def __init__(self,
N=127,
Vtrap=(0., -1750., -2000.),
Vwall=5.,
frot=180.,
B=4.4588):
"""
Assumes many of the following parameters, each set as default in Freericks/
Meiser codes. Can be adjusted in later methods.
"""
self.Nion = N
self.Vtrap = Vtrap
self.Vwall = Vwall
self.frot = frot
self.mode_analysis = mode_analysis_code.ModeAnalysis(N=self.Nion,
Vtrap=self.Vtrap,
Vwall=self.Vwall,
frot=self.frot)
self.omega = omega
self.trap_potential = coldatoms.HarmonicTrapPotential(
self.kx, self.ky, self.kz)
def reset_phase(self):
self.phi = self.phi_0
def force(self, dt, ensemble, f):
self.phi += self.omega * 0.5 * dt
self.trap_potential.phi = self.phi
self.trap_potential.force(dt, ensemble, f)
self.phi += self.omega * 0.5 * dt
mode_analysis = mode_analysis_code.ModeAnalysis(N=num_ions,
Vtrap=(0.0, -1750.0, -1970.0),
Vwall=v_wall,
frot=1.0e-3 * frot)
mode_analysis.run()
trap_potential = TrapPotential(2.0 * mode_analysis.Coeff[2], mode_analysis.Cw,
mode_analysis.wrot, np.pi / 2.0)
forces = [coulomb_force, trap_potential]
def evolve_ensemble(dt, t_max, ensemble, Bz, forces):
num_steps = int(t_max / dt)
coldatoms.bend_kick(dt, Bz, ensemble, forces, num_steps=num_steps)
coldatoms.bend_kick(t_max - dt * num_steps, Bz, ensemble, forces)
initial_state = coldatoms.json_to_ensemble(
# From coldatoms lib, create a function to evolve the crystal
def evolve_ensemble(dt, t_max, ensemble, Bz, forces):
num_steps = int(t_max / dt)
coldatoms.bend_kick(dt, Bz, ensemble, forces, num_steps=num_steps)
coldatoms.bend_kick(t_max - num_steps * dt, Bz, ensemble, forces)
##############################################################
############### INSTANTIATE CRYSTAL & TRAP ###################
mode_analysis = mode_analysis_code.ModeAnalysis(N=127,
Vtrap=(0.0, -1750.0, -2000.0),
Vwall=5.0,
frot=180.0)
mode_analysis.run()
trap_potential = TrapPotential(2.0 * mode_analysis.Coeff[2], mode_analysis.Cw,
mode_analysis.wrot, np.pi / 2.0)
##############################################################
####################### EVOLUTION ###########################
x = mode_analysis.u[:mode_analysis.Nion]
y = mode_analysis.u[mode_analysis.Nion:]
dx = x.reshape((x.size, 1)) - x
dy = y.reshape((y.size, 1)) - y
'text.latex.preamble': [r'\usepackage{siunitx}', r'\usepackage{amsmath}'],
'xtick.labelsize': 'medium',
'ytick.labelsize': 'medium',
'axes.labelsize': 'medium'
}
plt.rcParams.update(params)
line_width = 246.0 / 72.0
default_width = 0.95 * line_width
golden_ratio = 1.61803398875
default_height = default_width / golden_ratio
# Preparation for computation of frequency sweep
mode_analysis = mode_analysis_code.ModeAnalysis(N=127,
Vtrap=(0.0, -1750.0, -1970.0),
Vwall=1.0,
frot=185.0)
mode_analysis.run()
def create_ensemble(uE, omega_z, mass, charge):
num_ions = int(uE.size / 2)
x = uE[:num_ions]
y = uE[num_ions:]
r = np.sqrt(x**2 + y**2)
r_hat = np.transpose(np.array([x / r, y / r]))
phi_hat = np.transpose(np.array([-y / r, x / r]))
v = np.zeros([num_ions, 2], dtype=np.float64)
for i in range(num_ions):
v[i, 0] = omega_z * r[i] * phi_hat[i, 0]
v[i, 1] = omega_z * r[i] * phi_hat[i, 1]
import matplotlib.pyplot as plt
import matplotlib.lines
import numpy as np
import scipy.signal
import scipy.optimize
import mode_analysis_code
import argparse
plt.style.use('ggplot')
mode_analysis = mode_analysis_code.ModeAnalysis()
nu_z = np.sqrt(2 * mode_analysis.q * mode_analysis.Coeff[2] /
mode_analysis.m_Be) / (2 * np.pi)
def lorentzian(x, A, FWHM, x0): #(x, height, FWHM, x0):
p = (x0 - x) / (FWHM / 2)
L = A / (1 + p**2)
# A = np.pi * FWHM * height / 2
# L = (A / np.pi) * (0.5 * FWHM / ((x - x0)**2 + (0.5 * FWHM)**2))
return L
def double_lorentzian(x, A, FWHM_A, x0_A, B, FWHM_B, x0_B, C):
pA = (x0_A - x) / (FWHM_A / 2)
pB = (x0_B - x) / (FWHM_B / 2)
L = C * (A / (1 + pA**2) + B / (1 + pB**2))
return L
def report_values(value, error):
a = int(np.floor(np.log10(np.abs(error))))