{ "cells": [ { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "%config InlineBackend.figure_format = \"retina\"\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import sympy as sp\n", "from IPython.display import Math, display\n", "from matplotlib.axes import Axes\n", "from scipy import constants as const\n", "from scipy.integrate import quad\n", "from scipy.optimize import root_scalar\n", "from tqdm import tqdm\n", "\n", "import fewfermions.analysis.units as si\n", "from fewfermions.simulate.traps.twod.trap import PancakeTrap\n", "from fewfermions.style import FIGS_PATH, setup\n", "\n", "colors, colors_alpha = setup()\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Determining good parameters for Dysprosium\n", "\n", "power\n", "\n", "gradient\n", "\n", "w_0\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "initial_power = 291.5 * si.uW\n", "trap: PancakeTrap = PancakeTrap(\n", " power=0, # Set pancake laser power to 0, no 2D trap\n", " grad_z= 0.6 * si.G / si.cm,\n", " grad_r=0,\n", " power_tweezer=initial_power,\n", " waist_tweezer= 1.838 * si.um,\n", " a=184.4*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n", ")\n", "axial_width = trap.get_tweezer_rayleigh()\n", "\n", "x, y, z = trap.x, trap.y, trap.z" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 15.35$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "aspect_ratio = trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer()\n", "_aspect_ratio_latex = sp.latex(trap.omega_r_tweezer / trap.omega_ax_tweezer)\n", "display(Math(f\"{_aspect_ratio_latex} \\\\approx {trap.subs(aspect_ratio).evalf():.2f}\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Same parameters as for Li6 gives no trapped atoms -> reduce magnetic gradient from 15 G/cm to 0.6 G/cm:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " 0%| | 0/100 [00:00:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.14251275879322e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.65700510351729e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.14251275879322e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.65700510351729e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.14251275879322e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", "c:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\numpy\\core\\fromnumeric.py:3504: RuntimeWarning: Mean of empty slice.\n", " return _methods._mean(a, axis=axis, dtype=dtype,\n", "c:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\numpy\\core\\_methods.py:129: RuntimeWarning: invalid value encountered in scalar divide\n", " ret = ret.dtype.type(ret / rcount)\n", " 1%| | 1/100 [00:00<00:40, 2.44it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.15701300347347e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.66280520138939e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.15701300347347e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.66280520138939e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.15701300347347e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 2%|▏ | 2/100 [00:00<00:27, 3.52it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.17151324815371e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.66860529926148e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.17151324815371e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.66860529926148e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.17151324815371e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 3%|▎ | 3/100 [00:00<00:23, 4.11it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.18601349283396e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.67440539713358e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.18601349283396e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.67440539713358e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.18601349283396e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 4%|▍ | 4/100 [00:01<00:21, 4.42it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.2005137375142e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.68020549500568e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.2005137375142e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 5%|▌ | 5/100 [00:01<00:19, 4.81it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.21501398219444e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.68600559287778e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.21501398219444e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 6%|▌ | 6/100 [00:01<00:18, 4.97it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.22951422687469e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.69180569074988e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.22951422687469e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.69180569074988e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.22951422687469e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 7%|▋ | 7/100 [00:01<00:18, 5.02it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.24401447155493e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.69760578862197e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.24401447155493e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.69760578862197e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.24401447155493e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 8%|▊ | 8/100 [00:01<00:17, 5.35it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.25851471623518e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.70340588649407e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.25851471623518e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.70340588649407e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.25851471623518e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 9%|▉ | 9/100 [00:01<00:16, 5.37it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.70920598436617e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.27301496091542e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.27301496091542e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.70920598436617e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.27301496091542e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 36%|███▌ | 36/100 [00:07<00:12, 5.21it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.66452156728202e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.86580862691281e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.66452156728202e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 37%|███▋ | 37/100 [00:07<00:11, 5.35it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8716087247849e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.67902181196226e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.67902181196226e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.8716087247849e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.67902181196226e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 38%|███▊ | 38/100 [00:07<00:11, 5.40it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.69352205664251e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.877408822657e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.69352205664251e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.877408822657e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.69352205664251e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 39%|███▉ | 39/100 [00:07<00:11, 5.13it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.70802230132275e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8832089205291e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.70802230132275e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 40%|████ | 40/100 [00:07<00:12, 4.95it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8890090184012e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.72252254600299e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 41%|████ | 41/100 [00:08<00:11, 4.98it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8948091162733e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.73702279068324e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.73702279068324e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.8948091162733e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.73702279068324e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 42%|████▏ | 42/100 [00:08<00:11, 4.91it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.75152303536348e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.90060921414539e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.75152303536348e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", "100%|██████████| 100/100 [03:36<00:00, 2.17s/it]\n" ] } ], "source": [ "n_spill_steps = 100\n", "\n", "trap[trap.power_tweezer] = initial_power\n", "\n", "#spill_power_factor = np.linspace(0.7, 0.52, num=n_spill_steps)\n", "#powers = trap[trap.power_tweezer] * spill_power_factor\n", "powers = np.linspace(151.5,204,n_spill_steps)*si.uW\n", "t_spill = 25 * si.ms\n", "atom_number = np.zeros_like(powers)\n", "#array to store mean lifetime at specific power\n", "mean_lifetime = np.zeros_like(powers)\n", "\n", "# Number of energy levels to compute\n", "# will change over time to avoid calculating too many levels\n", "n_levels = 30\n", "# Resolution of the potential when solving numerically\n", "n_pot_steps = 1000\n", "\n", "for i, power in enumerate(tqdm(powers)):\n", " trap[trap.power_tweezer] = power\n", " # Solve the hamiltonian numerically in axial direction\n", " energies, states, potential, coords = trap.nstationary_solution(\n", " trap.z, (-0.5 * axial_width, 1.8 * axial_width), n_pot_steps, k=n_levels\n", " )\n", "\n", " # Determine the potential and its derivatives\n", " pot_ax = trap.subs(trap.get_potential())\n", " pot_diff_ax = sp.diff(pot_ax, trap.z)\n", " pot_diff2_ax = sp.diff(pot_diff_ax, trap.z)\n", " pot_diff3_ax = sp.diff(pot_diff2_ax, trap.z)\n", " pot_diff_ax_numpy = sp.lambdify(trap.z, pot_diff_ax.subs({x: 0, y: 0}))\n", " pot_diff2_ax_numpy = sp.lambdify(trap.z, pot_diff2_ax.subs({x: 0, y: 0}))\n", " pot_diff3_ax_numpy = sp.lambdify(trap.z, pot_diff3_ax.subs({x: 0, y: 0}))\n", "\n", " barrier = root_scalar(\n", " pot_diff_ax_numpy,\n", " x0=1.5 * float(trap.subs(axial_width)),\n", " fprime=pot_diff2_ax_numpy,\n", " xtol=1e-28,\n", " fprime2=pot_diff2_ax_numpy,\n", " ).root\n", " minimum = root_scalar(\n", " pot_diff_ax_numpy,\n", " x0=0,\n", " fprime=pot_diff2_ax_numpy,\n", " xtol=1e-28,\n", " fprime2=pot_diff2_ax_numpy,\n", " ).root\n", " # States that are below the potential barrier\n", " bound_states = energies < potential(barrier)\n", "\n", " n_bound_states = np.sum(bound_states)\n", " n_levles = n_bound_states + 3 # add 3 more levels to be safe\n", "\n", " # Density of states is larger on the left than on the right\n", " # Likely that the state in question is a true bound state\n", " true_bound_states = np.logical_and(\n", " bound_states,\n", " np.sum(states[:, coords[z] < barrier] ** 2, axis=1)\n", " > np.sum(states[:, coords[z] > barrier] ** 2, axis=1),\n", " )\n", "\n", " transmission_probability = np.full_like(energies, np.nan, dtype=float)\n", " for j, energy in enumerate(energies):\n", " if not true_bound_states[j]:\n", " continue\n", " intersect_end = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(barrier, 3 * float(trap.subs(axial_width))),\n", " ).root\n", " intersect_start = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(minimum, barrier),\n", " ).root\n", " barrier_interval = np.logical_and(\n", " coords[z] > intersect_start, coords[z] < intersect_end\n", " )\n", " s = quad(\n", " lambda x: np.sqrt(\n", " 2\n", " * float(trap.subs(trap.m))\n", " * np.clip(potential(x) - energy, a_min=0, a_max=None)\n", " )\n", " / const.hbar,\n", " intersect_start,\n", " intersect_end,\n", " )\n", " transmission_probability[j] = sp.exp(-2 * s[0])\n", " tunneling_rate = (\n", " transmission_probability * np.abs(energies - potential(minimum)) / const.h\n", " )\n", " atom_number[i] = np.sum(np.exp(-t_spill * tunneling_rate[true_bound_states]))\n", " mean_lifetime[i] = np.mean(1/tunneling_rate[~np.isnan(tunneling_rate)])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 373, "width": 373 } }, "output_type": "display_data" } ], "source": [ "ax: plt.Axes\n", "fig: plt.Figure\n", "fig, ax = plt.subplots(figsize=(2.5, 2.5))\n", "\n", "ax.set_xlabel(\"absolute tweezer power (uW)\")\n", "ax.set_ylabel(\"atom number\")\n", "ax.plot(powers*1e6, atom_number, marker=\".\")\n", "ax.fill_between(powers*1e6, atom_number, fc=colors_alpha[\"red\"], alpha=0.5)\n", "#fig.savefig(FIGS_PATH / \"twodtrap\" / \"1D Stufenplot.pdf\")" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " nan, nan, nan, nan,\n", " 8.27675472e+050, 3.07939768e+052, 1.17486595e+054, 2.29748735e+055,\n", " 9.20816603e+056, 3.78080760e+058, 1.05989904e+060, 4.56318759e+061,\n", " 2.01086112e+063, 9.06749076e+064, 3.13711176e+066, 1.48005251e+068,\n", " 7.13973785e+069, 2.81663920e+071, 1.41952485e+073, 7.30986932e+074,\n", " 3.20445893e+076, 1.72166412e+078, 9.44538796e+079, 4.53455646e+081,\n", " 2.59240128e+083, 1.51249075e+085, 9.00380305e+086, 4.78444796e+088,\n", " 2.96358894e+090, 1.87205311e+092, 1.07178459e+094, 7.03753264e+095,\n", " 4.71015809e+097, 3.21281298e+099, 2.00977371e+101, 1.42321818e+103,\n", " 1.02668749e+105, 6.85793876e+106, 5.13172052e+108, 3.91016647e+110,\n", " 3.03342356e+112, 2.19599755e+114, 1.76528129e+116, 1.44423216e+118,\n", " 1.10990663e+120, 9.40231821e+121, 8.10344970e+123, 7.10463855e+125])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean_lifetime" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compare different \"n_levels\" (should not make a difference)\n", "\n", "### 10" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " 0%| | 0/100 [00:00:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.14251275879322e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.65700510351729e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.14251275879322e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.65700510351729e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.14251275879322e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", "c:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\scipy\\optimize\\_root_scalar.py:326: RuntimeWarning: Derivative was zero.\n", " r, sol = methodc(f, x0, args=args, fprime=fprime, fprime2=fprime2, **kwargs)\n", "c:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\numpy\\core\\fromnumeric.py:3504: RuntimeWarning: Mean of empty slice.\n", " return _methods._mean(a, axis=axis, dtype=dtype,\n", "c:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\numpy\\core\\_methods.py:129: RuntimeWarning: invalid value encountered in scalar divide\n", " ret = ret.dtype.type(ret / rcount)\n", " 1%| | 1/100 [00:00<01:04, 1.54it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.15701300347347e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.66280520138939e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.15701300347347e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.66280520138939e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.15701300347347e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 2%|▏ | 2/100 [00:01<00:48, 2.01it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.17151324815371e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.66860529926148e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.17151324815371e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.66860529926148e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.17151324815371e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 3%|▎ | 3/100 [00:01<00:47, 2.06it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.18601349283396e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.67440539713358e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.18601349283396e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.67440539713358e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.18601349283396e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 4%|▍ | 4/100 [00:02<00:46, 2.05it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.2005137375142e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.68020549500568e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.2005137375142e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 5%|▌ | 5/100 [00:02<00:45, 2.08it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.21501398219444e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.68600559287778e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.21501398219444e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 6%|▌ | 6/100 [00:02<00:43, 2.16it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.22951422687469e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.69180569074988e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.22951422687469e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.69180569074988e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.22951422687469e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 7%|▋ | 7/100 [00:03<00:43, 2.15it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.24401447155493e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.69760578862197e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.24401447155493e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.69760578862197e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.24401447155493e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 8%|▊ | 8/100 [00:03<00:43, 2.09it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.25851471623518e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.70340588649407e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.25851471623518e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.70340588649407e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.25851471623518e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 9%|▉ | 9/100 [00:04<00:43, 2.10it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.70920598436617e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.27301496091542e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.27301496091542e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.70920598436617e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.27301496091542e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 36%|███▌ | 36/100 [00:16<00:28, 2.26it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.66452156728202e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.86580862691281e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.66452156728202e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 37%|███▋ | 37/100 [00:17<00:28, 2.21it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8716087247849e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.67902181196226e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.67902181196226e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.8716087247849e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.67902181196226e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 38%|███▊ | 38/100 [00:17<00:28, 2.20it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.69352205664251e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.877408822657e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.69352205664251e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.877408822657e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.69352205664251e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 39%|███▉ | 39/100 [00:18<00:27, 2.20it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.70802230132275e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8832089205291e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.70802230132275e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 40%|████ | 40/100 [00:18<00:26, 2.26it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8890090184012e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.72252254600299e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 41%|████ | 41/100 [00:18<00:26, 2.27it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8948091162733e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.73702279068324e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.73702279068324e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.8948091162733e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.73702279068324e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 42%|████▏ | 42/100 [00:19<00:25, 2.24it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.75152303536348e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.90060921414539e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.75152303536348e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", "100%|██████████| 100/100 [00:51<00:00, 1.95it/s]\n" ] } ], "source": [ "n_spill_steps = 100\n", "\n", "trap[trap.power_tweezer] = initial_power\n", "\n", "#spill_power_factor = np.linspace(0.7, 0.52, num=n_spill_steps)\n", "#powers = trap[trap.power_tweezer] * spill_power_factor\n", "powers = np.linspace(151.5,204,n_spill_steps)*si.uW\n", "t_spill = 25 * si.ms\n", "atom_number = np.zeros_like(powers)\n", "#array to store mean lifetime at specific power\n", "mean_lifetime = np.zeros_like(powers)\n", "\n", "# Number of energy levels to compute\n", "# will change over time to avoid calculating too many levels\n", "n_levels = 10\n", "# Resolution of the potential when solving numerically\n", "n_pot_steps = 1000\n", "\n", "for i, power in enumerate(tqdm(powers)):\n", " trap[trap.power_tweezer] = power\n", " # Solve the hamiltonian numerically in axial direction\n", " energies, states, potential, coords = trap.nstationary_solution(\n", " trap.z, (-0.5 * axial_width, 1.8 * axial_width), n_pot_steps, k=n_levels\n", " )\n", "\n", " # Determine the potential and its derivatives\n", " pot_ax = trap.subs(trap.get_potential())\n", " pot_diff_ax = sp.diff(pot_ax, trap.z)\n", " pot_diff2_ax = sp.diff(pot_diff_ax, trap.z)\n", " pot_diff3_ax = sp.diff(pot_diff2_ax, trap.z)\n", " pot_diff_ax_numpy = sp.lambdify(trap.z, pot_diff_ax.subs({x: 0, y: 0}))\n", " pot_diff2_ax_numpy = sp.lambdify(trap.z, pot_diff2_ax.subs({x: 0, y: 0}))\n", " pot_diff3_ax_numpy = sp.lambdify(trap.z, pot_diff3_ax.subs({x: 0, y: 0}))\n", "\n", " barrier = root_scalar(\n", " pot_diff_ax_numpy,\n", " x0=1.5 * float(trap.subs(axial_width)),\n", " fprime=pot_diff2_ax_numpy,\n", " xtol=1e-28,\n", " fprime2=pot_diff2_ax_numpy,\n", " ).root\n", " minimum = root_scalar(\n", " pot_diff_ax_numpy,\n", " x0=0,\n", " fprime=pot_diff2_ax_numpy,\n", " xtol=1e-28,\n", " fprime2=pot_diff2_ax_numpy,\n", " ).root\n", " # States that are below the potential barrier\n", " bound_states = energies < potential(barrier)\n", "\n", " n_bound_states = np.sum(bound_states)\n", " n_levles = n_bound_states + 3 # add 3 more levels to be safe\n", "\n", " # Density of states is larger on the left than on the right\n", " # Likely that the state in question is a true bound state\n", " true_bound_states = np.logical_and(\n", " bound_states,\n", " np.sum(states[:, coords[z] < barrier] ** 2, axis=1)\n", " > np.sum(states[:, coords[z] > barrier] ** 2, axis=1),\n", " )\n", "\n", " transmission_probability = np.full_like(energies, np.nan, dtype=float)\n", " for j, energy in enumerate(energies):\n", " if not true_bound_states[j]:\n", " continue\n", " intersect_end = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(barrier, 3 * float(trap.subs(axial_width))),\n", " ).root\n", " intersect_start = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(minimum, barrier),\n", " ).root\n", " barrier_interval = np.logical_and(\n", " coords[z] > intersect_start, coords[z] < intersect_end\n", " )\n", " s = quad(\n", " lambda x: np.sqrt(\n", " 2\n", " * float(trap.subs(trap.m))\n", " * np.clip(potential(x) - energy, a_min=0, a_max=None)\n", " )\n", " / const.hbar,\n", " intersect_start,\n", " intersect_end,\n", " )\n", " transmission_probability[j] = sp.exp(-2 * s[0])\n", " tunneling_rate = (\n", " transmission_probability * np.abs(energies - potential(minimum)) / const.h\n", " )\n", " atom_number[i] = np.sum(np.exp(-t_spill * tunneling_rate[true_bound_states]))\n", " mean_lifetime[i] = 1/np.mean(tunneling_rate[~np.isnan(tunneling_rate)])" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 373, "width": 373 } }, "output_type": "display_data" } ], "source": [ "ax: plt.Axes\n", "fig: plt.Figure\n", "fig, ax = plt.subplots(figsize=(2.5, 2.5))\n", "\n", "ax.set_xlabel(\"absolute tweezer power (uW)\")\n", "ax.set_ylabel(\"atom number\")\n", "ax.plot(powers*1e6, atom_number, marker=\".\")\n", "ax.fill_between(powers*1e6, atom_number, fc=colors_alpha[\"red\"], alpha=0.5)\n", "#fig.savefig(FIGS_PATH / \"twodtrap\" / \"1D Stufenplot.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 40" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " 0%| | 0/100 [00:00:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.14251275879322e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.65700510351729e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.14251275879322e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.65700510351729e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.14251275879322e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 1%| | 1/100 [00:00<00:25, 3.92it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.15701300347347e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.66280520138939e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.15701300347347e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.66280520138939e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.15701300347347e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 2%|▏ | 2/100 [00:00<00:25, 3.81it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.17151324815371e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.66860529926148e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.17151324815371e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.66860529926148e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.17151324815371e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 3%|▎ | 3/100 [00:00<00:23, 4.21it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.18601349283396e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.67440539713358e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.18601349283396e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.67440539713358e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.18601349283396e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 4%|▍ | 4/100 [00:00<00:21, 4.41it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.2005137375142e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.68020549500568e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.2005137375142e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 5%|▌ | 5/100 [00:01<00:20, 4.69it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.21501398219444e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.68600559287778e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.21501398219444e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 6%|▌ | 6/100 [00:01<00:19, 4.91it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.22951422687469e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.69180569074988e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.22951422687469e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.69180569074988e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.22951422687469e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 7%|▋ | 7/100 [00:01<00:18, 4.99it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.24401447155493e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.69760578862197e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.24401447155493e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.69760578862197e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.24401447155493e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 8%|▊ | 8/100 [00:01<00:18, 5.10it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.25851471623518e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.70340588649407e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.25851471623518e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.70340588649407e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.25851471623518e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 9%|▉ | 9/100 [00:01<00:17, 5.20it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.70920598436617e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.27301496091542e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.27301496091542e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.70920598436617e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.27301496091542e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 36%|███▌ | 36/100 [00:06<00:12, 5.01it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.66452156728202e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.86580862691281e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.66452156728202e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 37%|███▋ | 37/100 [00:07<00:12, 4.93it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8716087247849e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.67902181196226e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.67902181196226e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.8716087247849e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.67902181196226e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 38%|███▊ | 38/100 [00:07<00:12, 4.91it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.69352205664251e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.877408822657e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.69352205664251e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.877408822657e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.69352205664251e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 39%|███▉ | 39/100 [00:07<00:12, 4.84it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.70802230132275e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8832089205291e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.70802230132275e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 40%|████ | 40/100 [00:07<00:12, 4.92it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8890090184012e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.72252254600299e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 41%|████ | 41/100 [00:07<00:11, 5.02it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8948091162733e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.73702279068324e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.73702279068324e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.8948091162733e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.73702279068324e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 42%|████▏ | 42/100 [00:08<00:11, 4.97it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.75152303536348e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.90060921414539e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.75152303536348e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", "100%|██████████| 100/100 [06:09<00:00, 3.70s/it]\n" ] } ], "source": [ "n_spill_steps = 100\n", "\n", "trap[trap.power_tweezer] = initial_power\n", "\n", "#spill_power_factor = np.linspace(0.7, 0.52, num=n_spill_steps)\n", "#powers = trap[trap.power_tweezer] * spill_power_factor\n", "powers = np.linspace(151.5,204,n_spill_steps)*si.uW\n", "t_spill = 25 * si.ms\n", "atom_number = np.zeros_like(powers)\n", "#array to store mean lifetime at specific power\n", "mean_lifetime = np.zeros_like(powers)\n", "\n", "# Number of energy levels to compute\n", "# will change over time to avoid calculating too many levels\n", "n_levels = 40\n", "# Resolution of the potential when solving numerically\n", "n_pot_steps = 1000\n", "\n", "for i, power in enumerate(tqdm(powers)):\n", " trap[trap.power_tweezer] = power\n", " # Solve the hamiltonian numerically in axial direction\n", " energies, states, potential, coords = trap.nstationary_solution(\n", " trap.z, (-0.5 * axial_width, 1.8 * axial_width), n_pot_steps, k=n_levels\n", " )\n", "\n", " # Determine the potential and its derivatives\n", " pot_ax = trap.subs(trap.get_potential())\n", " pot_diff_ax = sp.diff(pot_ax, trap.z)\n", " pot_diff2_ax = sp.diff(pot_diff_ax, trap.z)\n", " pot_diff3_ax = sp.diff(pot_diff2_ax, trap.z)\n", " pot_diff_ax_numpy = sp.lambdify(trap.z, pot_diff_ax.subs({x: 0, y: 0}))\n", " pot_diff2_ax_numpy = sp.lambdify(trap.z, pot_diff2_ax.subs({x: 0, y: 0}))\n", " pot_diff3_ax_numpy = sp.lambdify(trap.z, pot_diff3_ax.subs({x: 0, y: 0}))\n", "\n", " barrier = root_scalar(\n", " pot_diff_ax_numpy,\n", " x0=1.5 * float(trap.subs(axial_width)),\n", " fprime=pot_diff2_ax_numpy,\n", " xtol=1e-28,\n", " fprime2=pot_diff2_ax_numpy,\n", " ).root\n", " minimum = root_scalar(\n", " pot_diff_ax_numpy,\n", " x0=0,\n", " fprime=pot_diff2_ax_numpy,\n", " xtol=1e-28,\n", " fprime2=pot_diff2_ax_numpy,\n", " ).root\n", " # States that are below the potential barrier\n", " bound_states = energies < potential(barrier)\n", "\n", " n_bound_states = np.sum(bound_states)\n", " n_levles = n_bound_states + 3 # add 3 more levels to be safe\n", "\n", " # Density of states is larger on the left than on the right\n", " # Likely that the state in question is a true bound state\n", " true_bound_states = np.logical_and(\n", " bound_states,\n", " np.sum(states[:, coords[z] < barrier] ** 2, axis=1)\n", " > np.sum(states[:, coords[z] > barrier] ** 2, axis=1),\n", " )\n", "\n", " transmission_probability = np.full_like(energies, np.nan, dtype=float)\n", " for j, energy in enumerate(energies):\n", " if not true_bound_states[j]:\n", " continue\n", " intersect_end = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(barrier, 3 * float(trap.subs(axial_width))),\n", " ).root\n", " intersect_start = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(minimum, barrier),\n", " ).root\n", " barrier_interval = np.logical_and(\n", " coords[z] > intersect_start, coords[z] < intersect_end\n", " )\n", " s = quad(\n", " lambda x: np.sqrt(\n", " 2\n", " * float(trap.subs(trap.m))\n", " * np.clip(potential(x) - energy, a_min=0, a_max=None)\n", " )\n", " / const.hbar,\n", " intersect_start,\n", " intersect_end,\n", " )\n", " transmission_probability[j] = sp.exp(-2 * s[0])\n", " tunneling_rate = (\n", " transmission_probability * np.abs(energies - potential(minimum)) / const.h\n", " )\n", " atom_number[i] = np.sum(np.exp(-t_spill * tunneling_rate[true_bound_states]))\n", " mean_lifetime[i] = 1/np.mean(tunneling_rate[~np.isnan(tunneling_rate)])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 373, "width": 373 } }, "output_type": "display_data" } ], "source": [ "ax: plt.Axes\n", "fig: plt.Figure\n", "fig, ax = plt.subplots(figsize=(2.5, 2.5))\n", "\n", "ax.set_xlabel(\"absolute tweezer power (uW)\")\n", "ax.set_ylabel(\"atom number\")\n", "ax.plot(powers*1e6, atom_number, marker=\".\")\n", "ax.fill_between(powers*1e6, atom_number, fc=colors_alpha[\"red\"], alpha=0.5)\n", "#fig.savefig(FIGS_PATH / \"twodtrap\" / \"1D Stufenplot.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 60" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " 0%| | 0/100 [00:00:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.14251275879322e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.65700510351729e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.14251275879322e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.65700510351729e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.14251275879322e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 1%| | 1/100 [00:00<00:32, 3.06it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.15701300347347e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.66280520138939e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.15701300347347e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.66280520138939e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.15701300347347e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 2%|▏ | 2/100 [00:00<00:29, 3.31it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.17151324815371e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.66860529926148e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.17151324815371e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.66860529926148e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.17151324815371e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 3%|▎ | 3/100 [00:00<00:28, 3.42it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.18601349283396e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.67440539713358e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.18601349283396e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.67440539713358e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.18601349283396e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 4%|▍ | 4/100 [00:01<00:28, 3.36it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.2005137375142e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.68020549500568e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.2005137375142e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 5%|▌ | 5/100 [00:01<00:27, 3.48it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.21501398219444e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.68600559287778e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.21501398219444e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 6%|▌ | 6/100 [00:01<00:26, 3.60it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.22951422687469e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.69180569074988e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.22951422687469e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.69180569074988e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.22951422687469e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 7%|▋ | 7/100 [00:01<00:25, 3.72it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.24401447155493e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.69760578862197e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.24401447155493e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.69760578862197e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.24401447155493e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 8%|▊ | 8/100 [00:02<00:24, 3.75it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.25851471623518e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.70340588649407e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.25851471623518e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.70340588649407e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.25851471623518e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 9%|▉ | 9/100 [00:02<00:28, 3.19it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.70920598436617e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.27301496091542e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.27301496091542e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.70920598436617e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.27301496091542e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 36%|███▌ | 36/100 [00:09<00:15, 4.11it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.66452156728202e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.86580862691281e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.66452156728202e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 37%|███▋ | 37/100 [00:10<00:15, 4.17it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8716087247849e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.67902181196226e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.67902181196226e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.8716087247849e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.67902181196226e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 38%|███▊ | 38/100 [00:10<00:14, 4.15it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.69352205664251e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.877408822657e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.69352205664251e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.877408822657e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.69352205664251e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 39%|███▉ | 39/100 [00:10<00:14, 4.18it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.70802230132275e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8832089205291e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.70802230132275e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 40%|████ | 40/100 [00:10<00:14, 4.04it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8890090184012e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.72252254600299e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 41%|████ | 41/100 [00:11<00:14, 4.01it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.8948091162733e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.73702279068324e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.73702279068324e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: invalid value encountered in scalar divide\n", " return -1.8948091162733e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.73702279068324e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", " 42%|████▏ | 42/100 [00:11<00:14, 3.94it/s]:2: RuntimeWarning: overflow encountered in scalar power\n", " return 4.75152303536348e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 5.52545520465114e-25\n", ":2: RuntimeWarning: overflow encountered in scalar power\n", " return -1.90060921414539e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 4.75152303536348e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n", "100%|██████████| 100/100 [11:43<00:00, 7.03s/it]\n" ] } ], "source": [ "n_spill_steps = 100\n", "\n", "trap[trap.power_tweezer] = initial_power\n", "\n", "#spill_power_factor = np.linspace(0.7, 0.52, num=n_spill_steps)\n", "#powers = trap[trap.power_tweezer] * spill_power_factor\n", "powers = np.linspace(151.5,204,n_spill_steps)*si.uW\n", "t_spill = 25 * si.ms\n", "atom_number = np.zeros_like(powers)\n", "#array to store mean lifetime at specific power\n", "mean_lifetime = np.zeros_like(powers)\n", "\n", "# Number of energy levels to compute\n", "# will change over time to avoid calculating too many levels\n", "n_levels = 60\n", "# Resolution of the potential when solving numerically\n", "n_pot_steps = 1000\n", "\n", "for i, power in enumerate(tqdm(powers)):\n", " trap[trap.power_tweezer] = power\n", " # Solve the hamiltonian numerically in axial direction\n", " energies, states, potential, coords = trap.nstationary_solution(\n", " trap.z, (-0.5 * axial_width, 1.8 * axial_width), n_pot_steps, k=n_levels\n", " )\n", "\n", " # Determine the potential and its derivatives\n", " pot_ax = trap.subs(trap.get_potential())\n", " pot_diff_ax = sp.diff(pot_ax, trap.z)\n", " pot_diff2_ax = sp.diff(pot_diff_ax, trap.z)\n", " pot_diff3_ax = sp.diff(pot_diff2_ax, trap.z)\n", " pot_diff_ax_numpy = sp.lambdify(trap.z, pot_diff_ax.subs({x: 0, y: 0}))\n", " pot_diff2_ax_numpy = sp.lambdify(trap.z, pot_diff2_ax.subs({x: 0, y: 0}))\n", " pot_diff3_ax_numpy = sp.lambdify(trap.z, pot_diff3_ax.subs({x: 0, y: 0}))\n", "\n", " barrier = root_scalar(\n", " pot_diff_ax_numpy,\n", " x0=1.5 * float(trap.subs(axial_width)),\n", " fprime=pot_diff2_ax_numpy,\n", " xtol=1e-28,\n", " fprime2=pot_diff2_ax_numpy,\n", " ).root\n", " minimum = root_scalar(\n", " pot_diff_ax_numpy,\n", " x0=0,\n", " fprime=pot_diff2_ax_numpy,\n", " xtol=1e-28,\n", " fprime2=pot_diff2_ax_numpy,\n", " ).root\n", " # States that are below the potential barrier\n", " bound_states = energies < potential(barrier)\n", "\n", " n_bound_states = np.sum(bound_states)\n", " n_levles = n_bound_states + 3 # add 3 more levels to be safe\n", "\n", " # Density of states is larger on the left than on the right\n", " # Likely that the state in question is a true bound state\n", " true_bound_states = np.logical_and(\n", " bound_states,\n", " np.sum(states[:, coords[z] < barrier] ** 2, axis=1)\n", " > np.sum(states[:, coords[z] > barrier] ** 2, axis=1),\n", " )\n", "\n", " transmission_probability = np.full_like(energies, np.nan, dtype=float)\n", " for j, energy in enumerate(energies):\n", " if not true_bound_states[j]:\n", " continue\n", " intersect_end = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(barrier, 3 * float(trap.subs(axial_width))),\n", " ).root\n", " intersect_start = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(minimum, barrier),\n", " ).root\n", " barrier_interval = np.logical_and(\n", " coords[z] > intersect_start, coords[z] < intersect_end\n", " )\n", " s = quad(\n", " lambda x: np.sqrt(\n", " 2\n", " * float(trap.subs(trap.m))\n", " * np.clip(potential(x) - energy, a_min=0, a_max=None)\n", " )\n", " / const.hbar,\n", " intersect_start,\n", " intersect_end,\n", " )\n", " transmission_probability[j] = sp.exp(-2 * s[0])\n", " tunneling_rate = (\n", " transmission_probability * np.abs(energies - potential(minimum)) / const.h\n", " )\n", " atom_number[i] = np.sum(np.exp(-t_spill * tunneling_rate[true_bound_states]))\n", " mean_lifetime[i] = 1/np.mean(tunneling_rate[~np.isnan(tunneling_rate)])" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 373, "width": 373 } }, "output_type": "display_data" } ], "source": [ "ax: plt.Axes\n", "fig: plt.Figure\n", "fig, ax = plt.subplots(figsize=(2.5, 2.5))\n", "\n", "ax.set_xlabel(\"absolute tweezer power (uW)\")\n", "ax.set_ylabel(\"atom number\")\n", "ax.plot(powers*1e6, atom_number, marker=\".\")\n", "ax.fill_between(powers*1e6, atom_number, fc=colors_alpha[\"red\"], alpha=0.5)\n", "#fig.savefig(FIGS_PATH / \"twodtrap\" / \"1D Stufenplot.pdf\")" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-4.778250005541249e-30\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, 'E / h (kHz)')" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 373, "width": 373 } }, "output_type": "display_data" } ], "source": [ "n_pot_steps = 1000\n", "n_levels = 30\n", "\n", "trap[trap.power_tweezer] = 200*si.uW\n", "# Solve the hamiltonian numerically in axial direction\n", "energies, states, potential, coords = trap.nstationary_solution(\n", " trap.z, (-0.5 * axial_width, 3 * axial_width), n_pot_steps, k=n_levels\n", ")\n", "\n", "pot_ax = trap.subs(trap.get_potential())\n", "pot_diff_ax = sp.diff(pot_ax, trap.z)\n", "pot_diff2_ax = sp.diff(pot_diff_ax, trap.z)\n", "pot_diff3_ax = sp.diff(pot_diff2_ax, trap.z)\n", "pot_diff_ax_numpy = sp.lambdify(trap.z, pot_diff_ax.subs({x: 0, y: 0}))\n", "pot_diff2_ax_numpy = sp.lambdify(trap.z, pot_diff2_ax.subs({x: 0, y: 0}))\n", "pot_diff3_ax_numpy = sp.lambdify(trap.z, pot_diff3_ax.subs({x: 0, y: 0}))\n", "\n", "barrier = root_scalar(\n", " pot_diff_ax_numpy,\n", " x0=1.5 * float(trap.subs(axial_width)),\n", " fprime=pot_diff2_ax_numpy,\n", " xtol=1e-18,\n", " fprime2=pot_diff2_ax_numpy,\n", ").root\n", "\n", "# States that are below the potential barrier\n", "bound_states = energies < potential(barrier)\n", "\n", "\n", "# Density of states is larger on the left than on the right\n", "# Likely that the state in question is a true bound state\n", "true_bound_states = np.logical_and(\n", " bound_states,\n", " np.sum(states[:, coords[z] < barrier] ** 2, axis=1)\n", " > np.sum(states[:, coords[z] > barrier] ** 2, axis=1),\n", ")\n", "\n", "width_np = float(trap.subs(axial_width))\n", "\n", "z_np = np.linspace(-0.5 * width_np, 2 * width_np, num=1000)\n", "\n", "ax: plt.Axes\n", "fig, ax = plt.subplots(figsize=(2.5, 2.5))\n", "# ax.set_title(\"Axial\")\n", "abs_min = np.min(potential(z_np))\n", "print(abs_min)\n", "ax.fill_between(\n", " z_np / si.um,\n", " potential(z_np) / const.h / si.kHz,\n", " abs_min / const.h / si.kHz,\n", " fc=colors_alpha[\"red\"],\n", " alpha=0.5,\n", ")\n", "# ax2 = ax.twinx()\n", "\n", "for i, bound in enumerate(true_bound_states):\n", " if not bound:\n", " continue\n", " energy = energies[i]\n", " state = states[i]\n", " ax.plot(\n", " z_np / si.um,\n", " np.where(\n", " (energy > potential(z_np)) & (z_np < barrier),\n", " energy / const.h / si.kHz,\n", " np.nan,\n", " ),\n", " c=\"k\",\n", " lw=0.5,\n", " marker=\"None\",\n", " )\n", " #print(energy)\n", " ax.plot(z_np/si.um, state**2 *300, marker=\"None\", c=\"k\")\n", "\n", "ax.plot(z_np / si.um, potential(z_np) / const.h / si.kHz, marker=\"None\")\n", "ax.set_xlabel(r\"z ($\\mathrm{\\mu m}$)\")\n", "ax.set_ylabel(r\"E / h (kHz)\")" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False])" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "true_bound_states" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Make 2D plots for power and gradient" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " 0%| | 0/10 [00:00 np.sum(states[:, coords[z] > barrier] ** 2, axis=1),\n", " )\n", "\n", " transmission_probability = np.full_like(energies, np.nan, dtype=float)\n", " for j, energy in enumerate(energies):\n", " if not true_bound_states[j]:\n", " continue\n", " intersect_end = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(barrier, 3 * float(trap.subs(axial_width))),\n", " ).root\n", " intersect_start = root_scalar(\n", " lambda x: potential(x) - energy,\n", " bracket=(minimum, barrier),\n", " ).root\n", " barrier_interval = np.logical_and(\n", " coords[z] > intersect_start, coords[z] < intersect_end\n", " )\n", " s = quad(\n", " lambda x: np.sqrt(\n", " 2\n", " * float(trap.subs(trap.m))\n", " * np.clip(potential(x) - energy, a_min=0, a_max=None)\n", " )\n", " / const.hbar,\n", " intersect_start,\n", " intersect_end,\n", " )\n", " transmission_probability[j] = sp.exp(-2 * s[0])\n", " tunneling_rate = (\n", " transmission_probability * np.abs(energies - potential(minimum)) / const.h\n", " )\n", " atom_number[i,k] = np.sum(np.exp(-t_spill * tunneling_rate[true_bound_states]))\n", " mean_lifetime[i,k] = 1/np.mean(tunneling_rate[~np.isnan(tunneling_rate)])\n", " except:\n", " atom_number[i,k] = np.nan\n", " mean_lifetime[i,k] = np.nan" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "image/png": { "height": 506, "width": 505 } }, "output_type": "display_data" } ], "source": [ "# Plot the main data\n", "fig, ax1 = plt.subplots()\n", "im = ax1.imshow(\n", " atom_number,\n", " extent=[\n", " np.min(gradients)/si.G*si.cm,\n", " np.max(gradients)/si.G*si.cm,\n", " np.min(powers)/si.mW,\n", " np.max(powers)/si.mW\n", " ],\n", " aspect=\"auto\",\n", " origin=\"lower\",\n", " cmap=\"viridis\"\n", ")\n", "\n", "# Add colorbar\n", "plt.colorbar(im, ax=ax1, label=\"Occupation\")\n", "\n", "# Primary axis labels\n", "ax1.set_xlabel(\"Magnetic gradient [G/cm]\")\n", "ax1.set_ylabel(\"Beam power [mW]\")\n", "ax1.set_title(f\"w_0={trap.subs(trap.waist_tweezer)*1e6}um\")\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "base", "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": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 2 }