{
 "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 import sparse\n",
    "from scipy.optimize import minimize_scalar\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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trap parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "omega_r1: 2169.9Hz, omega_r2: 2169.9Hz\n",
      "omega_z1: 472.4Hz, omega_z2: 472.4Hz\n"
     ]
    }
   ],
   "source": [
    "initial_power = 50* si.uW\n",
    "initial_waist = 1.1*si.uW\n",
    "initial_distance = 0.808*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= 161 * const.value(\"atomic mass constant\"),\n",
    "    a_s= 85* const.value(\"Bohr radius\"),\n",
    "    mu_b= 9.93 * const.value(\"Bohr magneton\" ),\n",
    "    a= 184*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "    wvl = 1064 * si.nm,\n",
    "\n",
    "    g = 0,\n",
    ")\n",
    "\n",
    "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",
    "print(f\"omega_r1: {float(trap.subs(omega_r1)/2/np.pi):.1f}Hz, omega_r2: {float(trap.subs(omega_r2)/2/np.pi):.1f}Hz\")\n",
    "print(f\"omega_z1: {float(trap.subs(omega_z1)/2/np.pi):.1f}Hz, omega_z2: {float(trap.subs(omega_z2)/2/np.pi):.1f}Hz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "depth 1: 0.2778 Hz\n",
      "depth 2: 0.2778 Hz\n",
      "target trap frequency x: 3000.00 HZ\n",
      "trapping frequency x 1: 1061.62 Hz\n",
      "trapping frequency x 2: 1061.62 Hz\n",
      "trapping frequency y 1: 3387.98 Hz\n",
      "trapping frequency y 2: 3387.98 Hz\n",
      "trapping frequency z 1: 546.57 Hz\n",
      "trapping frequency z 2: 546.57 Hz\n",
      "harmonic oscillator length x: 243.18 nm\n",
      "harmonic oscillator length z: 338.91 nm\n",
      "tunneling distance: 0.00 nm\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1800x500 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "depth 1: 2012.3643 Hz\n",
      "depth 2: 2086.0124 Hz\n",
      "target trap frequency x: 3000.00 HZ\n",
      "trapping frequency x 1: 2022.19 Hz\n",
      "trapping frequency x 2: 2022.19 Hz\n",
      "trapping frequency y 1: 3149.18 Hz\n",
      "trapping frequency y 2: 3149.18 Hz\n",
      "trapping frequency z 1: 576.15 Hz\n",
      "trapping frequency z 2: 576.15 Hz\n",
      "harmonic oscillator length x: 176.20 nm\n",
      "harmonic oscillator length z: 330.10 nm\n",
      "tunneling distance: 916.91 nm\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x500 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "depth 1: 8370.8575 Hz\n",
      "depth 2: 8284.3949 Hz\n",
      "target trap frequency x: 3000.00 HZ\n",
      "trapping frequency x 1: 2619.39 Hz\n",
      "trapping frequency x 2: 2619.39 Hz\n",
      "trapping frequency y 1: 3056.76 Hz\n",
      "trapping frequency y 2: 3056.76 Hz\n",
      "trapping frequency z 1: 619.72 Hz\n",
      "trapping frequency z 2: 619.72 Hz\n",
      "harmonic oscillator length x: 154.81 nm\n",
      "harmonic oscillator length z: 318.28 nm\n",
      "tunneling distance: 1328.43 nm\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x500 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "#define trap frequencies to look at\n",
    "trap_freqs = np.array([3*si.kHz])*2*np.pi\n",
    "#find good separation for all frequencies\n",
    "\n",
    "#calculate corresponding power\n",
    "trap_powers = np.zeros_like(trap_freqs)\n",
    "for i, freq in enumerate(trap_freqs):\n",
    "    trap_powers[i] = float(trap.subs(trap.m*trap.waist_tweezer1**4*sp.pi*freq**2/8/trap.a))\n",
    "    harm_osc_len_est = float(trap.subs(sp.sqrt(const.hbar/trap.m/freq)))\n",
    "\n",
    "    trap[trap.power_tweezer1] = trap_powers[i]\n",
    "    trap[trap.power_tweezer2] = trap_powers[i]\n",
    "    \n",
    "    dist0 = float(trap.subs(trap.waist_tweezer1)) + harm_osc_len_est\n",
    "    trap_spacings = np.linspace(dist0 -200*si.nm, dist0 +200*si.nm, 3)\n",
    "    #loop over distances\n",
    "    for j, dist in enumerate(trap_spacings):\n",
    "\n",
    "        trap[trap.distance_tweezers] = dist\n",
    "\n",
    "        \n",
    "        ##################\n",
    "        #print trap parameters\n",
    "        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, trap.y:0, trap.z:0}))\n",
    "\n",
    "        x_right = minimize_scalar(V_func,bracket=[0,a]).x\n",
    "        x_left = minimize_scalar(V_func,bracket=[-a,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",
    "            continue\n",
    "            #raise Exception(\"potential has only one minimum\")\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\n",
    "        omega_x1, omega_x2 = trap.get_both_omega(trap.x)\n",
    "        omega_y1, omega_y2 = trap.get_both_omega(trap.y)\n",
    "        omega_z1, omega_z2 = trap.get_both_omega(trap.z)\n",
    "\n",
    "        harm_osc_len_x = float(trap.subs(sp.sqrt(const.hbar/trap.m/omega_x1)))\n",
    "        harm_osc_len_z = float(trap.subs(sp.sqrt(const.hbar/trap.m/omega_z1)))\n",
    "\n",
    "        #print results\n",
    "        print(f\"depth 1: {V_1/const.h:.4f} Hz\")\n",
    "        print(f\"depth 2: {V_2/const.h:.4f} Hz\")\n",
    "        #print(f\"estimated tilt: {abs(V_1 - V_2)/const.h:.2f} Hz\")\n",
    "\n",
    "        print(f\"target trap frequency x: {freq/2/np.pi:.2f} HZ\")\n",
    "        print(f\"trapping frequency x 1: {trap.subs(omega_x1)/2/np.pi:.2f} Hz\")\n",
    "        print(f\"trapping frequency x 2: {trap.subs(omega_x2)/2/np.pi:.2f} Hz\")\n",
    "        print(f\"trapping frequency y 1: {trap.subs(omega_y1)/2/np.pi:.2f} Hz\")\n",
    "        print(f\"trapping frequency y 2: {trap.subs(omega_y2)/2/np.pi:.2f} Hz\")\n",
    "        print(f\"trapping frequency z 1: {trap.subs(omega_z1)/2/np.pi:.2f} Hz\")\n",
    "        print(f\"trapping frequency z 2: {trap.subs(omega_z2)/2/np.pi:.2f} Hz\")\n",
    "\n",
    "        print(f\"harmonic oscillator length x: {harm_osc_len_x/si.nm:.2f} nm\")\n",
    "        print(f\"harmonic oscillator length z: {harm_osc_len_z/si.nm:.2f} nm\")\n",
    "        print(f\"tunneling distance: {tunneling_dist/si.nm:.2f} nm\")\n",
    "\n",
    "        #############\n",
    "        #test 3D diag\n",
    "\n",
    "        n_grid_1D = 25  \n",
    "\n",
    "        n_pot_steps = [n_grid_1D,n_grid_1D,n_grid_1D]\n",
    "        n_levels = 6\n",
    "\n",
    "        left_cutoff = -0.5*tunneling_dist-5*harm_osc_len_x\n",
    "        right_cutoff = 0.5*tunneling_dist+5*harm_osc_len_x\n",
    "        back_cutoff = -5*harm_osc_len_x\n",
    "        front_cutoff = 5*harm_osc_len_x\n",
    "        bottom_cutoff = -5*harm_osc_len_z\n",
    "        top_cutoff = 5*harm_osc_len_z\n",
    "\n",
    "        extend = [(left_cutoff,right_cutoff),\n",
    "                (back_cutoff,front_cutoff),\n",
    "                (bottom_cutoff,top_cutoff)]\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=False)\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",
    "\n",
    "        n_states = 6\n",
    "\n",
    "        # Create a 1xn_states grid of subplots (1 row, n_states columns)\n",
    "        fig, axes = plt.subplots(1, n_states, figsize=(18/6*n_states, 5))  # Adjust the size as needed\n",
    "\n",
    "        # Loop over the state numbers from 0 to 5\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(np.abs(states[state_number, :, int(len(y)/2), :].T)**2, extent=[*extend[0], *extend[2]], origin=\"lower\",\n",
    "                        vmin=np.min(np.abs(states[state_number])**2), vmax=np.max(np.abs(states[state_number])**2))\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",
    "\n",
    "        print(\"_________________________________________________________________\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.04466052, 1.24466052, 1.44466052])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trap_spacings/si.uW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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