{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": [
    "### Reproducing the spilling behaviour for the Li6 experiment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 291.5 * 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": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 7.67$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "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": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  8%|▊         | 8/100 [00:42<07:59,  5.21s/it]"
     ]
    }
   ],
   "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 = 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] = 2 * np.sum(np.exp(-t_spill * tunneling_rate[true_bound_states]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x294e7c32930>"
      ]
     },
     "execution_count": 5,
     "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)\n",
    "#fig.savefig(FIGS_PATH / \"twodtrap\" / \"1D Stufenplot.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now with absolute power:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [04:45<00:00,  2.85s/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] = 2 * 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": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x1a2092ddcd0>"
      ]
     },
     "execution_count": 12,
     "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(\"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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.27898241e-01, 7.55190291e-01, 1.08764880e+00, 7.88754368e-01,\n",
       "       1.14789644e+00, 1.74176623e+00, 2.50321259e+00, 3.70671199e+00,\n",
       "       5.52288736e+00, 8.27219254e+00, 1.24512166e+01, 1.88301231e+01,\n",
       "       2.86073590e+01, 4.36544601e+01, 6.69044499e+01, 1.02969864e+02,\n",
       "       1.59136113e+02, 2.46919886e+02, 3.84645515e+02, 6.01510043e+02,\n",
       "       9.44268355e+02, 1.48774340e+03, 2.35267259e+03, 3.73384346e+03,\n",
       "       3.96455358e+03, 6.33627267e+03, 1.01615545e+04, 1.63512456e+04,\n",
       "       2.63988219e+04, 4.27603106e+04, 6.94864566e+04, 1.13277517e+05,\n",
       "       1.85247942e+05, 3.03886818e+05, 5.00037299e+05, 8.25294399e+05,\n",
       "       1.36620483e+06, 2.26834009e+06, 3.77721281e+06, 4.73100003e+06,\n",
       "       7.92349099e+06, 1.33079289e+07, 2.24141334e+07, 3.78563466e+07,\n",
       "       6.41133944e+07, 1.08878113e+08, 1.85397077e+08, 3.16537180e+08,\n",
       "       5.41870498e+08, 9.30046964e+08, 1.60045252e+09, 2.76121019e+09,\n",
       "       4.77601152e+09, 8.28192336e+09, 1.43975283e+10, 2.50915069e+10,\n",
       "       4.38368169e+10, 7.67743844e+10, 1.34787786e+11, 1.89768264e+11,\n",
       "       3.34770886e+11, 5.91977469e+11, 1.04927325e+12, 1.86419204e+12,\n",
       "       3.31974079e+12, 5.92546164e+12, 1.06007808e+13, 1.90083522e+13,\n",
       "       3.41613858e+13, 6.15324855e+13, 1.11082363e+14, 2.00979274e+14,\n",
       "       3.64432329e+14, 6.62271481e+14, 1.20615447e+15, 2.20146519e+15,\n",
       "       4.02677289e+15, 6.15109072e+15, 1.12993617e+16, 2.08006036e+16,\n",
       "       3.83718741e+16, 7.09349106e+16, 1.31405023e+17, 2.43929266e+17,\n",
       "       4.53744114e+17, 8.45762635e+17, 1.57968938e+18, 2.95648726e+18,\n",
       "       5.54443007e+18, 1.04186138e+19, 1.96169154e+19, 3.17225541e+19,\n",
       "       5.99668949e+19, 1.13582127e+20, 2.15555617e+20, 4.09878891e+20,\n",
       "       7.80898586e+20, 1.49063961e+21, 2.85092485e+21, 5.46298684e+21])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_lifetime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Different \"n_levels\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/100 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [04:28<00:00,  2.68s/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 = 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] = 2 * 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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x1a20a6ce7e0>"
      ]
     },
     "execution_count": 20,
     "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(\"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": 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
}