LennartNaeve_code/merging_tweezer_code/bosons/2025_03_26 (extended parameters).ipynb
2025-04-25 20:52:11 +02:00

371 lines
210 KiB
Plaintext

{
"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\n",
"from boson_helpers import *"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"line_number_1 = 45 #for AR=1\n",
"state0_1 = 0\n",
"state1_1 = 1\n",
"\n",
"line_number_2 = 46 #for AR=2\n",
"state0_2 = 0\n",
"state1_2 = 1"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"AR=1:\n",
"J = h* 27.481287 Hz\n",
"U_s = h* 3748.210 Hz\n",
"\n",
"\n",
"AR=2:\n",
"J = h* 27.481287 Hz\n",
"U_s = h* 1774.199 Hz\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 500x900 with 3 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#import data for AR=1\n",
"trap, func_ham, res = import_results(line_number_1)\n",
"GS_left_1, GS_right_1 = get_localised_GS(res[\"states\"][state0_1], res[\"states\"][state1_1])\n",
"\n",
"J_1, U_s_1, U_dds_1, angles_1, V_lrs_1, DeltaJs_1 = analyse_diagonalisation(line_number_1,\n",
" state_nr0=state0_1,\n",
" state_nr1=state1_1)\n",
"print(\"AR=1:\")\n",
"print(f\"J = h* {J_1/const.h :3f} Hz\")\n",
"print(f\"U_s = h* {U_s_1/const.h :.3f} Hz\")\n",
"\n",
"#omega_left, omega_right = trap.get_both_omega(trap.x)\n",
"#print(f\"omega_x = 2pi* {float(trap.subs(omega_left))/2/np.pi:.2f}Hz\")\n",
"#omega_left, omega_right = trap.get_both_omega(trap.z)\n",
"#print(f\"omega_z = 2pi* {float(trap.subs(omega_left))/2/np.pi:.2f}Hz\")\n",
"\n",
"print(\"\\n\")\n",
"\n",
"#import data for AR=2\n",
"trap, func_ham, res = import_results(line_number_2)\n",
"GS_left_2, GS_right_2 = get_localised_GS(res[\"states\"][state0_2], res[\"states\"][state1_2])\n",
"\n",
"J_2, U_s_2, U_dds_2, angles_2, V_lrs_2, DeltaJs_2 = analyse_diagonalisation(line_number_2,\n",
" state_nr0=state0_2,\n",
" state_nr1=state1_2)\n",
"print(\"AR=2:\")\n",
"print(f\"J = h* {J_2/const.h :3f} Hz\")\n",
"print(f\"U_s = h* {U_s_2/const.h :.3f} Hz\")\n",
"\n",
"#omega_left, omega_right = trap.get_both_omega(trap.x)\n",
"#print(f\"omega_x = 2pi* {float(trap.subs(omega_left))/2/np.pi:.2f}Hz\")\n",
"#omega_left, omega_right = trap.get_both_omega(trap.z)\n",
"#print(f\"omega_z = 2pi* {float(trap.subs(omega_left))/2/np.pi:.2f}Hz\")\n",
"\n",
"\n",
"# Create figure with subplots\n",
"fig, axes = plt.subplots(3, 1, figsize=(5, 9), sharex=True)\n",
"\n",
"# Define colors\n",
"colors = ['red', 'green']\n",
"\n",
"# Plot U_dd\n",
"axes[0].plot(np.rad2deg(angles_1), U_dds_1 / const.h, color=colors[0], label=\"AR=1\")\n",
"axes[0].plot(np.rad2deg(angles_2), U_dds_2 / const.h, color=colors[1], label=\"AR=2\")\n",
"axes[0].axhline(0, color=\"black\", ls=\"--\")\n",
"axes[0].set_ylabel(r\"$U_{dd} / h$ [Hz]\")\n",
"axes[0].legend()\n",
"\n",
"# Plot NNI\n",
"axes[1].plot(np.rad2deg(angles_1), V_lrs_1 / const.h, color=colors[0], label=\"AR=1\")\n",
"axes[1].plot(np.rad2deg(angles_2), V_lrs_2 / const.h, color=colors[1], label=\"AR=2\")\n",
"axes[1].axhline(0, color=\"black\", ls=\"--\")\n",
"axes[1].set_ylabel(r\"$V_{lr} / h$ [Hz]\")\n",
"axes[1].legend()\n",
"\n",
"# Plot DIT\n",
"axes[2].plot(np.rad2deg(angles_1), DeltaJs_1 / const.h, color=colors[0], label=\"AR=1\")\n",
"axes[2].plot(np.rad2deg(angles_2), DeltaJs_2 / const.h, color=colors[1], label=\"AR=2\")\n",
"axes[2].axhline(0, color=\"black\", ls=\"--\")\n",
"axes[2].set_xlabel(r\"$\\theta$ [deg]\")\n",
"axes[2].set_ylabel(r\"$\\Delta J / h$ [Hz]\")\n",
"axes[2].legend()\n",
"\n",
"# Customize ticks for all subplots\n",
"for ax in axes:\n",
" ax.tick_params(axis='both', which='both', direction='in', length=5) # Tick marks inside\n",
" ax.tick_params(axis='both', which='major', length=7) # Major ticks longer\n",
" ax.tick_params(axis='both', which='minor', length=4) # Minor ticks shorter\n",
" ax.minorticks_on() # Enable minor ticks\n",
"\n",
"# Adjust layout and show the plot\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Plot wavefunctions\n",
"## AR=1"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 1300x400 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#plot wavefunctions\n",
"n_states = 2\n",
"\n",
"states_plot = [GS_left_1.real, GS_right_1.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=(13, 4)) # 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",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1300x400 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n_states = 2\n",
"\n",
"states_plot = [GS_left_1.real, GS_right_1.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=(13, 4)) # 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": "markdown",
"metadata": {},
"source": [
"## AR=2"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1300x400 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#plot wavefunctions\n",
"n_states = 2\n",
"\n",
"states_plot = [GS_left_2.real, GS_right_2.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=(13, 4)) # 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",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1300x400 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n_states = 2\n",
"\n",
"states_plot = [GS_left_2.real, GS_right_2.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=(13, 4)) # 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()"
]
}
],
"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
}