LennartNaeve_code/merging_tweezer_code/bosons/2025_03_24 (match paper conditions).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "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",
    "from scipy.optimize import minimize_scalar\n",
    "from scipy import sparse\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 DoubleTweezer, TwoSiteLattice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trap parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Erbium ###\n",
    "\n",
    "initial_power = 100* si.uW\n",
    "initial_waist = 1.1*si.uW\n",
    "initial_distance = 1.266*si.um\n",
    "\n",
    "trap: DoubleTweezer = DoubleTweezer(\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_tweezer1 = initial_power,     #stationary\n",
    "    power_tweezer2 = initial_power,     #transfer tweezer\n",
    "    waist_tweezer1 = initial_waist,     #stationary\n",
    "    waist_tweezer2 = initial_waist,     #transfer tweezer\n",
    "    distance_tweezers = initial_distance,\n",
    "\n",
    "    m = 168 * const.value(\"atomic mass constant\"),\n",
    "    mu_b = 6.982806* const.value(\"Bohr magneton\"),\n",
    "    a_s = 85* const.value(\"Bohr radius\"),\n",
    "    a=180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "    wvl = 532 * si.nm,\n",
    "\n",
    "    g = 0,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate $E_r = h^2/8ma^2$ and depth of tweezers (single tweezer depth not accuarte if close together)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "E_r = const.h**2/(8*trap.m*trap.distance_tweezers**2)\n",
    "\n",
    "depth_tweezer1 = trap.a*2*trap.power_tweezer1/sp.pi/trap.waist_tweezer1**2\n",
    "depth_tweezer2 = trap.a*2*trap.power_tweezer2/sp.pi/trap.waist_tweezer2**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 P_{t1} a}{\\pi W_{t1}^{2}}$"
      ],
      "text/plain": [
       "2*P_t1*a/(pi*W_t1**2)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "depth_tweezer1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4196.086090663433"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(trap.subs(E_r))/const.h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Match depth to Lauriane's paper:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P_{t1}\\left(V_1 = 15 E_r \\right) = 17729.10 \\mathrm{\\mu W}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "power = trap.subs(\n",
    "    sp.solve(\n",
    "        depth_tweezer1/E_r - 15,\n",
    "        trap.power_tweezer1,\n",
    "    )[0]\n",
    ").evalf()\n",
    "\n",
    "display(\n",
    "    Math(\n",
    "        f\"{sp.latex(trap.power_tweezer1)}\\\\left(V_1 = 15 E_r \\\\right)\"\n",
    "        f\" = {power/si.uW:.2f} \\\\mathrm{{\\\\mu W}}\"\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.365855450757438"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(trap.subs(depth_tweezer1/E_r))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate trapping frequencies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "omega_z1 = sp.sqrt(4*trap.power_tweezer1*trap.a/sp.pi**3/trap.m) * trap.wvl/trap.waist_tweezer1**3\n",
    "omega_z2 = sp.sqrt(4*trap.power_tweezer2*trap.a/sp.pi**3/trap.m) * trap.wvl/trap.waist_tweezer2**3\n",
    "\n",
    "omega_r1 = sp.sqrt(2*trap.power_tweezer1*trap.a/sp.pi/trap.m) * 2/trap.waist_tweezer1**2\n",
    "omega_r2 = sp.sqrt(2*trap.power_tweezer2*trap.a/sp.pi/trap.m) * 2/trap.waist_tweezer2**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 \\sqrt{2} \\sqrt{P_{t1}} \\sqrt{a}}{\\sqrt{\\pi} W_{t1}^{2} \\sqrt{m}}$"
      ],
      "text/plain": [
       "2*sqrt(2)*sqrt(P_t1)*sqrt(a)/(sqrt(pi)*W_t1**2*sqrt(m))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omega_r1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Match trapping frequency to Lauriane's paper:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle W_{t1}\\left(\\omega_x = 2\\pi \\cdot 29.0 \\right) = 40.87 \\mathrm{\\mu m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "waist = trap.subs(\n",
    "    sp.solve(\n",
    "        omega_r1 - 2*np.pi *29.0,\n",
    "        trap.waist_tweezer1,\n",
    "    )[0]\n",
    ").evalf()\n",
    "\n",
    "display(\n",
    "    Math(\n",
    "        f\"{sp.latex(trap.waist_tweezer1)}\\\\left(\\\\omega_x = 2\\\\pi \\\\cdot 29.0 \\\\right)\"\n",
    "        f\" = {waist/si.um:.2f} \\\\mathrm{{\\\\mu m}}\"\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "320.25388559018154"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(trap.subs(omega_r1))/(2*np.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analytically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w_0 = 134.21um\n",
      "P = 2110639.42uW\n"
     ]
    }
   ],
   "source": [
    "depth_in_Er = 15\n",
    "trap_freq = 29.0 #Hz\n",
    "\n",
    "waist_analytic = sp.sqrt(depth_in_Er /2)* const.h/trap.m/trap.distance_tweezers/(2*sp.pi*trap_freq)\n",
    "power_analytic = (2*sp.pi*trap_freq)**2 *sp.pi*trap.m*waist_analytic**4/8/trap.a \n",
    "\n",
    "print(f\"w_0 = {float(trap.subs(waist_analytic))/si.um:.2f}um\")\n",
    "print(f\"P = {float(trap.subs(power_analytic))/si.uW:.2f}uW\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Erbium ###\n",
    "\n",
    "initial_power = float(trap.subs(power_analytic))\n",
    "initial_waist = float(trap.subs(waist_analytic))\n",
    "initial_distance = 0.266*si.um\n",
    "\n",
    "trap: DoubleTweezer = DoubleTweezer(\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_tweezer1 = initial_power,     #stationary\n",
    "    power_tweezer2 = initial_power,     #transfer tweezer\n",
    "    waist_tweezer1 = initial_waist,     #stationary\n",
    "    waist_tweezer2 = initial_waist,     #transfer tweezer\n",
    "    distance_tweezers = initial_distance,\n",
    "\n",
    "    m = 168 * const.value(\"atomic mass constant\"),\n",
    "    mu_b = 6.982806* const.value(\"Bohr magneton\"),\n",
    "    a_s = 85* const.value(\"Bohr radius\"),\n",
    "    a=180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "    wvl = 532 * si.nm,\n",
    "\n",
    "    g = 0,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.000000000000009"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_r = const.h**2/(8*trap.m*trap.distance_tweezers**2)\n",
    "\n",
    "depth_tweezer1 = trap.a*2*trap.power_tweezer1/sp.pi/trap.waist_tweezer1**2\n",
    "depth_tweezer2 = trap.a*2*trap.power_tweezer2/sp.pi/trap.waist_tweezer2**2\n",
    "\n",
    "float(trap.subs(depth_tweezer1/E_r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29.00000000000001"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omega_z1 = sp.sqrt(4*trap.power_tweezer1*trap.a/sp.pi**3/trap.m) * trap.wvl/trap.waist_tweezer1**3\n",
    "omega_z2 = sp.sqrt(4*trap.power_tweezer2*trap.a/sp.pi**3/trap.m) * trap.wvl/trap.waist_tweezer2**3\n",
    "\n",
    "omega_r1 = sp.sqrt(2*trap.power_tweezer1*trap.a/sp.pi/trap.m) * 2/trap.waist_tweezer1**2\n",
    "omega_r2 = sp.sqrt(2*trap.power_tweezer2*trap.a/sp.pi/trap.m) * 2/trap.waist_tweezer2**2\n",
    "\n",
    "float(trap.subs(omega_r1))/2/np.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## See how that looks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "left_cutoff = -0.5*float(trap.subs(trap.distance_tweezers))-3*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
    "right_cutoff = 0.5*float(trap.subs(trap.distance_tweezers))+3*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
    "\n",
    "\n",
    "# Solve the hamiltonian numerically in axial direction\n",
    "energies, states, potential, coords = trap.nstationary_solution(\n",
    "    trap.x, (left_cutoff, right_cutoff), 500, k=4\n",
    ")\n",
    "\n",
    "# States that are below the potential barrier\n",
    "bound_states = energies < potential(left_cutoff)\n",
    "\n",
    "\n",
    "z_np = np.linspace(left_cutoff, right_cutoff, num=500)\n",
    "ax: plt.Axes\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.plot(z_np / si.um, potential(z_np) / const.h / si.kHz,color=\"cornflowerblue\" ,marker=\"None\")\n",
    "ax.set_title(f\"{np.sum(bound_states)} bound solutions, tweezer distance: {trap.subs(trap.distance_tweezers)/si.um}um\")\n",
    "ax.set_xlabel(r\"x ($\\mathrm{\\mu m}$)\")\n",
    "ax.set_ylabel(r\"E / h (kHz)\")\n",
    "abs_min = np.min(potential(z_np))\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",
    "    alpha=0.5,\n",
    "    color=\"cornflowerblue\"\n",
    ")\n",
    "\n",
    "count = 0\n",
    "for i, bound in enumerate(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)),\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 *1e1, marker=\"None\",label=f\"state {count}\")#, c=\"k\")\n",
    "    count += 1\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "185.24233721850484"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(trap.subs(E_r))/const.h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## This probably doesn't work, since the depth is not accurate when d is small\n",
    "\n",
    "# Let's properly estimate the depths and trapping frequencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Erbium ###\n",
    "\n",
    "initial_power = 5600* si.uW\n",
    "initial_waist = 22*si.uW\n",
    "initial_distance = 22.01*si.um\n",
    "\n",
    "trap: DoubleTweezer = DoubleTweezer(\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_tweezer1 = initial_power,     #stationary\n",
    "    power_tweezer2 = initial_power,     #transfer tweezer\n",
    "    waist_tweezer1 = initial_waist,     #stationary\n",
    "    waist_tweezer2 = initial_waist,     #transfer tweezer\n",
    "    distance_tweezers = initial_distance,\n",
    "\n",
    "    m = 168 * const.value(\"atomic mass constant\"),\n",
    "    mu_b = 6.982806* const.value(\"Bohr magneton\"),\n",
    "    a_s = 85* const.value(\"Bohr radius\"),\n",
    "    a=180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "    wvl = 532 * si.nm,\n",
    "\n",
    "    g = 0,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "left_cutoff = -0.5*float(trap.subs(trap.distance_tweezers))-3*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
    "right_cutoff = 0.5*float(trap.subs(trap.distance_tweezers))+3*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
    "\n",
    "\n",
    "# Solve the hamiltonian numerically in axial direction\n",
    "energies, states, potential, coords = trap.nstationary_solution(\n",
    "    trap.x, (left_cutoff, right_cutoff), 500, k=4\n",
    ")\n",
    "\n",
    "# States that are below the potential barrier\n",
    "bound_states = energies < potential(left_cutoff)\n",
    "\n",
    "\n",
    "z_np = np.linspace(left_cutoff, right_cutoff, num=500)\n",
    "ax: plt.Axes\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.plot(z_np / si.um, potential(z_np) / const.h / si.kHz,color=\"cornflowerblue\" ,marker=\"None\")\n",
    "ax.set_title(f\"{np.sum(bound_states)} bound solutions, tweezer distance: {trap.subs(trap.distance_tweezers)/si.um}um\")\n",
    "ax.set_xlabel(r\"x ($\\mathrm{\\mu m}$)\")\n",
    "ax.set_ylabel(r\"E / h (kHz)\")\n",
    "abs_min = np.min(potential(z_np))\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",
    "    alpha=0.5,\n",
    "    color=\"cornflowerblue\"\n",
    ")\n",
    "\n",
    "count = 0\n",
    "for i, bound in enumerate(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)),\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 *1e-3, marker=\"None\",label=f\"state {count}\")#, c=\"k\")\n",
    "    count += 1\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'x' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[4], line 20\u001b[0m\n\u001b[0;32m     17\u001b[0m V_2 \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mabs\u001b[39m(V_func(x_right) \u001b[38;5;241m-\u001b[39m V_func(\u001b[38;5;241m0\u001b[39m))\n\u001b[0;32m     19\u001b[0m \u001b[38;5;66;03m#trapping frequencies through second derivative\u001b[39;00m\n\u001b[1;32m---> 20\u001b[0m V_prime \u001b[38;5;241m=\u001b[39m sp\u001b[38;5;241m.\u001b[39mdiff(V, x)\n\u001b[0;32m     21\u001b[0m V_double_prime \u001b[38;5;241m=\u001b[39m sp\u001b[38;5;241m.\u001b[39mdiff(V_prime, x)\n\u001b[0;32m     23\u001b[0m omega_x1 \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mfloat\u001b[39m(trap\u001b[38;5;241m.\u001b[39msubs(sp\u001b[38;5;241m.\u001b[39msqrt(V_double_prime\u001b[38;5;241m.\u001b[39msubs(trap\u001b[38;5;241m.\u001b[39mx,x_left)\u001b[38;5;241m.\u001b[39msubs(trap\u001b[38;5;241m.\u001b[39my,\u001b[38;5;241m0\u001b[39m)\u001b[38;5;241m.\u001b[39msubs(trap\u001b[38;5;241m.\u001b[39mz,\u001b[38;5;241m0\u001b[39m)\u001b[38;5;241m/\u001b[39mtrap\u001b[38;5;241m.\u001b[39mm)))\n",
      "\u001b[1;31mNameError\u001b[0m: name 'x' is not defined"
     ]
    }
   ],
   "source": [
    "V = trap.subs(trap.get_potential(apply_zero_offset=False))\n",
    "a = float(trap.subs(trap.distance_tweezers))\n",
    "\n",
    "#find minima of potential\n",
    "def V_func(x):\n",
    "    return float(V.subs(trap.x,x).subs(trap.y,0).subs(trap.z,0))\n",
    "x_right = minimize_scalar(V_func,bracket=[0,a/2]).x\n",
    "x_left = minimize_scalar(V_func,bracket=[-a/2,0]).x\n",
    "\n",
    "#catch case where both potentials have already merged\n",
    "tunneling_dist = abs(x_right-x_left)\n",
    "if tunneling_dist < 1e-15:\n",
    "    raise Exception(\"potential has only one minmum\")\n",
    "\n",
    "#depts of both tweezers\n",
    "V_1 = abs(V_func(x_left) - V_func(0))\n",
    "V_2 = abs(V_func(x_right) - V_func(0))\n",
    "\n",
    "#trapping frequencies through second derivative\n",
    "V_prime = sp.diff(V, x)\n",
    "V_double_prime = sp.diff(V_prime, x)\n",
    "\n",
    "omega_x1 = float(trap.subs(sp.sqrt(V_double_prime.subs(trap.x,x_left).subs(trap.y,0).subs(trap.z,0)/trap.m)))\n",
    "omega_x2 = float(trap.subs(sp.sqrt(V_double_prime.subs(trap.x,x_right).subs(trap.y,0).subs(trap.z,0)/trap.m)))\n",
    "\n",
    "#recoil energy\n",
    "E_r = const.h**2/(8*trap.m*trap.distance_tweezers**2)\n",
    "\n",
    "#print results\n",
    "print(f\"depth: {V_2/float(trap.subs(E_r)):.2f} E_r\")\n",
    "print(f\"trapping frequency: {omega_x1/2/np.pi:.2f} Hz\")\n",
    "print(f\"tunneling distance: {tunneling_dist/si.nm:.2f} um\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### It seems that the desired parameters are not realisable with the tweezer potential\n",
    "\n",
    "## Let's try to implement a lattice potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Erbium ###\n",
    "\n",
    "initial_spacing = 0\n",
    "initial_depth = 0\n",
    "\n",
    "\n",
    "trap: TwoSiteLattice = TwoSiteLattice(\n",
    "\n",
    "    lattice_depth = initial_depth,\n",
    "    lattice_spacing = initial_spacing,\n",
    "\n",
    "\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 = 0,\n",
    "    waist_tweezer = 0,\n",
    "\n",
    "    m = 168 * const.value(\"atomic mass constant\"),\n",
    "    mu_b = 6.982806* const.value(\"Bohr magneton\"),\n",
    "    a_s = 137* const.value(\"Bohr radius\"),\n",
    "    a = 180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "    wvl = 532 * si.nm,\n",
    "\n",
    "    g = 0,\n",
    ")\n",
    "\n",
    "E_r = const.h**2/(2*trap.m*trap.lattice_spacing**2)\n",
    "\n",
    "trap[trap.lattice_depth] = 15*E_r\n",
    "#lattice spacing is double the actual distance between sites\n",
    "trap[trap.lattice_spacing] = trap.wvl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "left_cutoff = -1.3*0.5*float(trap.subs(trap.lattice_spacing))\n",
    "right_cutoff = 1.3*0.5*float(trap.subs(trap.lattice_spacing))\n",
    "\n",
    "\n",
    "# Solve the hamiltonian numerically in axial direction\n",
    "energies, states, potential, coords = trap.nstationary_solution(\n",
    "    trap.x, (left_cutoff, right_cutoff), 500, k=4\n",
    ")\n",
    "\n",
    "# States that are below the potential barrier\n",
    "#bound_states = energies < potential(left_cutoff)\n",
    "bound_states = energies < np.inf\n",
    "\n",
    "z_np = np.linspace(left_cutoff, right_cutoff, num=500)\n",
    "ax: plt.Axes\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.plot(z_np / si.um, potential(z_np) / const.h / si.kHz,color=\"cornflowerblue\" ,marker=\"None\")\n",
    "ax.set_title(f\"{np.sum(bound_states)} bound solutions, tweezer distance: {trap.subs(trap.lattice_spacing)/si.um}um\")\n",
    "ax.set_xlabel(r\"x ($\\mathrm{\\mu m}$)\")\n",
    "ax.set_ylabel(r\"E / h (kHz)\")\n",
    "abs_min = np.min(potential(z_np))\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",
    "    alpha=0.5,\n",
    "    color=\"cornflowerblue\"\n",
    ")\n",
    "\n",
    "count = 0\n",
    "for i, bound in enumerate(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)),\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 *1e2, marker=\"None\",label=f\"state {count}\")#, c=\"k\")\n",
    "    count += 1\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "depth: 15.00 E_r\n",
      "trapping frequency x: 32502.74 Hz\n",
      "trapping frequency y: 32502.74 Hz\n",
      "trapping frequency z: 32502.74 Hz\n",
      "aspect ratio: 1.00\n",
      "tunneling distance: 266.00 um\n"
     ]
    }
   ],
   "source": [
    "V = trap.subs(trap.get_potential(apply_zero_offset=False))\n",
    "a = float(trap.subs(trap.lattice_spacing))\n",
    "\n",
    "#find minima of potential\n",
    "def V_func(x):\n",
    "    return float(V.subs({trap.x:x, trap.y:0, trap.z:0}))\n",
    "#x_right = minimize_scalar(V_func,bracket=[1e-3*a,a/2],bounds=[0,a/2]).x\n",
    "#x_left = minimize_scalar(V_func,bracket=[-a/2,-1e-3*a],bounds=[-a/2,0]).x\n",
    "x_right = a/4\n",
    "x_left = -a/4\n",
    "\n",
    "#catch case where both potentials have already merged\n",
    "tunneling_dist = abs(x_right-x_left)\n",
    "if tunneling_dist < 1e-15:\n",
    "    raise Exception(\"potential has only one minmum\")\n",
    "\n",
    "#depts of both tweezers\n",
    "V_1 = abs(V_func(x_left) - V_func(0))\n",
    "V_2 = abs(V_func(x_right) - V_func(0)) \n",
    "\n",
    "#trapping frequencies through second derivative\n",
    "#trapping frequencies through second derivative\n",
    "V_double_prime_x = sp.diff(V, trap.x, 2)\n",
    "omega_x1 = float(trap.subs(sp.sqrt(V_double_prime_x.subs({trap.x:x_left, trap.y:0, trap.z:0})/trap.m)))\n",
    "omega_x2 = float(trap.subs(sp.sqrt(V_double_prime_x.subs({trap.x:x_right, trap.y:0, trap.z:0})/trap.m)))\n",
    "\n",
    "V_double_prime_y = sp.diff(V, trap.y, 2)\n",
    "omega_y1 = float(trap.subs(sp.sqrt(V_double_prime_y.subs({trap.x:x_left, trap.y:0, trap.z:0})/trap.m)))\n",
    "omega_y2 = float(trap.subs(sp.sqrt(V_double_prime_y.subs({trap.x:x_right, trap.y:0, trap.z:0})/trap.m)))\n",
    "\n",
    "V_double_prime_z = sp.diff(V, trap.z, 2)\n",
    "omega_z1 = float(trap.subs(sp.sqrt(V_double_prime_z.subs({trap.x:x_left, trap.y:0, trap.z:0})/trap.m)))\n",
    "omega_z2 = float(trap.subs(sp.sqrt(V_double_prime_z.subs({trap.x:x_right, trap.y:0, trap.z:0})/trap.m)))\n",
    "\n",
    "#recoil energy\n",
    "E_r = const.h**2/(2*trap.m*trap.lattice_spacing**2)\n",
    "\n",
    "#print results\n",
    "print(f\"depth: {V_2/float(trap.subs(E_r)):.2f} E_r\")\n",
    "\n",
    "print(f\"trapping frequency x: {omega_x1/2/np.pi:.2f} Hz\")\n",
    "print(f\"trapping frequency y: {omega_y1/2/np.pi:.2f} Hz\")\n",
    "print(f\"trapping frequency z: {omega_z1/2/np.pi:.2f} Hz\")\n",
    "\n",
    "print(f\"aspect ratio: {omega_x1/omega_z1:.2f}\")\n",
    "\n",
    "print(f\"tunneling distance: {tunneling_dist/si.nm:.2f} um\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now do diagonalisation for this potential:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "files saved with ...._2025-03-26_15-58-59\n"
     ]
    }
   ],
   "source": [
    "n_grid_1D = 50\n",
    "\n",
    "n_pot_steps = [n_grid_1D,n_grid_1D,n_grid_1D]\n",
    "n_levels = 8\n",
    "\n",
    "left_cutoff = -0.5*float(trap.subs(trap.lattice_spacing))*1.3\n",
    "right_cutoff = 0.5*float(trap.subs(trap.lattice_spacing))*1.3\n",
    "back_cutoff = -0.25*float(trap.subs(trap.lattice_spacing))*1.3\n",
    "front_cutoff = 0.25*float(trap.subs(trap.lattice_spacing))*1.3\n",
    "bottom_cutoff = -0.5*float(trap.subs(trap.lattice_spacing))*1.7\n",
    "top_cutoff = 0.5*float(trap.subs(trap.lattice_spacing))*1.7\n",
    "\n",
    "extend = [(left_cutoff,right_cutoff),\n",
    "          (back_cutoff,front_cutoff),\n",
    "          (bottom_cutoff,top_cutoff)]\n",
    "\n",
    "\n",
    "# Solve the hamiltonian numerically\n",
    "energies, states, potential, coords = trap.nstationary_solution(\n",
    "        [trap.x,trap.y,trap.z], extend, n_pot_steps, k=n_levels,\n",
    "        method=\"matrix_free\", export=True)\n",
    "\n",
    "\n",
    "x = coords[trap.x]\n",
    "y = coords[trap.y]\n",
    "z = coords[trap.z]\n",
    "x3D,y3D,z3D = np.meshgrid(coords[trap.x],coords[trap.y],coords[trap.z],indexing=\"ij\")\n",
    "pot = potential(x3D,y3D,z3D)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from boson_helpers import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "________________________________________________________________\n",
      "d = 266.00nm\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "J = 27.481287 Hz\n",
      "U_s = 2607.617 Hz\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(25,26):\n",
    "\n",
    "    trap, func_ham, res =  import_results(i)\n",
    "\n",
    "    print(\"________________________________________________________________\")\n",
    "    print(f\"d = {float(trap.subs(trap.lattice_spacing)/2) /si.nm :.2f}nm\")\n",
    "\n",
    "    GS_left, GS_right = get_localised_GS(res[\"states\"][0], res[\"states\"][1])\n",
    "    \n",
    "    plt.plot(res[\"x\"],np.abs(GS_left[:,int(res[\"size\"][1]/2),int(res[\"size\"][2]/2)])**2, label=\"left state\")\n",
    "    plt.plot(res[\"x\"],np.abs(GS_right[:,int(res[\"size\"][1]/2),int(res[\"size\"][2]/2)])**2, label=\"right state\")\n",
    "\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(r\"$|\\Psi|^2$\")\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "    J, U_s, U_dds, angles, V_lrs = analyse_diagonalisation(i)\n",
    "\n",
    "    print(f\"J = {J/const.h :3f} Hz\")\n",
    "    print(f\"U_s = {U_s/const.h :.3f} Hz\")\n",
    "\n",
    "    plt.plot(np.rad2deg(angles), U_dds/const.h)\n",
    "\n",
    "    plt.axhline(0,color=\"black\",ls=\"--\")\n",
    "\n",
    "    plt.xlabel(\"theta [deg]\")\n",
    "    plt.ylabel(r\"$U_{dd} / h$ [Hz]\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2666.67x500 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_states = 8\n",
    "\n",
    "states_plot = res[\"states\"].real\n",
    "#states_plot = np.angle(states)\n",
    "#states_plot = states.imag\n",
    "#states_plot = np.abs(states)**2\n",
    "\n",
    "# Create a 1xn_states grid of subplots (1 row, n_states columns)\n",
    "fig, axes = plt.subplots(1, n_states, figsize=(20/6*n_states, 5))  # Adjust the size as needed\n",
    "\n",
    "# Loop over the state numbers from 0 to n_states-1\n",
    "for state_number, ax in zip(range(n_states), axes):\n",
    "    # Slice through the y-direction and rotate the x-z plane (by swapping x and z)\n",
    "    im = ax.imshow(states_plot[state_number, :, int(res[\"size\"][1]/2), :].T,\n",
    "                   extent=[*res[\"extend\"][0], *res[\"extend\"][2]], origin=\"lower\",\n",
    "                   vmin=np.min(states_plot[state_number]), vmax=np.max(states_plot[state_number]))\n",
    "\n",
    "    # Set labels for each subplot\n",
    "    ax.set_xlabel(\"x\")\n",
    "    ax.set_ylabel(\"z\")\n",
    "    ax.set_title(f\"State {state_number}\")\n",
    "    fig.colorbar(im, ax=ax)  \n",
    "\n",
    "# Adjust layout for better spacing\n",
    "plt.tight_layout()\n",
    "\n",
    "# Show the plots\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 666.667x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_states = 2\n",
    "\n",
    "states_plot = [GS_left.real, GS_right.real]\n",
    "#states_plot = np.angle(states)\n",
    "#states_plot = states.imag\n",
    "#states_plot = np.abs(states)**2\n",
    "\n",
    "# Create a 1xn_states grid of subplots (1 row, n_states columns)\n",
    "fig, axes = plt.subplots(1, n_states, figsize=(20/6*n_states, 5))  # Adjust the size as needed\n",
    "\n",
    "# Loop over the state numbers from 0 to n_states-1\n",
    "for state_number, ax in zip(range(n_states), axes):\n",
    "    # Slice through the y-direction and rotate the x-z plane (by swapping x and z)\n",
    "    im = ax.imshow(states_plot[state_number][:, int(res[\"size\"][1]/2), :].T,\n",
    "                   extent=[*res[\"extend\"][0], *res[\"extend\"][2]], origin=\"lower\",\n",
    "                   vmin=np.min(states_plot[state_number]), vmax=np.max(states_plot[state_number]))\n",
    "\n",
    "    # Set labels for each subplot\n",
    "    ax.set_xlabel(\"x\")\n",
    "    ax.set_ylabel(\"z\")\n",
    "    ax.set_title(f\"State {state_number}\")\n",
    "    fig.colorbar(im, ax=ax)  \n",
    "\n",
    "# Adjust layout for better spacing\n",
    "plt.tight_layout()\n",
    "\n",
    "# Show the plots\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 666.667x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_states = 2\n",
    "\n",
    "states_plot = [GS_left.real, GS_right.real]\n",
    "#states_plot = np.angle(states)\n",
    "#states_plot = states.imag\n",
    "#states_plot = np.abs(states)**2\n",
    "\n",
    "# Create a 1xn_states grid of subplots (1 row, n_states columns)\n",
    "fig, axes = plt.subplots(1, n_states, figsize=(20/6*n_states, 5))  # Adjust the size as needed\n",
    "\n",
    "# Loop over the state numbers from 0 to n_states-1\n",
    "for state_number, ax in zip(range(n_states), axes):\n",
    "    # Slice through the y-direction and rotate the x-z plane (by swapping x and z)\n",
    "    im = ax.imshow(states_plot[state_number][:, :, int(res[\"size\"][2]/2)].T,\n",
    "                   extent=[*res[\"extend\"][0], *res[\"extend\"][1]], origin=\"lower\",\n",
    "                   vmin=np.min(states_plot[state_number]), vmax=np.max(states_plot[state_number]))\n",
    "\n",
    "    # Set labels for each subplot\n",
    "    ax.set_xlabel(\"x\")\n",
    "    ax.set_ylabel(\"y\")\n",
    "    ax.set_title(f\"State {state_number}\")\n",
    "    fig.colorbar(im, ax=ax)  \n",
    "\n",
    "# Adjust layout for better spacing\n",
    "plt.tight_layout()\n",
    "\n",
    "# Show the plots\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}