561 lines
231 KiB
Plaintext
561 lines
231 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Use this notebook to diagonalise 3D Hamiltonian"
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]
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},
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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 import sparse\n",
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"from scipy.optimize import minimize_scalar\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"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Trap parameters:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"omega_r1: 60954.0Hz, omega_r2: 60954.0Hz\n",
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"omega_z1: 10279.9Hz, omega_z2: 10279.9Hz\n"
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]
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}
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],
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"source": [
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"initial_power = 7000* si.uW\n",
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"initial_waist = 0.71*si.uW\n",
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"initial_distance = 0.808*si.um\n",
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"\n",
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"trap: DoubleTweezer = DoubleTweezer(\n",
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" power=0, # Set pancake laser power to 0, no 2D trap\n",
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" grad_z= 0*si.G/si.cm,\n",
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" grad_r=0,\n",
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" power_tweezer1 = initial_power, #stationary\n",
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" power_tweezer2 = initial_power, #transfer tweezer\n",
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" waist_tweezer1 = initial_waist, #stationary\n",
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" waist_tweezer2 = initial_waist, #transfer tweezer\n",
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" distance_tweezers = initial_distance,\n",
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"\n",
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" m= 161 * const.value(\"atomic mass constant\"),\n",
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" a_s= 85* const.value(\"Bohr radius\"),\n",
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" mu_b= 9.93 * const.value(\"Bohr magneton\" ),\n",
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" a= 180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
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" wvl = 532 * si.nm,\n",
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"\n",
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" g = 0,\n",
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")\n",
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"\n",
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"omega_z1 = sp.sqrt(4*trap.power_tweezer1*trap.a/sp.pi**3/trap.m) * trap.wvl/trap.waist_tweezer1**3\n",
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"omega_z2 = sp.sqrt(4*trap.power_tweezer2*trap.a/sp.pi**3/trap.m) * trap.wvl/trap.waist_tweezer2**3\n",
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"\n",
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"omega_r1 = sp.sqrt(2*trap.power_tweezer1*trap.a/sp.pi/trap.m) * 2/trap.waist_tweezer1**2\n",
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"omega_r2 = sp.sqrt(2*trap.power_tweezer2*trap.a/sp.pi/trap.m) * 2/trap.waist_tweezer2**2\n",
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"\n",
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"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",
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"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\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 500x500 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"left_cutoff = -0.5*float(trap.subs(trap.distance_tweezers))-1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
"right_cutoff = 0.5*float(trap.subs(trap.distance_tweezers))+1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
"\n",
|
|
"\n",
|
|
"# Solve the hamiltonian numerically in axial direction\n",
|
|
"energies, states, potential, coords = trap.nstationary_solution(\n",
|
|
" trap.x, (left_cutoff, right_cutoff), 500, k=6\n",
|
|
")\n",
|
|
"\n",
|
|
"# States that are below the potential barrier\n",
|
|
"bound_states = energies < potential(left_cutoff)\n",
|
|
"\n",
|
|
"\n",
|
|
"z_np = np.linspace(left_cutoff, right_cutoff, num=500)\n",
|
|
"ax: plt.Axes\n",
|
|
"fig, ax = plt.subplots(figsize=(5, 5))\n",
|
|
"ax.plot(z_np / si.um, potential(z_np) / const.h / si.kHz,color=\"cornflowerblue\" ,marker=\"None\")\n",
|
|
"\n",
|
|
"ax.set_title(f\"{np.sum(bound_states)} bound solutions, tweezer distance: {trap.subs(trap.distance_tweezers)/si.um}um\")\n",
|
|
"ax.set_xlabel(r\"x ($\\mathrm{\\mu m}$)\")\n",
|
|
"ax.set_ylabel(r\"E / h (kHz)\")\n",
|
|
"abs_min = np.min(potential(z_np))\n",
|
|
"ax.fill_between(\n",
|
|
" z_np / si.um,\n",
|
|
" potential(z_np) / const.h / si.kHz,\n",
|
|
" abs_min / const.h / si.kHz,\n",
|
|
" alpha=0.5,\n",
|
|
" color=\"cornflowerblue\"\n",
|
|
")\n",
|
|
"\n",
|
|
"count = 0\n",
|
|
"for i, bound in enumerate(bound_states):\n",
|
|
" if not bound:\n",
|
|
" continue\n",
|
|
" energy = energies[i]\n",
|
|
" state = states[i]\n",
|
|
" ax.plot(\n",
|
|
" z_np / si.um,\n",
|
|
" np.where(\n",
|
|
" (energy > potential(z_np)),\n",
|
|
" energy / const.h / si.kHz,\n",
|
|
" np.nan,\n",
|
|
" ),\n",
|
|
" c=\"k\",\n",
|
|
" lw=0.5,\n",
|
|
" marker=\"None\",\n",
|
|
" )\n",
|
|
" ax.plot(z_np/si.um, state *1e1, marker=\"None\",label=f\"state {count}\")#, c=\"k\")\n",
|
|
" count += 1\n",
|
|
"\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 24,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
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"text/plain": [
|
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"<Figure size 500x500 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"left_cutoff = -1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
"right_cutoff = 1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
"\n",
|
|
"\n",
|
|
"# Solve the hamiltonian numerically in axial direction\n",
|
|
"energies, states, potential, coords = trap.nstationary_solution(\n",
|
|
" trap.y, (left_cutoff, right_cutoff), 500, k=6\n",
|
|
")\n",
|
|
"\n",
|
|
"# States that are below the potential barrier\n",
|
|
"bound_states = energies < potential(left_cutoff)\n",
|
|
"\n",
|
|
"\n",
|
|
"z_np = np.linspace(left_cutoff, right_cutoff, num=500)\n",
|
|
"ax: plt.Axes\n",
|
|
"fig, ax = plt.subplots(figsize=(5, 5))\n",
|
|
"ax.plot(z_np / si.um, potential(z_np) / const.h / si.kHz,color=\"cornflowerblue\" ,marker=\"None\")\n",
|
|
"\n",
|
|
"ax.set_title(f\"{np.sum(bound_states)} bound solutions, tweezer distance: {trap.subs(trap.distance_tweezers)/si.um}um\")\n",
|
|
"ax.set_xlabel(r\"y ($\\mathrm{\\mu m}$)\")\n",
|
|
"ax.set_ylabel(r\"E / h (kHz)\")\n",
|
|
"abs_min = np.min(potential(z_np))\n",
|
|
"ax.fill_between(\n",
|
|
" z_np / si.um,\n",
|
|
" potential(z_np) / const.h / si.kHz,\n",
|
|
" abs_min / const.h / si.kHz,\n",
|
|
" alpha=0.5,\n",
|
|
" color=\"cornflowerblue\"\n",
|
|
")\n",
|
|
"\n",
|
|
"count = 0\n",
|
|
"for i, bound in enumerate(bound_states):\n",
|
|
" if not bound:\n",
|
|
" continue\n",
|
|
" energy = energies[i]\n",
|
|
" state = states[i]\n",
|
|
" ax.plot(\n",
|
|
" z_np / si.um,\n",
|
|
" np.where(\n",
|
|
" (energy > potential(z_np)),\n",
|
|
" energy / const.h / si.kHz,\n",
|
|
" np.nan,\n",
|
|
" ),\n",
|
|
" c=\"k\",\n",
|
|
" lw=0.5,\n",
|
|
" marker=\"None\",\n",
|
|
" )\n",
|
|
" ax.plot(z_np/si.um, state *1e1, marker=\"None\",label=f\"state {count}\")#, c=\"k\")\n",
|
|
" count += 1\n",
|
|
"\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"C:\\Users\\naeve\\AppData\\Local\\Temp\\ipykernel_13056\\2474033355.py:51: UserWarning: No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n",
|
|
" plt.legend()\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 500x500 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"left_cutoff = -0.5*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
|
|
"right_cutoff = 0.5*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
|
|
"\n",
|
|
"\n",
|
|
"# Solve the hamiltonian numerically in axial direction\n",
|
|
"energies, states, potential, coords = trap.nstationary_solution(\n",
|
|
" trap.z, (left_cutoff, right_cutoff), 500, k=6\n",
|
|
")\n",
|
|
"\n",
|
|
"# States that are below the potential barrier\n",
|
|
"bound_states = energies < potential(left_cutoff)\n",
|
|
"\n",
|
|
"\n",
|
|
"z_np = np.linspace(left_cutoff, right_cutoff, num=500)\n",
|
|
"ax: plt.Axes\n",
|
|
"fig, ax = plt.subplots(figsize=(5, 5))\n",
|
|
"ax.plot(z_np / si.um, potential(z_np) / const.h / si.kHz,color=\"cornflowerblue\" ,marker=\"None\")\n",
|
|
"\n",
|
|
"ax.set_title(f\"{np.sum(bound_states)} bound solutions, tweezer distance: {trap.subs(trap.distance_tweezers)/si.um}um\")\n",
|
|
"ax.set_xlabel(r\"z ($\\mathrm{\\mu m}$)\")\n",
|
|
"ax.set_ylabel(r\"E / h (kHz)\")\n",
|
|
"abs_min = np.min(potential(z_np))\n",
|
|
"ax.fill_between(\n",
|
|
" z_np / si.um,\n",
|
|
" potential(z_np) / const.h / si.kHz,\n",
|
|
" abs_min / const.h / si.kHz,\n",
|
|
" alpha=0.5,\n",
|
|
" color=\"cornflowerblue\"\n",
|
|
")\n",
|
|
"\n",
|
|
"count = 0\n",
|
|
"for i, bound in enumerate(bound_states):\n",
|
|
" if not bound:\n",
|
|
" continue\n",
|
|
" energy = energies[i]\n",
|
|
" state = states[i]\n",
|
|
" ax.plot(\n",
|
|
" z_np / si.um,\n",
|
|
" np.where(\n",
|
|
" (energy > potential(z_np)),\n",
|
|
" energy / const.h / si.kHz,\n",
|
|
" np.nan,\n",
|
|
" ),\n",
|
|
" c=\"k\",\n",
|
|
" lw=0.5,\n",
|
|
" marker=\"None\",\n",
|
|
" )\n",
|
|
" #ax.plot(z_np/si.um, state *1e1, marker=\"None\",label=f\"state {count}\")#, c=\"k\")\n",
|
|
" count += 1\n",
|
|
"\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 26,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"depth 1: 18.3716 uK\n",
|
|
"depth 2: 18.3716 uK\n",
|
|
"estimated tilt: 0.00 Hz\n",
|
|
"trapping frequency x 1: 41891.68 Hz\n",
|
|
"trapping frequency x 2: 41891.68 Hz\n",
|
|
"trapping frequency y 1: 63870.24 Hz\n",
|
|
"trapping frequency y 2: 63870.24 Hz\n",
|
|
"trapping frequency z 1: 9108.96 Hz\n",
|
|
"trapping frequency z 2: 9108.96 Hz\n",
|
|
"tunneling distance: 604.67 um\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"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",
|
|
" raise Exception(\"potential has only one minmum\")\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",
|
|
"#recoil energy\n",
|
|
"E_r = const.h**2/(8*trap.m*trap.distance_tweezers**2)\n",
|
|
"\n",
|
|
"#print results\n",
|
|
"print(f\"depth 1: {V_1/const.k /si.uK:.4f} uK\")\n",
|
|
"print(f\"depth 2: {V_2/const.k /si.uK:.4f} uK\")\n",
|
|
"print(f\"estimated tilt: {abs(V_1 - V_2)/const.h:.2f} Hz\")\n",
|
|
"\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\"tunneling distance: {tunneling_dist/si.nm:.2f} um\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Diagonalisation parameters"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"distances = [808*si.nm ]\n",
|
|
"\n",
|
|
"for i, dist in enumerate(distances):\n",
|
|
"\n",
|
|
" trap[trap.distance_tweezers] = dist\n",
|
|
"\n",
|
|
" n_grid_1D = 100 \n",
|
|
"\n",
|
|
" n_pot_steps = [n_grid_1D,n_grid_1D,n_grid_1D]\n",
|
|
" n_levels = 6\n",
|
|
"\n",
|
|
" left_cutoff = -0.5*initial_distance-1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
" right_cutoff = 0.5*initial_distance+1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
" back_cutoff = -1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
" front_cutoff = 1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
" bottom_cutoff = -0.5*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
|
|
" top_cutoff = 0.5*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
|
|
"\n",
|
|
" extend = [(left_cutoff,right_cutoff),\n",
|
|
" (back_cutoff,front_cutoff),\n",
|
|
" (bottom_cutoff,top_cutoff)]\n",
|
|
"\n",
|
|
" try:\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=True)\n",
|
|
" except:\n",
|
|
" continue\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)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 27,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"files saved with ...._2025-03-31_16-07-07\n",
|
|
"files saved with ...._2025-03-31_17-02-40\n",
|
|
"files saved with ...._2025-03-31_17-56-25\n",
|
|
"files saved with ...._2025-03-31_18-46-11\n",
|
|
"files saved with ...._2025-03-31_19-34-16\n",
|
|
"files saved with ...._2025-03-31_20-21-21\n",
|
|
"files saved with ...._2025-03-31_21-07-40\n",
|
|
"files saved with ...._2025-03-31_21-53-18\n",
|
|
"files saved with ...._2025-03-31_22-38-09\n",
|
|
"files saved with ...._2025-03-31_23-21-53\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"distances = np.linspace(730,850,10)*si.nm\n",
|
|
"\n",
|
|
"for i, dist in enumerate(distances):\n",
|
|
"\n",
|
|
" trap[trap.distance_tweezers] = dist\n",
|
|
"\n",
|
|
" n_grid_1D = 100 \n",
|
|
"\n",
|
|
" n_pot_steps = [n_grid_1D,n_grid_1D,n_grid_1D]\n",
|
|
" n_levels = 6\n",
|
|
"\n",
|
|
" left_cutoff = -0.5*initial_distance-1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
" right_cutoff = 0.5*initial_distance+1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
" back_cutoff = -1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
" front_cutoff = 1*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
|
|
" bottom_cutoff = -0.5*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
|
|
" top_cutoff = 0.5*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
|
|
"\n",
|
|
" extend = [(left_cutoff,right_cutoff),\n",
|
|
" (back_cutoff,front_cutoff),\n",
|
|
" (bottom_cutoff,top_cutoff)]\n",
|
|
"\n",
|
|
" try:\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=True)\n",
|
|
" except:\n",
|
|
" continue\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)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Visualise results"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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|
|
"text/plain": [
|
|
"<Figure size 1800x500 with 12 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"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"
|
|
]
|
|
},
|
|
{
|
|
"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
|
|
}
|