LennartNaeve_code/spilling_code/diagonalisation_clean/2025_04_03 (calculate eta).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Math, display\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "from scipy import constants as const\n",
    "\n",
    "#add relative path to backend\n",
    "import sys\n",
    "sys.path.append('../../clean_diag/backend')\n",
    "\n",
    "import trap_units as si\n",
    "from twod_trap import PancakeTrap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 49 * si.uW \n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= 0 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer= initial_power,\n",
    "    waist_tweezer=1 * si.um,\n",
    "\n",
    "    m= 161 * const.value(\"atomic mass constant\"),\n",
    "    mu_b= 9.93 * const.value(\"Bohr magneton\" ),\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",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient to cancel gravity:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.847 G/cm\n"
     ]
    }
   ],
   "source": [
    "grav_grad = float(trap.subs(trap.m*const.g/trap.mu_b) /si.G*si.cm)\n",
    "print(f\"{grav_grad:.3f} G/cm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Find waist for target aspect ration (1064nm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle W_{t}\\left(\\frac{\\omega_{t r}}{\\omega_{t ax}} = 9\\right) = 2.16\\mathrm{\\mu m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta_target = 9\n",
    "\n",
    "waist = trap.subs(\n",
    "    sp.solve(\n",
    "        trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer() - eta_target,\n",
    "        trap.waist_tweezer,\n",
    "    )[0]\n",
    ").evalf()\n",
    "\n",
    "_aspect_ratio_latex = sp.latex(trap.omega_r_tweezer / trap.omega_ax_tweezer)\n",
    "display(\n",
    "    Math(\n",
    "        f\"{sp.latex(trap.waist_tweezer)}\\\\left({_aspect_ratio_latex} = {eta_target}\\\\right)\"\n",
    "        f\" = {waist/si.um:.2f}\\\\mathrm{{\\\\mu m}}\"\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# For 532nm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "trap[trap.wvl] = 532*si.nm\n",
    "trap[trap.a] = 180* (4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle W_{t}\\left(\\frac{\\omega_{t r}}{\\omega_{t ax}} = 9\\right) = 1.08\\mathrm{\\mu m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta_target = 9\n",
    "\n",
    "waist = trap.subs(\n",
    "    sp.solve(\n",
    "        trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer() - eta_target,\n",
    "        trap.waist_tweezer,\n",
    "    )[0]\n",
    ").evalf()\n",
    "\n",
    "_aspect_ratio_latex = sp.latex(trap.omega_r_tweezer / trap.omega_ax_tweezer)\n",
    "display(\n",
    "    Math(\n",
    "        f\"{sp.latex(trap.waist_tweezer)}\\\\left({_aspect_ratio_latex} = {eta_target}\\\\right)\"\n",
    "        f\" = {waist/si.um:.2f}\\\\mathrm{{\\\\mu m}}\"\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ploting for different target aspect ratios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wvls = np.array([532, 1064]) * si.nm\n",
    "waists = np.linspace(0.5,4) * si.um\n",
    "\n",
    "for i, wvl in enumerate(wvls):\n",
    "    eta = np.sqrt(2)*np.pi * waists/wvl\n",
    "    plt.plot(waists/si.um,eta,label=f\"{wvl/si.nm}nm\")\n",
    "\n",
    "plt.ylabel(\"eta\")\n",
    "plt.xlabel(\"waist [um]\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}