LennartNaeve_code/merging_tweezer_code/bosons/2025_03_19 (second try J,U).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Try again to calculate J and U. This time use functional Hamiltonian since that is used for diagonalisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "from IPython.display import Math, display\n",
    "from scipy import constants as const\n",
    "from scipy import sparse\n",
    "from scipy.fft import fftn, ifftn, fftfreq\n",
    "from scipy.optimize import root_scalar\n",
    "import pickle\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 trap_numerics import functional_hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "line_number = 7 # line of file in overview.txt\n",
    "\n",
    "with open(\"data/overview.txt\", \"r\") as file:\n",
    "    for current_line_number, line in enumerate(file, start=1):\n",
    "        if current_line_number == line_number:\n",
    "            timecode = line[:19]  # Get the first 19 characters\n",
    "            break  # Stop reading once we get the desired line\n",
    "\n",
    "data = np.load(f\"data/{timecode}_results.npz\",allow_pickle=True)\n",
    "for key in data.keys():\n",
    "    globals()[key] = data[key]\n",
    "\n",
    "with open(f\"data/{timecode}_trap.npz\", 'rb') as file:\n",
    "    trap = pickle.load(file)\n",
    "\n",
    "ham = sparse.load_npz(f\"data/{timecode}_hamiltonian.npz\")\n",
    "func_ham = functional_hamiltonian(dvol,pot,float(trap.subs(trap.m)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "omega_r1: 7331.9Hz, omega_r2: 7331.9Hz\n",
      "omega_z1: 418.1Hz, omega_z2: 418.1Hz\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 17.54$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 17.54$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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",
    "print(f\"omega_r1: {float(trap.subs(omega_r1)):.1f}Hz, omega_r2: {float(trap.subs(omega_r2)):.1f}Hz\")\n",
    "print(f\"omega_z1: {float(trap.subs(omega_z1)):.1f}Hz, omega_z2: {float(trap.subs(omega_z2)):.1f}Hz\")\n",
    "\n",
    "aspect_ratio1 = omega_r1 / omega_z1\n",
    "_aspect_ratio1_latex = sp.latex(trap.omega_r_tweezer / trap.omega_ax_tweezer)\n",
    "display(Math(f\"{_aspect_ratio1_latex} \\\\approx {trap.subs(aspect_ratio1).evalf():.2f}\"))\n",
    "\n",
    "aspect_ratio2 = omega_r2 / omega_z2\n",
    "_aspect_ratio2_latex = sp.latex(trap.omega_r_tweezer / trap.omega_ax_tweezer)\n",
    "display(Math(f\"{_aspect_ratio2_latex} \\\\approx {trap.subs(aspect_ratio2).evalf():.2f}\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Turn state vector into real space wavefunction by adjusting normalisation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999993"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.abs(states[0]**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dV = np.prod(dvol)\n",
    "\n",
    "states_r = states/ np.sqrt(dV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999993"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.abs(states_r[0]**2))*dV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check how diagonalisation looks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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 = 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(len(y)/2), :].T,\n",
    "                   extent=[*extend[0], *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": "markdown",
   "metadata": {},
   "source": [
    "Find localised wave functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#rotate resulting wavefunctions into symmetric and anti-symm. states \n",
    "def f(alpha):\n",
    "\n",
    "    state_S1 = np.cos(alpha) * states[0].real + np.sin(alpha)* states[1].real\n",
    "    state_S1 /= np.sqrt(np.sum(np.abs(state_S1)**2))\n",
    "\n",
    "    state_A1 = np.sin(alpha) * states[0].real - np.cos(alpha)* states[1].real\n",
    "    state_A1 /= np.sqrt(np.sum(np.abs(state_A1)**2))\n",
    "\n",
    "    return np.sum(state_S1[int(len(x)/2):]) - np.sum(state_S1[:int(len(x)/2)])\n",
    "\n",
    "#find optimal angle\n",
    "# alpha = minimize_scalar(f,bounds=(-2*np.pi, 2*np.pi+0.1)).x\n",
    "alpha = root_scalar(f, x0=0).root\n",
    "\n",
    "state_S1 = np.cos(alpha) * states[0].real + np.sin(alpha)* states[1].real\n",
    "state_S1 /= np.sqrt(np.sum(np.abs(state_S1)**2))\n",
    "\n",
    "state_A1 = np.sin(alpha) * states[0].real - np.cos(alpha)* states[1].real\n",
    "state_A1 /= np.sqrt(np.sum(np.abs(state_A1)**2))\n",
    "\n",
    "#then transform to localised wavefunctions\n",
    "GS_LR1 = (state_S1 + state_A1)/np.sqrt(2)\n",
    "GS_LR2 = (state_S1 - state_A1)/np.sqrt(2)\n",
    "\n",
    "#asign left and right\n",
    "if abs(np.sum(GS_LR1[int(len(x)/2):])) < abs(np.sum(GS_LR1[:int(len(x)/2)])):\n",
    "    GS_left = GS_LR1\n",
    "    GS_right = GS_LR2\n",
    "else:\n",
    "    GS_left = GS_LR2\n",
    "    GS_right = GS_LR1"
   ]
  },
  {
   "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(len(y)/2), :].T,\n",
    "                   extent=[*extend[0], *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": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "state_number = 0\n",
    "phase_mult0 = 1\n",
    "\n",
    "plt.plot(x,(phase_mult0*GS_left[:,int(len(y)/2),int(len(z)/2)]).real, label=\"real part\")\n",
    "plt.plot(x,(phase_mult0*GS_left[:,int(len(y)/2),int(len(z)/2)]).imag, label=\"imaginary part\")\n",
    "#plt.plot(x,pot[:,int(len(y)/2),int(len(z)/2)], label=\"potential (rescaled)\")\n",
    "plt.legend()\n",
    "\n",
    "state_number = 1\n",
    "phase_mult1 = 1\n",
    "\n",
    "plt.plot(x,(phase_mult1*GS_right[:,int(len(y)/2),int(len(z)/2)]).real, label=\"real part\")\n",
    "plt.plot(x,(phase_mult1*GS_right[:,int(len(y)/2),int(len(z)/2)]).imag, label=\"imaginary part\")\n",
    "#plt.plot(x,pot[:,int(len(y)/2),int(len(z)/2)], label=\"potential (rescaled)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate parameters:\n",
    "\n",
    "### Start with contact interactions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999993379817"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#make sure we're working with state vector\n",
    "np.sum(np.abs(GS_left)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U_s = 3.2123021180831275 Hz\n"
     ]
    }
   ],
   "source": [
    "#scattering length\n",
    "a_s = 85* const.physical_constants[\"Bohr radius\"][0]\n",
    "\n",
    "#calculate integral over psi^4 (divide by sqrt(dV) to convert to wavefunction)\n",
    "U_s = np.sum(np.abs(GS_left/np.sqrt(dV))**4)*dV\n",
    "U_s *= 4*np.pi*const.hbar**2*a_s/float(trap.subs(trap.m))\n",
    "\n",
    "print(f\"U_s = {U_s/const.h} Hz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Then do single-particle hopping:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999993379817"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#make sure we're working with state vector\n",
    "np.sum(np.abs(GS_left)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "J = 0.9876660072698075 Hz\n"
     ]
    }
   ],
   "source": [
    "#call Hamiltonian on one side\n",
    "H_psi = np.reshape(func_ham(np.reshape(GS_right, -1)), size)\n",
    "\n",
    "#calculate integral\n",
    "J = -(np.sum(GS_left.conj()/np.sqrt(dV)* H_psi/np.sqrt(dV))*dV)\n",
    "\n",
    "#check imaginary part of result (should vanish)\n",
    "if abs(J.real/J.imag) < 10:\n",
    "    raise Exception(f\"imaginary part of J too big: J = {J}\")\n",
    "else:\n",
    "    J = J.real\n",
    "\n",
    "print(f\"J = {J/const.h} Hz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finally dipole interactions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "angles= np.deg2rad(np.linspace(0,90))\n",
    "U_dds = np.zeros_like(angles, dtype=complex)\n",
    "\n",
    "for i, theta in enumerate(angles):\n",
    "    #compute dipolar interactions using fourier transform\n",
    "\n",
    "    #direction of polarisation (B-field) [x,y,z]\n",
    "    #theta = np.deg2rad(0)\n",
    "    pol =np.array([np.sin(theta),0,np.cos(theta)])\n",
    "\n",
    "    #density\n",
    "    rho = np.abs(GS_left/np.sqrt(dV))**2\n",
    "    # Compute Fourier transform of density\n",
    "    rho_k = fftn(rho)\n",
    "\n",
    "    #set up fourier space\n",
    "    kx = 2*np.pi*fftfreq(size[0], dvol[0])\n",
    "    ky = 2*np.pi*fftfreq(size[1], dvol[1])\n",
    "    kz = 2*np.pi*fftfreq(size[2], dvol[2])\n",
    "    KX, KY, KZ = np.meshgrid(kx, ky, kz, indexing='ij')\n",
    "    K2 = KX**2 + KY**2 + KZ**2\n",
    "    K2[K2 == 0] = np.inf  # Avoid division by zero\n",
    "\n",
    "    # Compute dipolar interaction kernel in Fourier space\n",
    "    V_k = (-1 + 3* (pol[0]*KX + pol[1]*KY + pol[2]*KZ)**2 / K2) /3\n",
    "\n",
    "    # Compute convolution in Fourier space\n",
    "    U_dd_k = V_k * rho_k\n",
    "\n",
    "    # Transform back to real space\n",
    "    U_dd_real = ifftn(U_dd_k)\n",
    "\n",
    "    # Integrate\n",
    "    U_dd = (np.sum(U_dd_real*rho) * dV) \n",
    "    #multiply by prefactor C_dd\n",
    "    U_dd *= const.mu_0*float(trap.subs(trap.mu_b))**2\n",
    "\n",
    "    #check imaginary part of result (should vanish)\n",
    "    if abs(U_dd.real/U_dd.imag) < 10:\n",
    "        raise Exception(f\"imaginary part of U_dd too big: U_dd = {U_dd}\")\n",
    "    else:\n",
    "        U_dd = U_dd.real\n",
    "\n",
    "    U_dds[i] = U_dd\n",
    "    #print(f\"U_dd = {U_dd/const.h} Hz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.rad2deg(angles), U_dds.real/const.h)\n",
    "#plt.plot(angles, U_dds.imag/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": "markdown",
   "metadata": {},
   "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
}