LennartNaeve_code/spilling_code/diagonalisation/dysprosium2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Troubleshooting for why \"n_levels\" changes result\n",
    "## Start with lithium1.ipynb and change all parameters one by one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "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 scipy.signal import argrelmax,argrelmin\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()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### original lithium1 code (adjust initial power to see 0 bound states), (n_levels=60 to check for bug)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 260 * si.uW\n",
    "\n",
    "#parameters for lithium setup\n",
    "wvl = 1064 * si.nm\n",
    "omega_l = 2 * np.pi * const.c / wvl\n",
    "omega_0 = 2 * np.pi * const.c / (671 * si.nm)\n",
    "gamma = 2 * np.pi * 5.8724 * const.mega\n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z=15 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer=initial_power,\n",
    "    waist_tweezer=1.838 * si.um,\n",
    "\n",
    "    wvl = 1064 * si.nm,\n",
    "    omega_0 = 2 * np.pi * const.c / (671 * si.nm),\n",
    "    a = (3 * sp.pi * const.c**2) / (2 * omega_0**3)* (gamma / (omega_0 - omega_l) + gamma / (omega_0 + omega_l)),\n",
    "    m = 6.0151228 * const.value(\"atomic mass constant\"),\n",
    "    mu_b = const.value(\"Bohr magneton\"),\n",
    ")\n",
    "axial_width = trap.get_tweezer_rayleigh()\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/100 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 68%|██████▊   | 68/100 [02:28<00:31,  1.00it/s]<lambdifygenerated-1230>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.75745677485922e-40*z/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-1231>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.90298270994369e-39*z**2/(pi**4*(z**2/pi**2 + 1.00808875956951e-11)**3) + 4.75745677485922e-40/(pi**2*(z**2/pi**2 + 1.00808875956951e-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",
      " 69%|██████▉   | 69/100 [02:28<00:25,  1.21it/s]<lambdifygenerated-1234>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.74244902478079e-40*z/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-1235>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.89697960991232e-39*z**2/(pi**4*(z**2/pi**2 + 1.00808875956951e-11)**3) + 4.74244902478079e-40/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 70%|███████   | 70/100 [02:29<00:22,  1.35it/s]<lambdifygenerated-1238>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.72744127470237e-40*z/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-1239>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.89097650988095e-39*z**2/(pi**4*(z**2/pi**2 + 1.00808875956951e-11)**3) + 4.72744127470237e-40/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 71%|███████   | 71/100 [02:29<00:19,  1.52it/s]<lambdifygenerated-1242>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.71243352462395e-40*z/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-1243>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.88497340984958e-39*z**2/(pi**4*(z**2/pi**2 + 1.00808875956951e-11)**3) + 4.71243352462395e-40/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-1243>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -1.88497340984958e-39*z**2/(pi**4*(z**2/pi**2 + 1.00808875956951e-11)**3) + 4.71243352462395e-40/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 72%|███████▏  | 72/100 [02:30<00:16,  1.68it/s]<lambdifygenerated-1246>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.69742577454553e-40*z/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-1247>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.87897030981821e-39*z**2/(pi**4*(z**2/pi**2 + 1.00808875956951e-11)**3) + 4.69742577454553e-40/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 73%|███████▎  | 73/100 [02:30<00:15,  1.78it/s]<lambdifygenerated-1250>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.68241802446711e-40*z/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-1251>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.87296720978685e-39*z**2/(pi**4*(z**2/pi**2 + 1.00808875956951e-11)**3) + 4.68241802446711e-40/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 99%|█████████▉| 99/100 [02:43<00:00,  2.25it/s]<lambdifygenerated-1354>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.29221652242819e-40*z/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-1355>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.71688660897128e-39*z**2/(pi**4*(z**2/pi**2 + 1.00808875956951e-11)**3) + 4.29221652242819e-40/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-1355>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -1.71688660897128e-39*z**2/(pi**4*(z**2/pi**2 + 1.00808875956951e-11)**3) + 4.29221652242819e-40/(pi**2*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "100%|██████████| 100/100 [02:43<00:00,  1.64s/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",
    "t_spill = 25 * si.ms\n",
    "atom_number = 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]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x20195d18320>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "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(\"rel. tweezer power (a.u.)\")\n",
    "ax.set_ylabel(\"atom number\")\n",
    "ax.plot(spill_power_factor, atom_number, marker=\"None\")\n",
    "ax.fill_between(spill_power_factor, atom_number, fc=colors_alpha[\"red\"], alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### changing polarisability and increase initial power (n_levels=60 to check for bug)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 400 * si.uW\n",
    "\n",
    "#parameters for lithium setup\n",
    "wvl = 1064 * si.nm\n",
    "omega_l = 2 * np.pi * const.c / wvl\n",
    "omega_0 = 2 * np.pi * const.c / (671 * si.nm)\n",
    "gamma = 2 * np.pi * 5.8724 * const.mega\n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z=15 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer=initial_power,\n",
    "    waist_tweezer=1.838 * si.um,\n",
    "\n",
    "    wvl = 1064 * si.nm,\n",
    "    omega_0 = 2 * np.pi * const.c / (671 * si.nm),\n",
    "    a=184.4*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "    m = 6.0151228 * const.value(\"atomic mass constant\"),\n",
    "    mu_b = const.value(\"Bohr magneton\"),\n",
    ")\n",
    "axial_width = trap.get_tweezer_rayleigh()\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/100 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 85%|████████▌ | 85/100 [03:33<00:13,  1.10it/s]<lambdifygenerated-3051>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.49145373853941e-39*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-3052>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -5.96581495415766e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 1.49145373853941e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-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",
      "<lambdifygenerated-3050>:3: RuntimeWarning: overflow encountered in scalar multiply\n",
      "  return 7.3974326386514e-29*x0 - 7.3974326386514e-29*x0/(99197614347.6731*z**2/pi**2 + 1) - 1.391101511745e-24*z\n",
      " 86%|████████▌ | 86/100 [03:34<00:11,  1.26it/s]<lambdifygenerated-3056>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -5.94592890431046e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 1.48648222607762e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 87%|████████▋ | 87/100 [03:34<00:09,  1.37it/s]<lambdifygenerated-3059>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.48151071361582e-39*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-3060>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -5.92604285446327e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 1.48151071361582e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 88%|████████▊ | 88/100 [03:35<00:08,  1.48it/s]<lambdifygenerated-3063>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.47653920115402e-39*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-3064>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -5.90615680461608e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 1.47653920115402e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 89%|████████▉ | 89/100 [03:35<00:07,  1.50it/s]<lambdifygenerated-3068>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -5.88627075476889e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 1.47156768869222e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-3067>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.47156768869222e-39*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 1.391101511745e-24\n",
      "<lambdifygenerated-3068>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -5.88627075476889e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 1.47156768869222e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "100%|██████████| 100/100 [03:42<00:00,  2.23s/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",
    "t_spill = 25 * si.ms\n",
    "atom_number = 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 = 100\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]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x20192a628a0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 373,
       "width": 375
      }
     },
     "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(\"rel. tweezer power (a.u.)\")\n",
    "ax.set_ylabel(\"atom number\")\n",
    "ax.plot(spill_power_factor, atom_number, marker=\"None\")\n",
    "ax.fill_between(spill_power_factor, atom_number, fc=colors_alpha[\"red\"], alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### n_levels=100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x2019c293170>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "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(\"rel. tweezer power (a.u.)\")\n",
    "ax.set_ylabel(\"atom number\")\n",
    "ax.plot(spill_power_factor, atom_number, marker=\"None\")\n",
    "ax.fill_between(spill_power_factor, atom_number, fc=colors_alpha[\"red\"], alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot potential for these parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-7.030454907724839e-30\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'E / h (kHz)')"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 373,
       "width": 373
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = 0.6 * initial_power\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",
    "    # ax1.plot(coords[trap.z], state**2, 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": "markdown",
   "metadata": {},
   "source": [
    "### Change mass and magnetic moment, adjust initial power (n_levels=60 to check for bug)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 3500 * si.uW\n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= 15 * 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",
    "    wvl = 1064 * si.nm,    \n",
    ")\n",
    "axial_width = trap.get_tweezer_rayleigh()\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  6%|▌         | 3/50 [01:01<15:57, 20.38s/it]\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[3], line 75\u001b[0m\n\u001b[0;32m     68\u001b[0m     intersect_start \u001b[38;5;241m=\u001b[39m root_scalar(\n\u001b[0;32m     69\u001b[0m         \u001b[38;5;28;01mlambda\u001b[39;00m x: potential(x) \u001b[38;5;241m-\u001b[39m energy,\n\u001b[0;32m     70\u001b[0m         bracket\u001b[38;5;241m=\u001b[39m(minimum, barrier),\n\u001b[0;32m     71\u001b[0m     )\u001b[38;5;241m.\u001b[39mroot\n\u001b[0;32m     72\u001b[0m     barrier_interval \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlogical_and(\n\u001b[0;32m     73\u001b[0m         coords[z] \u001b[38;5;241m>\u001b[39m intersect_start, coords[z] \u001b[38;5;241m<\u001b[39m intersect_end\n\u001b[0;32m     74\u001b[0m     )\n\u001b[1;32m---> 75\u001b[0m     s \u001b[38;5;241m=\u001b[39m quad(\n\u001b[0;32m     76\u001b[0m         \u001b[38;5;28;01mlambda\u001b[39;00m x: np\u001b[38;5;241m.\u001b[39msqrt(\n\u001b[0;32m     77\u001b[0m             \u001b[38;5;241m2\u001b[39m\n\u001b[0;32m     78\u001b[0m             \u001b[38;5;241m*\u001b[39m \u001b[38;5;28mfloat\u001b[39m(trap\u001b[38;5;241m.\u001b[39msubs(trap\u001b[38;5;241m.\u001b[39mm))\n\u001b[0;32m     79\u001b[0m             \u001b[38;5;241m*\u001b[39m np\u001b[38;5;241m.\u001b[39mclip(potential(x) \u001b[38;5;241m-\u001b[39m energy, a_min\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m, a_max\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m)\n\u001b[0;32m     80\u001b[0m         )\n\u001b[0;32m     81\u001b[0m         \u001b[38;5;241m/\u001b[39m const\u001b[38;5;241m.\u001b[39mhbar,\n\u001b[0;32m     82\u001b[0m         intersect_start,\n\u001b[0;32m     83\u001b[0m         intersect_end,\n\u001b[0;32m     84\u001b[0m     )\n\u001b[0;32m     85\u001b[0m     transmission_probability[j] \u001b[38;5;241m=\u001b[39m sp\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m2\u001b[39m \u001b[38;5;241m*\u001b[39m s[\u001b[38;5;241m0\u001b[39m])\n\u001b[0;32m     86\u001b[0m tunneling_rate \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m     87\u001b[0m     transmission_probability \u001b[38;5;241m*\u001b[39m np\u001b[38;5;241m.\u001b[39mabs(energies \u001b[38;5;241m-\u001b[39m potential(minimum)) \u001b[38;5;241m/\u001b[39m const\u001b[38;5;241m.\u001b[39mh\n\u001b[0;32m     88\u001b[0m )\n",
      "File \u001b[1;32mc:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\scipy\\integrate\\_quadpack_py.py:464\u001b[0m, in \u001b[0;36mquad\u001b[1;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points, weight, wvar, wopts, maxp1, limlst, complex_func)\u001b[0m\n\u001b[0;32m    461\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m retval\n\u001b[0;32m    463\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m weight \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m--> 464\u001b[0m     retval \u001b[38;5;241m=\u001b[39m _quad(func, a, b, args, full_output, epsabs, epsrel, limit,\n\u001b[0;32m    465\u001b[0m                    points)\n\u001b[0;32m    466\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m    467\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m points \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[1;32mc:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\scipy\\integrate\\_quadpack_py.py:611\u001b[0m, in \u001b[0;36m_quad\u001b[1;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points)\u001b[0m\n\u001b[0;32m    609\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m points \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m    610\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m infbounds \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[1;32m--> 611\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m _quadpack\u001b[38;5;241m.\u001b[39m_qagse(func,a,b,args,full_output,epsabs,epsrel,limit)\n\u001b[0;32m    612\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m    613\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m _quadpack\u001b[38;5;241m.\u001b[39m_qagie(func, bound, infbounds, args, full_output, \n\u001b[0;32m    614\u001b[0m                                 epsabs, epsrel, limit)\n",
      "Cell \u001b[1;32mIn[3], line 78\u001b[0m, in \u001b[0;36m<lambda>\u001b[1;34m(x)\u001b[0m\n\u001b[0;32m     68\u001b[0m     intersect_start \u001b[38;5;241m=\u001b[39m root_scalar(\n\u001b[0;32m     69\u001b[0m         \u001b[38;5;28;01mlambda\u001b[39;00m x: potential(x) \u001b[38;5;241m-\u001b[39m energy,\n\u001b[0;32m     70\u001b[0m         bracket\u001b[38;5;241m=\u001b[39m(minimum, barrier),\n\u001b[0;32m     71\u001b[0m     )\u001b[38;5;241m.\u001b[39mroot\n\u001b[0;32m     72\u001b[0m     barrier_interval \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlogical_and(\n\u001b[0;32m     73\u001b[0m         coords[z] \u001b[38;5;241m>\u001b[39m intersect_start, coords[z] \u001b[38;5;241m<\u001b[39m intersect_end\n\u001b[0;32m     74\u001b[0m     )\n\u001b[0;32m     75\u001b[0m     s \u001b[38;5;241m=\u001b[39m quad(\n\u001b[0;32m     76\u001b[0m         \u001b[38;5;28;01mlambda\u001b[39;00m x: np\u001b[38;5;241m.\u001b[39msqrt(\n\u001b[0;32m     77\u001b[0m             \u001b[38;5;241m2\u001b[39m\n\u001b[1;32m---> 78\u001b[0m             \u001b[38;5;241m*\u001b[39m \u001b[38;5;28mfloat\u001b[39m(trap\u001b[38;5;241m.\u001b[39msubs(trap\u001b[38;5;241m.\u001b[39mm))\n\u001b[0;32m     79\u001b[0m             \u001b[38;5;241m*\u001b[39m np\u001b[38;5;241m.\u001b[39mclip(potential(x) \u001b[38;5;241m-\u001b[39m energy, a_min\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m, a_max\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m)\n\u001b[0;32m     80\u001b[0m         )\n\u001b[0;32m     81\u001b[0m         \u001b[38;5;241m/\u001b[39m const\u001b[38;5;241m.\u001b[39mhbar,\n\u001b[0;32m     82\u001b[0m         intersect_start,\n\u001b[0;32m     83\u001b[0m         intersect_end,\n\u001b[0;32m     84\u001b[0m     )\n\u001b[0;32m     85\u001b[0m     transmission_probability[j] \u001b[38;5;241m=\u001b[39m sp\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m2\u001b[39m \u001b[38;5;241m*\u001b[39m s[\u001b[38;5;241m0\u001b[39m])\n\u001b[0;32m     86\u001b[0m tunneling_rate \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m     87\u001b[0m     transmission_probability \u001b[38;5;241m*\u001b[39m np\u001b[38;5;241m.\u001b[39mabs(energies \u001b[38;5;241m-\u001b[39m potential(minimum)) \u001b[38;5;241m/\u001b[39m const\u001b[38;5;241m.\u001b[39mh\n\u001b[0;32m     88\u001b[0m )\n",
      "File \u001b[1;32mc:\\users\\peter\\uni-bulk\\ferdy_chomaz\\code_jonas\\08-fewfermions-2dspilling\\fewfermions\\simulate\\traps\\twod\\trap\\__init__.py:130\u001b[0m, in \u001b[0;36mPancakeTrap.subs\u001b[1;34m(self, expr, symbolic_only)\u001b[0m\n\u001b[0;32m    127\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m expr_symbolic\n\u001b[0;32m    128\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m    129\u001b[0m     \u001b[38;5;66;03m# Also substitute all non-symbolic values\u001b[39;00m\n\u001b[1;32m--> 130\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m expr_symbolic\u001b[38;5;241m.\u001b[39msubs(\n\u001b[0;32m    131\u001b[0m         [\n\u001b[0;32m    132\u001b[0m             (key, value)\n\u001b[0;32m    133\u001b[0m             \u001b[38;5;28;01mfor\u001b[39;00m key, value \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_values\u001b[38;5;241m.\u001b[39mitems()\n\u001b[0;32m    134\u001b[0m             \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(value, sp\u001b[38;5;241m.\u001b[39mExpr)\n\u001b[0;32m    135\u001b[0m         ]\n\u001b[0;32m    136\u001b[0m     )\n",
      "File \u001b[1;32mc:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\sympy\\core\\basic.py:1079\u001b[0m, in \u001b[0;36mBasic.subs\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1076\u001b[0m \u001b[38;5;66;03m# skip if there is no change\u001b[39;00m\n\u001b[0;32m   1077\u001b[0m sequence \u001b[38;5;241m=\u001b[39m [(s1, s2) \u001b[38;5;28;01mfor\u001b[39;00m s1, s2 \u001b[38;5;129;01min\u001b[39;00m sequence \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m _aresame(s1, s2)]\n\u001b[1;32m-> 1079\u001b[0m simultaneous \u001b[38;5;241m=\u001b[39m kwargs\u001b[38;5;241m.\u001b[39mpop(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124msimultaneous\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;28;01mFalse\u001b[39;00m)\n\u001b[0;32m   1081\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m unordered:\n\u001b[0;32m   1082\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01msorting\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m _nodes, default_sort_key\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "n_spill_steps = 50\n",
    "\n",
    "trap[trap.power_tweezer] = initial_power\n",
    "\n",
    "spill_power_factor = np.linspace(0.65, 0.63, num=n_spill_steps)\n",
    "powers = trap[trap.power_tweezer] * spill_power_factor\n",
    "t_spill = 25 * si.ms\n",
    "atom_number = 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 = 100\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]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x2019acec920>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "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(\"rel. tweezer power (a.u.)\")\n",
    "ax.set_ylabel(\"atom number\")\n",
    "ax.plot(spill_power_factor, atom_number, marker=\"None\")\n",
    "ax.fill_between(spill_power_factor, atom_number, fc=colors_alpha[\"red\"], alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### n_levels=100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x2019c2730b0>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "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(\"rel. tweezer power (a.u.)\")\n",
    "ax.set_ylabel(\"atom number\")\n",
    "ax.plot(spill_power_factor, atom_number, marker=\"None\")\n",
    "ax.fill_between(spill_power_factor, atom_number, fc=colors_alpha[\"red\"], alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot potential for these parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "-1.2215042174494931e-28\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'E / h (kHz)')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 373,
       "width": 373
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_pot_steps = 1000\n",
    "n_levels = 500\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_diff3_ax_numpy,\n",
    ").root\n",
    "\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_diff3_ax_numpy,\n",
    "    ).root\n",
    "\n",
    "\n",
    "pot_min_ax_numpy = sp.lambdify(trap.z,pot_ax.subs({x: 0, y: 0}) - potential(minimum))\n",
    "right_cutoff = root_scalar(\n",
    "        pot_min_ax_numpy,\n",
    "        x0=barrier + np.abs(barrier - minimum),\n",
    "        fprime=pot_diff2_ax_numpy,\n",
    "        xtol=1e-28,\n",
    "        fprime2=pot_diff3_ax_numpy,\n",
    "    ).root\n",
    "right_cutoff = barrier + np.abs(barrier - minimum)\n",
    "left_cutoff = minimum - np.abs(barrier - minimum)\n",
    "\n",
    "trap[trap.power_tweezer] = 0.64 * initial_power\n",
    "# Solve the hamiltonian numerically in axial direction\n",
    "energies, states, potential, coords = trap.nstationary_solution(\n",
    "    trap.z, (left_cutoff, right_cutoff), n_pot_steps, k=n_levels\n",
    ")\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",
    "print(np.sum(true_bound_states))\n",
    "\n",
    "width_np = float(trap.subs(axial_width))\n",
    "\n",
    "z_np = np.linspace(left_cutoff, right_cutoff, 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",
    "    ax.plot(z_np/si.um, state**2 *600, 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": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.signal import argrelmax,argrelmin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.97696491e-06])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z_in = np.linspace(-1.5* float(trap.subs(axial_width)),3* float(trap.subs(axial_width)),1000)\n",
    "potential_z = sp.lambdify(trap.z, pot_ax.subs({x: 0, y: 0}))(z_in)\n",
    "mi = z_in[argrelmin(test)]\n",
    "mi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2ac1ca37680>]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 507.875x507.875 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 506,
       "width": 506
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(z_in,test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 3500 * si.uW\n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= 5 * 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",
    "    wvl = 1064 * si.nm,    \n",
    ")\n",
    "axial_width = trap.get_tweezer_rayleigh()\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x2ac1f71ecf0>"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 507.875x507.875 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 506,
       "width": 506
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_pot_steps = 1000\n",
    "n_levels = 500\n",
    "\n",
    "#get potential minimum and maximum\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",
    "\n",
    "z_in = np.linspace(-1.5* float(trap.subs(axial_width)),3* float(trap.subs(axial_width)),n_pot_steps)\n",
    "potential_in = sp.lambdify(trap.z, pot_ax.subs({x: 0, y: 0}))(z_in)\n",
    "barrier = z_in[argrelmax(potential_in)][0]\n",
    "E_max = potential_in[argrelmax(potential_in)][0]\n",
    "minimum = z_in[argrelmin(potential_in)][0]\n",
    "E_min = potential_in[argrelmin(potential_in)][0]\n",
    "\n",
    "#get cutoff values for solving SE\n",
    "pot_min_ax_numpy = sp.lambdify(trap.z,pot_ax.subs({x: 0, y: 0}) - (E_min - 0.5*np.abs(E_max-E_min)) )\n",
    "right_cutoff = root_scalar(\n",
    "        pot_min_ax_numpy,\n",
    "        x0=barrier + np.abs(barrier - minimum),\n",
    "        fprime=pot_diff_ax_numpy,\n",
    "        xtol=1e-28,\n",
    "        fprime2=pot_diff2_ax_numpy,\n",
    "    ).root\n",
    "\n",
    "pot_min_ax_numpy = sp.lambdify(trap.z,pot_ax.subs({x: 0, y: 0}) - (E_min + 4*np.abs(E_max-E_min)) )\n",
    "left_cutoff = root_scalar(\n",
    "        pot_min_ax_numpy,\n",
    "        x0=minimum - np.abs(barrier - minimum),\n",
    "        fprime=pot_diff_ax_numpy,\n",
    "        xtol=1e-28,\n",
    "        fprime2=pot_diff2_ax_numpy,\n",
    "    ).root\n",
    "\n",
    "#plot results\n",
    "plt.plot(z_in,potential_in)\n",
    "plt.vlines(barrier,np.min(potential_in),np.max(potential_in))\n",
    "plt.vlines(minimum,np.min(potential_in),np.max(potential_in))\n",
    "plt.vlines(left_cutoff,np.min(potential_in),np.max(potential_in))\n",
    "plt.vlines(right_cutoff,np.min(potential_in),np.max(potential_in))\n",
    "plt.hlines(E_min,np.min(z_in),np.max(z_in))\n",
    "plt.hlines(E_max,np.min(z_in),np.max(z_in))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-8.426358471408197e-29"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_min - np.abs(E_max-E_min)"
   ]
  },
  {
   "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
}