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Added harmonic fit to extract trap frequency of potential, corrected few bugs.

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Karthik 2023-01-12 15:18:46 +01:00
parent 435fbccbfa
commit 30e6a8b7a4
1 changed files with 72 additions and 27 deletions
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99
calculateDipoleTrapPotential.py
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@ -1,18 +1,20 @@
import math
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from astropy import units as u, constants as ac
def orderOfMagnitude(number):
return math.floor(math.log(number, 10))
def rotation_matrix(axis, theta):
"""
Return the rotation matrix associated with counterclockwise rotation about
the given axis by theta radians.
In 2-D it is just,
thetaInRadians = np.radians(theta)
c, s = np.cos(thetaInRadians), np.sin(thetaInRadians)
R = np.array(((c, -s), (s, c)))
In 3-D, one way to do it is use the Euler-Rodrigues Formula as is done here
"""
axis = np.asarray(axis)
@ -39,7 +41,7 @@ def trap_depth(w_1:"float|u.quantity.Quantity", w_2:"float|u.quantity.Quantity",
def gravitational_potential(positions: "np.ndarray|u.quantity.Quantity", m:"float|u.quantity.Quantity"):
return m * ac.g0 * positions
def single_gaussian_beam_potential(positions: "np.ndarray|u.quantity.Quantity", waists: "np.ndarray|u.quantity.Quantity", P:"float|u.quantity.Quantity"=1, wavelength:"float|u.quantity.Quantity"=1.064*u.um, alpha:"float|u.quantity.Quantity"=184.4)->np.ndarray:
def single_gaussian_beam_potential(positions: "np.ndarray|u.quantity.Quantity", waists: "np.ndarray|u.quantity.Quantity", alpha:"float|u.quantity.Quantity", P:"float|u.quantity.Quantity"=1, wavelength:"float|u.quantity.Quantity"=1.064*u.um)->np.ndarray:
A = 2*P/(np.pi*w(positions[1,:], waists[0], wavelength)*w(positions[1,:], waists[1], wavelength))
U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
U = - U_tilde * A * np.exp(-2 * ((positions[0,:]/w(positions[1,:], waists[0], wavelength))**2 + (positions[2,:]/w(positions[1,:], waists[1], wavelength))**2))
@ -48,44 +50,79 @@ def single_gaussian_beam_potential(positions: "np.ndarray|u.quantity.Quantity",
def single_gaussian_beam_potential_harmonic_approximation(positions: "np.ndarray|u.quantity.Quantity", waists: "np.ndarray|u.quantity.Quantity", depth:"float|u.quantity.Quantity"=1, wavelength:"float|u.quantity.Quantity"=1.064*u.um)->np.ndarray:
U = - depth * (1 - (2 * (positions[0,:]/waists[0])**2) - (2 * (positions[2,:]/waists[1])**2) - (0.5 * positions[1,:]**2 * np.sum(np.reciprocal(z_R(waists, wavelength)))**2))
return U
def harmonic_potential(pos, v, offset):
U_Harmonic = ((0.5 * 164*u.u * (2 * np.pi * v*u.Hz)**2 * (pos*u.um)**2)/ac.k_B).to(u.uK) + offset*u.uK
return U_Harmonic.value
def extractTrapFrequency(Positions, TrappingPotential, TrapDepthInKelvin, axis):
tmp_pos = Positions[axis, :]
center_idx = np.where(tmp_pos == 0)[0][0]
lb = int(round(center_idx - len(tmp_pos)/20, 1))
ub = int(round(center_idx + len(tmp_pos)/20, 1))
xdata = tmp_pos[lb:ub]
tmp_pot = TrappingPotential[axis]
Potential = tmp_pot[lb:ub]
p0=[1e3, -TrapDepthInKelvin.value]
popt, pcov = curve_fit(harmonic_potential, xdata, Potential, p0)
v = popt[0]
dv = pcov[0][0]**0.5
return v, dv, popt, pcov
def plotHarmonicFit(Positions, TrappingPotential, TrapDepthInKelvin, axis, popt, pcov):
v = popt[0]
dv = pcov[0][0]**0.5
happrox = harmonic_potential(Positions[axis, :].value, *popt)
plt.figure()
plt.plot(Positions[axis, :].value, happrox, '-r', label = '\u03BD = %.1f \u00B1 %.2f Hz'% tuple([v,dv]))
plt.plot(Positions[axis, :], TrappingPotential[axis], 'ob', label = 'Gaussian Potential')
plt.xlabel('Distance (um)', fontsize= 12, fontweight='bold')
plt.ylabel('Trap Potential (uK)', fontsize= 12, fontweight='bold')
plt.ylim([-TrapDepthInKelvin.value, max(TrappingPotential[axis].value)])
plt.tight_layout()
plt.grid(visible=1)
plt.legend(prop={'size': 12, 'weight': 'bold'})
plt.show()
def plotPotential(Positions, Powers, ComputedPotentials, axis, TrapDepthLabels):
## plot of the measured parameter vs. scan parameter
plt.figure(figsize=(9, 7))
for i in range(np.size(ComputedPotentials, 0)):
plt.plot(Positions[axis], ComputedPotentials[i][axis], label = 'P = ' + str(Powers[i]) + ' W; ' + TrapDepthLabels[i])
v, dv, popt, pcov = extractTrapFrequency(Positions, ComputedPotentials[i], TrapDepthInKelvin, axis)
unit = 'Hz'
if v <= 0:
v = np.nan
dv = np.nan
unit = 'Hz'
elif v > 0 and orderOfMagnitude(v) > 2:
v = v / 1e3 # in kHz
dv = dv / 1e3 # in kHz
unit = 'kHz'
tf_label = '\u03BD = %.1f \u00B1 %.2f %s'% tuple([v,dv,unit])
plt.plot(Positions[axis], ComputedPotentials[i][axis], label = 'P = ' + str(Powers[i]) + ' W; ' + TrapDepthLabels[i] + '; ' + tf_label)
if axis == 0:
dir = 'X'
elif axis == 1:
dir = 'Y'
else:
dir = 'Z'
# maxPotentialValue = max(ComputedPotentials.flatten())
# minPotentialValue = min(ComputedPotentials.flatten())
# PotentialValueRange = maxPotentialValue - minPotentialValue
# upperlimit = 5
# if maxPotentialValue > 0:
# upperlimit = maxPotentialValue
# lowerlimit = min(ComputedPotentials.flatten()) - PotentialValueRange/6
# plt.ylim([lowerlimit, upperlimit])
plt.xlabel(dir + ' Direction (um)', fontsize= 12, fontweight='bold')
plt.ylabel('Trap Potential (uK)', fontsize= 12, fontweight='bold')
plt.tight_layout()
plt.grid(visible=1)
plt.legend(prop={'size': 12, 'weight': 'bold'})
plt.tight_layout()
# plt.show()
plt.savefig('pot_' + dir + '.png')
plt.show()
# plt.savefig('pot_' + dir + '.png')
if __name__ == '__main__':
# Powers = [0.1, 0.5, 2]
# Powers = [5, 10, 20, 30, 40]
Powers = [40]
Polarizability = 160 # in a.u., should we use alpha = 136 or 160 or 184.4?
# w_x, w_z = 34*u.um, 27.5*u.um # Beam Waists in the x and y directions
w_x, w_z = 35*u.um, 35*u.um # Beam Waists in the x and y directions
Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability
w_x, w_z = 34*u.um, 27.5*u.um # Beam Waists in the x and y directions
# w_x, w_z = 70*u.um, 70*u.um # Beam Waists in the x and y directions
# w_x, w_z = 20.5*u.um, 20.5*u.um
axis = 1 # axis referenced to the beam along which you want the dipole trap potential
@ -95,11 +132,11 @@ if __name__ == '__main__':
ComputedPotentials = []
TrapDepthLabels = []
gravity = False
gravity = True
astigmatism = False
tilt_gravity = True
theta = 0 # in degrees
theta = 1 # in degrees
tilt_axis = [1, 0, 0] # lab space coordinates are rotated about x-axis in reference frame of beam
for p in Powers:
@ -111,10 +148,13 @@ if __name__ == '__main__':
TrapDepthLabels.append("Trap Depth = " + str(round(TrapDepthInKelvin.value, 2)) + " " + str(TrapDepthInKelvin.unit))
projection_axis = np.array([0, 1, 0]) # default
if axis == 0:
projection_axis = np.array([1, 0, 0]) # radial direction (X-axis)
elif axis == 1:
projection_axis = np.array([0, 1, 0]) # propagation direction (Y-axis)
elif axis == 2:
projection_axis = np.array([0, 0, 1]) # vertical direction (Z-axis)
@ -138,14 +178,19 @@ if __name__ == '__main__':
gravity_axis_positions = np.vstack((x_Positions, y_Positions, z_Positions)) * gravity_axis[:, np.newaxis]
TrappingPotential = single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, alpha = Polarizability) + gravitational_potential(gravity_axis_positions, m)
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
elif not gravity and astigmatism:
# Influence of Astigmatism
pass
else:
# Influence of Gravity and Astigmatism
pass
# v, dv, popt, pcov = extractTrapFrequency(Positions, TrappingPotential, TrapDepthInKelvin, axis)
# plotHarmonicFit(Positions, TrappingPotential, TrapDepthInKelvin, axis, popt, pcov)
ComputedPotentials.append(TrappingPotential)
ComputedPotentials = np.asarray(ComputedPotentials)
plotPotential(Positions, Powers, ComputedPotentials, axis, TrapDepthLabels)
# Influence of Astigmatism
# TrappingPotential = single_gaussian_beam_potential_harmonic_approximation(Positions, np.asarray([w_x.value, w_z.value])*u.um, depth = TrapDepth)
# TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
plotPotential(Positions, Powers, ComputedPotentials, axis, TrapDepthLabels)