LennartNaeve_code/spilling_code/diagonalisation/jonas_example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "colors, colors_alpha = setup()\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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=15 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer=initial_power,\n",
    "    waist_tweezer=1.838 * si.um,\n",
    ")\n",
    "axial_width = trap.get_tweezer_rayleigh()\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle W_{t}\\left(\\frac{\\omega_{t r}}{\\omega_{t ax}} = 7\\right) = 1.68\\mathrm{\\mu m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "waist = trap.subs(\n",
    "    sp.solve(\n",
    "        trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer() - 7,\n",
    "        trap.waist_tweezer,\n",
    "    )[0]\n",
    ").evalf()\n",
    "\n",
    "display(\n",
    "    Math(\n",
    "        f\"{sp.latex(trap.waist_tweezer)}\\\\left({_aspect_ratio_latex} = 7\\\\right)\"\n",
    "        f\" = {waist/si.um:.2f}\\\\mathrm{{\\\\mu m}}\"\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [00:26<00:00,  3.83it/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",
    "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": 29,
   "metadata": {},
   "outputs": [
    {
     "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": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "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",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "width_np = float(trap.subs(axial_width))\n",
    "\n",
    "z_np = np.linspace(-0.5 * width_np, 2 * width_np, num=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5.719499903379515e-30\n"
     ]
    },
    {
     "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, 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)\")\n",
    "\n",
    "fig.savefig(FIGS_PATH / \"twodtrap\" / \"1D Spilling Example.pdf\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.13.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}