223 lines
35 KiB
Plaintext
223 lines
35 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"from IPython.display import Math, display\n",
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"import numpy as np\n",
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"import sympy as sp\n",
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"from scipy import constants as const\n",
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"from scipy.optimize import minimize_scalar\n",
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"from scipy import sparse\n",
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"\n",
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"#add relative path to backend\n",
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"import sys\n",
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"sys.path.append('../../clean_diag/backend')\n",
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"\n",
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"import trap_units as si\n",
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"from twod_trap import DoubleTweezer, TwoSiteLattice\n",
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"from boson_helpers import *"
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]
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},
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{
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"attachments": {
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"image.png": {
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"image/png": 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"
|
|
}
|
|
},
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Paper:\n",
|
|
"\n",
|
|
"AR=1: J = 27 Hz, U_s = 3749 Hz\n",
|
|
"\n",
|
|
"\n",
|
|
"AR=2: J = 27 Hz, U_s = 1775 Hz\n",
|
|
"\n",
|
|
""
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"ename": "ValueError",
|
|
"evalue": "too many values to unpack (expected 4)",
|
|
"output_type": "error",
|
|
"traceback": [
|
|
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
|
|
"\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)",
|
|
"Cell \u001b[1;32mIn[3], line 6\u001b[0m\n\u001b[0;32m 1\u001b[0m line_number_1 \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m18\u001b[39m\n\u001b[0;32m 2\u001b[0m line_number_2 \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m20\u001b[39m\n\u001b[1;32m----> 6\u001b[0m J, U_s, U_dds_1, angles_1 \u001b[38;5;241m=\u001b[39m analyse_diagonalisation(line_number_1)\n\u001b[0;32m 7\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAR=1:\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m 8\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mJ = \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mJ\u001b[38;5;241m/\u001b[39mconst\u001b[38;5;241m.\u001b[39mh\u001b[38;5;250m \u001b[39m\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124m3f\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m Hz\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
|
|
"\u001b[1;31mValueError\u001b[0m: too many values to unpack (expected 4)"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"line_number_1 = 18\n",
|
|
"line_number_2 = 20\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"J, U_s, U_dds_1, angles_1 = analyse_diagonalisation(line_number_1)\n",
|
|
"print(\"AR=1:\")\n",
|
|
"print(f\"J = {J/const.h :3f} Hz\")\n",
|
|
"print(f\"U_s = {U_s/const.h :.3f} Hz\")\n",
|
|
"plt.plot(np.rad2deg(angles_1), U_dds_1/const.h, color='red',label=\"AR=1\")\n",
|
|
"\n",
|
|
"print(\"\\n\")\n",
|
|
"\n",
|
|
"J, U_s, U_dds_2, angles_2 = analyse_diagonalisation(line_number_2)\n",
|
|
"print(\"AR=2:\")\n",
|
|
"print(f\"J = {J/const.h :3f} Hz\")\n",
|
|
"print(f\"U_s = {U_s/const.h :.3f} Hz\")\n",
|
|
"plt.plot(np.rad2deg(angles_2), U_dds_2/const.h, color='green',label=\"AR=2\")\n",
|
|
"\n",
|
|
"\n",
|
|
"plt.axhline(0,color=\"black\",ls=\"--\")\n",
|
|
"plt.xlabel(\"theta [deg]\")\n",
|
|
"plt.ylabel(r\"$U_{dd} / h$ [Hz]\")\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Check parameters:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\displaystyle 137.0$"
|
|
],
|
|
"text/plain": [
|
|
"137.000000000000"
|
|
]
|
|
},
|
|
"execution_count": 12,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"trap.subs(trap.a_s/const.value(\"Bohr radius\"))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\displaystyle 168.0$"
|
|
],
|
|
"text/plain": [
|
|
"168.000000000000"
|
|
]
|
|
},
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"trap.subs(trap.m)/const.u"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\displaystyle 6.982806$"
|
|
],
|
|
"text/plain": [
|
|
"6.98280600000000"
|
|
]
|
|
},
|
|
"execution_count": 15,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"trap.subs(trap.mu_b/const.value(\"Bohr magneton\"))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Why are higher modes not excited?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"-61.588334691519904"
|
|
]
|
|
},
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"np.diff(res[\"energies\"])[0]/const.h"
|
|
]
|
|
},
|
|
{
|
|
"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
|
|
}
|