtVmPo0KGoV68eZs6c+dTj/9sZHU9PT+Tk5DyzKE0plUokJyfDz88Pcjk3ydMV9iwO9iweY+v68aNCXNjzLRbc8kXc/T/eRGgku4nZ9r9BaD4e/i16QBAE0XMZW8/6Slc9KxQKODo6VmrQkfytq6e5f/8+lEolXF1dK9zu6uqKq1evAgCOHz+ODRs2IDAwsPz6nnXr1iEgIOCJ45mbm8Pc3PyJ2+VyuU5e6DKZTGfHpr+wZ3GwZ/EYU9fWNnZo1v9N/KJW41jyfXx37CZ63FiGoEex2BojxzvxjhjZ0gd9gmvC0kzcn9eYetZnuuhZk2Pp9aBTGa1atYJKpZI6BhERPYUgCGhdxxmt6zjjdtIcnNy3BD9lNca1zHy8v/kCVu6OxZwah+HTZTLcvOtJHZeMiF4POk5OTpDL5cjMzKxwe2ZmJmrUqCFRKiIiehHedYPgXfdb+D8qxa9n0rD6xC10VWxF8/RfcO7bU5hZZwVGtPBBc9/qkrytRcZFr6/AMjMzQ2hoKA4cOFB+m0qlwoEDB9C8eXMJkxER0YuytzTFq619ceSd9ujQsRsumIdgTVln7L2UiaGrYtH9y0M49etCFObnSh2VDJjkZ3QKCgqQnJxc/vXNmzeRkJAAR0dHeHl5ISoqCiNGjECTJk3QtGlTLFq0CIWFhRg1apSEqYmISFvkMgFNOrwEdHgJ4zMUsD55G5vP3oX3/cNopliMW5dWYkHIJrzSwge1nLjqPWlG8kHnzJkzaN++ffnXUVFRAP74ZNXq1asxaNAgZGdnY/r06cjIyEBwcDD27NnzxAXKL4Lr6Bgu9iwO9iyeqt51bWdrfNLLH293qoMze9OQdtEdv5U2xXcnbuG7E7fQ2q86JvlmILhlF8hNnv8j6lW9Z7FwHR2JREdHIzo6GkqlEklJSVxHx4CxZ3GwZ/Gw64pUKiUS0xTYev0xTt8pQj0hFXvM38MduOL7+qvQqV51OFhq/m929iwOrqMjMYVCAXt7e66jY8DYszjYs3jY9X9LzSlC/N516Jg8B8eV/phYOgVmcgFdGtXA6PpKNGoUDKGSv0zZszi4jo6e4Do6ho09i4M9i4dd/7tazrao9fJ4PH40AuqzSQg6V4jEO3k4kngd869OQNp2d8S1W4tu4Y1gY/7sX2/sWRxcR4eIiEgDFpbW6NmyMXq2BC7cyUNszK9Q3ZLhURnw7q47mLU/A70b18TwIBvU960ldVySGN+YJCIigxXgYY9XR72K0imXcbXFAvg626CwRIn1sbdgsyYCSf8Lw84jx/GohBcdV1U8o0NERAbP3tEJfbt0wkuRapy6kYMjR/bD5fZDFJY+Rs/dWTA7tB99G9fE0BAn1PPkgrNVCQcdIiIyGoIgoHnt6mheexAeZLbEsRNH4XLdHmk5j7Dm5G1EnnkNSeZK3Go2Cy41vKWOSyLgoAOuo2PI2LM42LN42LX2ODi5oUevQeimUuPEjQfYcSIRTW5dg7xUhZH7s5BrqkafxqUYGuKKBp7OUsc1SlxHRyJcR8d4sGdxsGfxsGvdys/Jwq1LJ7AgszEyCsoAAHNMVqGJWSoSfcfCN7ANrM3Yu7ZwHR2JcR0dw8eexcGexcOuxVFaWobNxy/i+L1SfJrcD45CAQaXfIREeQC6B9TA4FBXBHs5VXpdHvp3XEdHT3AdHcPGnsXBnsXDrsURUtMag9rVQd6DOBw78AOy7zbBo/tF2Hj2LqolroCL+VFcbzABQV3HwMnGXOq4Bovr6BAREUnI0cUdrYa8i/1qNeJvP8T6uDT0uXgSXqo7WJaQgtfPHUBEA1cMCnVH6zrVYWJqJnVk0gAHHSIiIvzxia0mPo5o4uMIReeDiN33PW6lB6DsXin2XMqA6sp2NDJbjUtew+Dd6wPupG4gOOgQERH9g529I8IHvIX1AK5mKPBL3B00iV8GZzzE1Ru3MPKLw2jq44j+TTzQvb49rG20e50naQ8HHSIioqeoX8MO03v6o7jzRsQf+gU3Uh0guwmcvpWDh7fPo4fZx4itFgF1zyUI960OQRCkjkx/w0GHiIioEszNLRHaZQRCAUTlPcams3dgfnInrEqKkfcgA2NXxcLL0Qr9QjzQv4Elatb0kDoygYMOERGRxmrYW2BCez+o2y7FlTMv4WpSLmyumyA1pwjf7E/A2N/H47J5PVzvsBIRjevCuhK7qZNusHlwZWRDxp7FwZ7Fw67Foc2e64Z2QN1QYHSJEnsvZ+Lm8U0wf1AKk8c5mLL1Bqx2pSKyoSuG1FGhccNGkJlUnV+9XBlZIlwZ2XiwZ3GwZ/Gwa3Houue87Ds4n5KK1fc8cFdRCgEqHDV7E2YyJX72+gQN/YPg6WD8H1PnysgS48rIho89i4M9i4ddi0OsntVqNc6l5eLIqTi8dm0MBLUKYcVfoxhmCKxpjxF1H6NNUF04OtfUWQYpcWVkPcGVkQ0bexYHexYPuxaHWD2H1XJCWK2uePwoGWfijqPVDQccScrG+bt5cMmag2onLuNbl2lwbz0cEQ1cYWFqXP+/c2VkIiKiKsDC0gqt2nRCqzbA/YJi7Dx3G85HymBSpsLaO66489M52JqbYHjdEnTzVqFBs+5V6noeXWGDREREInOyMceI1nWB1rG4lXIFvZMFbD13D3dzH8H1yho0vB6DXw92RXKTGejTuCYauHFBwufFQYeIiEhCPrUb4J3awFud6iHuVg4e7d4JRbY1fnschN+P3sCKozcQ7lyGN51Ow6fdcNTwrid1ZIPCQYeIiEgPyGQCwn2rAxOW4fGjLzAsOQfWCZk4eDUL/jkxaJa/DmdT9mCy+1L0CnZHtwA3OFob/ye3XhQHHSIiIj1jYWmFLgFW6BLggbyiUiQeuI+LF85ja2FjnL6Vg9O3cvC/3xKxptp3kNeLRIOIEbC2spI6tl7ioENERKTH7K1M0abnK0DPV1A9twie5zOwNeEunDOOIrzwELLj49E0zhPtGrijd5A72tZzhrmJcX1y60Vw0CEiIjIQbg5WeK2NL15r44tbKc44efghLmQ8RmG+gJ3n07HzfDp+tJgHMwd3qNu+h5DAQJjIq/bCkxx0wC0gDBl7Fgd7Fg+7Focx9OzpUweeI+chTK1G2F0FdpxPx9nEc2hZlgjlw/MI39AL6h3Z6NaoBnrVt0JwbU/IRF6biVtASIRbQBgP9iwO9iwedi0OY+1ZpVIiM+kM7t++gE9zOkJRrAIALDRdhlbyS9jhOh6OjTqjnpM5BEEQIQ+3gJAUt4AwfOxZHOxZPOxaHFWh51KlCidSHmDX+Xt463J/uAkP0Ld4Js6q68KjmiUG1pWji7cavgEtIeho2OMWEHqCW0AYNvYsDvYsHnYtDmPvWS6Xo0ODGujQoAYeP7qIs8e3wyOrDq5ezcKdh49QemYz6iZuxK5dHXEpbA66BbjB381O62d6uAUEERER6ZSFpRVCIgYhBMCjEiUOXcuC/OAOFOWY4+AjP2w8lILoQyloUF2OGQ674Rw+GL6NwnV2pkdMHHSIiIiqEEszOboFuAEBX6Mw/zO0u/4ABZce4tC1LPg+PI5mhatxe+MudNy7El0D3XR2pkcsHHSIiIiqKGtbe/QIsUePEKCguAznjpXh7NnWOKZwxY0HRYg+lILoQ8n4xfoLqFwDYN/xLdT39TaooYeDDhEREcHG3AStO/YEOvZE3eIyeF/JxO4LGbh3LQ5NledQfPciQla1haPjDXRr5IYeda3QyNdT79/e4qBDREREFdiYm6B3cE30Dq6JwoI6OHPEFKk3r0KZaY20nEdYcfQGwk5+Dhd5KmL8PkTdli8h1Lsa5DL9O9PDQYeIiIj+k7WNHZp0H4MmALqUlOHItWzsvZCGkGvJcEQ+1l4qRdLFk3CyMcdQvxJ0di9BvWZdYWpmLnV0ABx0iIiIqJKszEzQNcANXQPc8PjRNcSf2IVG2X5Iv5qF+wXFsL74Ixpd3YmtB9vjd/9ZiPR3QQ2oJM3MQYeIiIg0ZmFpjdCOAxAKoKRMhZM3HqD0wH48yLTH3pJA7D57B5vO3oGliYAj79aCi52lJDk56BAREdELMTORoW1dZ6Dul1CWfY4Rtx7A9fJ97LmUASuZCtWtzSTLxkEH3NTTkLFncbBn8bBrcbBnHRIEhNVyQlgtJ7wf6YczF5Mk3dSzSg46f9/UEwBSUlJ0tqlncnKyUW0Yp2/YszjYs3jYtTjYszhUKhXUj/K03nNBQUGl78tNPbmpp0Fjz+Jgz+Jh1+Jgz+Lgpp56gpt6Gjb2LA72LB52LQ72LA6pN/Xk+ToiIiIyWhx0iIiIyGhx0CEiIiKjxUGHiIiIjBYHHSIiIjJaHHSIiIjIaHHQISIiIqPFQYeIiIiMFgcdIiIiMlocdIiIiMhocdAhIiIio1Wl97r6cz9ThUKh9WMrlUoUFBRAoVBwHxUdYs/iYM/iYdfiYM/i0FXPf/7ersy+5FV60MnPzwcAeHp6SpyEiIiINJWfnw97e/un3kdQV2YcMlIqlQr37t2Dra0tBEHQ6rEVCgU8PT2Rlpb2zC3k6fmxZ3GwZ/Gwa3GwZ3Hoqme1Wo38/Hy4u7tDJnv6VThV+oyOTCaDh4eHTp/Dzs6O/xGJgD2Lgz2Lh12Lgz2LQxc9P+tMzp94MTIREREZLQ46REREZLQ46OiIubk5ZsyYAXNzc6mjGDX2LA72LB52LQ72LA596LlKX4xMRERExo1ndIiIiMhocdAhIiIio8VBh4iIiIwWBx0iIiIyWhx0dCA6Oho+Pj6wsLBAeHg4Tp8+LXUko3P06FH07NkT7u7uEAQBW7dulTqSUZo7dy7CwsJga2sLFxcX9OnTB9euXZM6ltH5+uuvERgYWL6oWvPmzbF7926pYxm9zz77DIIgYOrUqVJHMTozZ86EIAgV/le/fn1JsnDQ0bINGzYgKioKM2bMwNmzZxEUFITIyEhkZWVJHc2oFBYWIigoCNHR0VJHMWpHjhzBhAkTcOrUKcTExKC0tBSdO3dGYWGh1NGMioeHBz777DPEx8fjzJkz6NChA3r37o1Lly5JHc1oxcXFYcWKFQgMDJQ6itFq2LAh0tPTy/937NgxSXLw4+VaFh4ejrCwMCxduhTAH/tpeXp6YtKkSXjvvfckTmecBEHAli1b0KdPH6mjGL3s7Gy4uLjgyJEjaNOmjdRxjJqjoyM+//xzjBkzRuooRqegoAAhISFYtmwZ/ve//yE4OBiLFi2SOpZRmTlzJrZu3YqEhASpo/CMjjaVlJQgPj4eERER5bfJZDJERETg5MmTEiYj0o68vDwAf/wSJt1QKpVYv349CgsL0bx5c6njGKUJEyage/fuFf6uJu27fv063N3d4evri2HDhiE1NVWSHFV6U09tu3//PpRKJVxdXSvc7urqiqtXr0qUikg7VCoVpk6dipYtW6JRo0ZSxzE6Fy5cQPPmzfH48WPY2Nhgy5Yt8Pf3lzqW0Vm/fj3Onj2LuLg4qaMYtfDwcKxevRr16tVDeno6Zs2ahdatW+PixYuwtbUVNQsHHSKqlAkTJuDixYuSvc9u7OrVq4eEhATk5eVh48aNGDFiBI4cOcJhR4vS0tIwZcoUxMTEwMLCQuo4Rq1r167lfw4MDER4eDi8vb3xyy+/iP52LAcdLXJycoJcLkdmZmaF2zMzM1GjRg2JUhG9uIkTJ2LHjh04evQoPDw8pI5jlMzMzODn5wcACA0NRVxcHBYvXowVK1ZInMx4xMfHIysrCyEhIeW3KZVKHD16FEuXLkVxcTHkcrmECY2Xg4MD6tati+TkZNGfm9foaJGZmRlCQ0Nx4MCB8ttUKhUOHDjA99rJIKnVakycOBFbtmzBwYMHUatWLakjVRkqlQrFxcVSxzAqHTt2xIULF5CQkFD+vyZNmmDYsGFISEjgkKNDBQUFSElJgZubm+jPzTM6WhYVFYURI0agSZMmaNq0KRYtWoTCwkKMGjVK6mhGpaCgoMK/DG7evImEhAQ4OjrCy8tLwmTGZcKECfjpp5+wbds22NraIiMjAwBgb28PS0tLidMZj/fffx9du3aFl5cX8vPz8dNPP+Hw4cPYu3ev1NGMiq2t7RPXl1lbW6N69eq87kzL3n77bfTs2RPe3t64d+8eZsyYAblcjiFDhoiehYOOlg0aNAjZ2dmYPn06MjIyEBwcjD179jxxgTK9mDNnzqB9+/blX0dFRQEARowYgdWrV0uUyvh8/fXXAIB27dpVuP3777/HyJEjxQ9kpLKysjB8+HCkp6fD3t4egYGB2Lt3Lzp16iR1NKLncufOHQwZMgQPHjyAs7MzWrVqhVOnTsHZ2Vn0LFxHh4iIiIwWr9EhIiIio8VBh4iIiIwWBx0iIiIyWhx0iIiIyGhx0CEiIiKjxUGHiIiIjBYHHSIiIjJaHHSIiIjIaHHQISJR+Pj4YNGiRVLHIKIqhoMOkZETBAFbt24V7flWr14NBweHJ26Pi4vD2LFjRcthTGbOnIng4GCpYxAZJA46RFQpJSUlL/R4Z2dnWFlZaSmNuF70Z9cXxvJzEGmCgw6Rntu4cSMCAgJgaWmJ6tWrIyIiAoWFhQD+OEvSqVMnODk5wd7eHm3btsXZs2fLH+vj4wMAeOmllyAIQvnXI0eORJ8+fSo8z9SpUyts3tmuXTtMnDgRU6dOhZOTEyIjIwEACxcuREBAAKytreHp6Ynx48ejoKAAAHD48GGMGjUKeXl5EAQBgiBg5syZ5Vn+/tZVamoqevfuDRsbG9jZ2WHgwIHIzMws//6fZzHWrVsHHx8f2NvbY/DgwcjPz//Prv48m7R161bUqVMHFhYWiIyMRFpaWvl9UlJS0Lt3b7i6usLGxgZhYWHYv39/heP4+Pjg008/xfDhw2FnZ1d+JmratGmoW7curKys4Ovri48//hilpaVPZP7uu+/g5eUFGxsbjB8/HkqlEvPnz0eNGjXg4uKC2bNnV3i+3NxcvPrqq3B2doadnR06dOiAxMTE8p9p1qxZSExMLO/0z41rn/a4v+f55ptvUKtWLVhYWPxrb7dv30bPnj1RrVo1WFtbo2HDhti1a9d/9kxkSDjoEOmx9PR0DBkyBKNHj8aVK1dw+PBh9O3bF3/uxZufn48RI0bg2LFjOHXqFOrUqYNu3bqVDwNxcXEA/thtPD09vfzrylqzZg3MzMxw/PhxLF++HAAgk8mwZMkSXLp0CWvWrMHBgwfx7rvvAgBatGiBRYsWwc7ODunp6UhPT8fbb7/9xHFVKhV69+6NnJwcHDlyBDExMbhx4wYGDRpU4X4pKSnYunUrduzYgR07duDIkSP47LPPnpq5qKgIs2fPxtq1a3H8+HHk5uZi8ODB5d8vKChAt27dcODAAZw7dw5dunRBz549kZqaWuE4X3zxBYKCgnDu3Dl8/PHHAABbW1usXr0aly9fxuLFi7Fq1Sp8+eWXT2TevXs39uzZg59//hnffvstunfvjjt37uDIkSOYN28ePvroI8TGxpY/ZsCAAcjKysLu3bsRHx+PkJAQdOzYETk5ORg0aBDeeustNGzYsLzTP3t62uP+lJycjE2bNmHz5s1ISEj4184mTJiA4uJiHD16FBcuXMC8efNgY2Pz1J6JDIaaiPRWfHy8GoD61q1blbq/UqlU29raqrdv315+GwD1li1bKtxvxIgR6t69e1e4bcqUKeq2bduWf922bVt148aNn/mcv/76q7p69erlX3///fdqe3v7J+7n7e2t/vLLL9VqtVq9b98+tVwuV6emppZ//9KlS2oA6tOnT6vVarV6xowZaisrK7VCoSi/zzvvvKMODw//zyzff/+9GoD61KlT5bdduXJFDUAdGxv7n49r2LCh+quvvqqQtU+fPv/9Q/+/zz//XB0aGlr+9b9ljoyMVPv4+KiVSmX5bfXq1VPPnTtXrVar1b///rvazs5O/fjx4wrHrl27tnrFihXlxw0KCqrw/co+ztTUVJ2VlfXUnyMgIEA9c+bMZ/68RIbIRNIpi4ieKigoCB07dkRAQAAiIyPRuXNn9O/fH9WqVQMAZGZm4qOPPsLhw4eRlZUFpVKJoqKiJ85OPK/Q0NAnbtu/fz/mzp2Lq1evQqFQoKysDI8fP0ZRUVGlr8G5cuUKPD094enpWX6bv78/HBwccOXKFYSFhQH44y0kW1vb8vu4ubkhKyvrqcc2MTEpfzwA1K9fv/y4TZs2RUFBAWbOnImdO3ciPT0dZWVlePTo0ROdNWnS5Iljb9iwAUuWLEFKSgoKCgpQVlYGOzu7Cvf5Z2ZXV1fI5XLIZLIKt/35cyQmJqKgoADVq1evcJxHjx4hJSXlP3/Oyj7O29sbzs7O/3kcAJg8eTLeeOMN7Nu3DxEREejXrx8CAwOf+hgiQ8FBh0iPyeVyxMTE4MSJE9i3bx+++uorfPjhh4iNjUWtWrUwYsQIPHjwAIsXL4a3tzfMzc3RvHnzZ150KpPJyt/++tPfrzX5k7W1dYWvb926hR49euCNN97A7Nmz4ejoiGPHjmHMmDEoKSnR+sXGpqamFb4WBAEqleqFjvn2228jJiYGX3zxBfz8/GBpaYn+/fs/0dk/f/aTJ09i2LBhmDVrFiIjI2Fvb4/169djwYIFz8z8tJ+joKAAbm5uOHz48BNZ/+3Ta3+q7OP++XP8m1dffRWRkZHYuXMn9u3bh7lz52LBggWYNGnSMx9LpO846BDpOUEQ0LJlS7Rs2RLTp0+Ht7c3tmzZgqioKBw/fhzLli1Dt27dAABpaWm4f/9+hcebmppCqVRWuM3Z2RkXL16scFtCQsITv5D/KT4+HiqVCgsWLCg/Q/HLL79UuI+ZmdkTz/dPDRo0QFpaGtLS0srP6ly+fBm5ubnw9/d/6mOfpaysDGfOnEHTpk0BANeuXUNubi4aNGgAADh+/DhGjhyJl156CcAfA8OtW7eeedwTJ07A29sbH374Yfltt2/ffqGsABASEoKMjAyYmJiUXyz+T//WaWUepwlPT0+MGzcO48aNw/vvv49Vq1Zx0CGjwIuRifRYbGws5syZgzNnziA1NRWbN29GdnZ2+S/tOnXqYN26dbhy5QpiY2MxbNgwWFpaVjiGj48PDhw4gIyMDDx8+BAA0KFDB5w5cwZr167F9evXMWPGjCcGn3/j5+eH0tJSfPXVV7hx4wbWrVtXfpHy35+voKAABw4cwP3791FUVPTEcSIiIhAQEIBhw4bh7NmzOH36NIYPH462bdv+61tGmjA1NcWkSZMQGxuL+Ph4jBw5Es2aNSsffOrUqVN+YW5iYiKGDh1aqbNEderUQWpqKtavX4+UlBQsWbIEW7ZseaGswB9dNG/eHH369MG+fftw69YtnDhxAh9++CHOnDkD4I9Ob968iYSEBNy/fx/FxcWVelxlTZ06FXv37sXNmzdx9uxZHDp0qPw1RmToOOgQ6TE7OzscPXoU3bp1Q926dfHRRx9hwYIF6Nq1KwDg22+/xcOHDxESEoJXXnkFkydPhouLS4VjLFiwADExMfD09ETjxo0BAJGRkfj444/x7rvvIiwsDPn5+Rg+fPgz8wQFBWHhwoWYN28eGjVqhB9//BFz586tcJ8WLVpg3LhxGDRoEJydnTF//vwnjiMIArZt24Zq1aqhTZs2iIiIgK+vLzZs2PC8VZWzsrLCtGnTMHToULRs2RI2NjYVjrtw4UJUq1YNLVq0QM+ePREZGYmQkJBnHrdXr1548803MXHiRAQHB+PEiRPln8Z6EYIgYNeuXWjTpg1GjRqFunXrYvDgwbh9+zZcXV0BAP369UOXLl3Qvn17ODs74+eff67U4ypLqVRiwoQJaNCgAbp06YK6deti2bJlL/yzEekDQf3PN+qJiAzU6tWrMXXqVOTm5kodhYj0BM/oEBERkdHioENERERGi29dERERkdHiGR0iIiIyWhx0iIiIyGhx0CEiIiKjxUGHiIiIjBYHHSIiIjJaHHSIiIjIaHHQISIiIqPFQYeIiIiM1v8BN74s0tnFpDsAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v0_sim = np.asanyarray(v0_sim)\n", "v0_th = alpha * s / (1 + 4 * delta_list ** 2)\n", "\n", "plt.figure()\n", "plt.plot(delta_list, v0_sim)\n", "plt.plot(delta_list, v0_th, ':')\n", "plt.semilogy()\n", "plt.grid(which='both', alpha=0.5)\n", "plt.xlabel(\"saturation parameter s\")\n", "plt.ylabel(\"initial speed (m/s)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0b6c7948", "metadata": {}, "source": [ "## Test #2 : Doppler friction\n", "\n", "We now consider an atom with initial speed $v_0 \\ll \\Gamma / k$ in a 1D Molasse. For an ytterbium atom on the main transition (399nm), the typical speed is $\\Gamma / k \\approx 11\\,\\mathrm{m/s}$." ] }, { "cell_type": "code", "execution_count": 7, "id": "e28e68d9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────\n", "| main |\n", "────────\n", ". Parameters :\n", " ├── λ : 398.91 nm\n", " ├── Γ : 2π × 2.89e+07 Hz\n", " ├── Isat : 59.51 mw/cm²\n", " ├── Doppler temp. : 6.93e-04 K\n", " └── lande factor g : 1.035\n", "\n", "\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# - init config\n", "# atom\n", "atom = Ytterbium()\n", "transition = atom.trans[\"main\"]\n", "transition.print_info()\n", "# lasers\n", "s = 0.01\n", "laser_1 = PlaneWaveLaserBeam(\n", " wavelength=transition.wavelength, direction=(1, 0, 0), tag=\"399+\"\n", ")\n", "laser_2 = PlaneWaveLaserBeam(\n", " wavelength=transition.wavelength, direction=(-1, 0, 0), tag=\"399-\"\n", ")\n", "laser_1.set_power_from_I(s * transition.Isat)\n", "laser_2.set_power_from_I(s * transition.Isat)\n", "\n", "# config\n", "delta = -0.5 * transition.Gamma\n", "config = Configuration(atom=atom) + laser_1 + laser_2\n", "config.add_atomlight_coupling(\"399+\", \"main\", detuning=delta)\n", "config.add_atomlight_coupling(\"399-\", \"main\", detuning=delta)\n", "\n", "# simulator\n", "sim = RK4(config)\n", "\n", "# - simulate\n", "# physical parameters\n", "k = transition.k\n", "Γ = transition.Gamma\n", "δ = delta\n", "m = atom.mass\n", "gamma = - csts.hbar * k ** 2 / m * s * δ * Γ / (δ ** 2 + Γ ** 2 / 4)\n", "tau = 1 / gamma\n", "# simulation parameters\n", "v0 = 1\n", "t = np.linspace(0, 20 * tau, 1_000)\n", "u0 = np.zeros(6)\n", "u0[3] = v0\n", "\n", "# run\n", "res = sim.integrate(u0, t)\n", "\n", "# - plot results\n", "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n", "for cax in ax:\n", " cax.plot(res.t * 1e6, res.y[3, :], label=\"sim\")\n", " cax.plot(res.t * 1e6, v0 * np.exp(- gamma * res.t), label=\"sim\", dashes=[2,2])\n", " cax.grid()\n", " cax.set_xlabel(\"time (µs)\")\n", " cax.set_ylabel(\"speed (m/s)\")\n", "ax[1].set_yscale(\"log\")\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "atomsmltr-KmviZRuT-py3.12", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }