LennartNaeve_code/merging_tweezer_code/bosons/2025_03_21 (outsourcing calc J,U).ipynb
2025-04-25 20:52:11 +02:00

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{
"cells": [
{
"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\n",
"from boson_helpers import *"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"trap, ham, res = import_results(9)\n",
"\n",
"globals().update(res)"
]
},
{
"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": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"GS_left, GS_right = get_localised_GS(states[0],states[1])"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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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": 6,
"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 J, U_s, U_dd, U:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"J = 0.0009612848724873431\n"
]
}
],
"source": [
"print(f\"J = {get_J(GS_left, GS_right, ham, dvol)/const.h}\")"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"U_s = 3.849482910362117\n"
]
}
],
"source": [
"#scattering length\n",
"a_s = 85* const.physical_constants[\"Bohr radius\"][0]\n",
"#mass\n",
"mass = float(trap.subs(trap.m))\n",
"\n",
"print(f\"U_s = {get_U_s(trap, GS_left, dvol)/const.h}\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#magnetic moment\n",
"mu = float(trap.subs(trap.mu_b))\n",
"\n",
"#polarisation\n",
"angles= np.deg2rad(np.linspace(0,90))\n",
"U_dds = np.zeros_like(angles)\n",
"polarisations = np.zeros((len(angles),3))\n",
"polarisations[:,0] = np.sin(angles)\n",
"polarisations[:,2] = np.cos(angles)\n",
"\n",
"for i, pol in enumerate(polarisations):\n",
" trap[trap.B_x] = pol[0]\n",
" trap[trap.B_y] = pol[1]\n",
" trap[trap.B_z] = pol[2]\n",
"\n",
" U_dds[i] = get_U_dd(trap, GS_left, dvol)\n",
"\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": 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
}