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Corrected minor bugs, added detailed plotting of crossed beam potential in different directions.

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Karthik 2023-03-15 11:29:21 +01:00
parent 6f018c0281
commit 6976e0ef91
2 changed files with 443 additions and 132 deletions
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417
ODTCalculations.ipynb
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156
calculateDipoleTrapPotential.py
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@ -6,6 +6,10 @@ from scipy import signal, interpolate
from scipy.optimize import curve_fit from scipy.optimize import curve_fit
from astropy import units as u, constants as ac from astropy import units as u, constants as ac
DY_POLARIZABILITY = 184.4 # in a.u, most precise measured value of Dy polarizability
DY_MASS = 164*u.u
DY_DIPOLE_MOMENT = 9.93 * ac.muB
##################################################################### #####################################################################
# HELPER FUNCTIONS # # HELPER FUNCTIONS #
##################################################################### #####################################################################
@ -80,20 +84,20 @@ def w(pos, w_0, lamb):
# COLLISION RATES, PSD # # COLLISION RATES, PSD #
##################################################################### #####################################################################
def calculateAtomNumber(NCount, pixel_size = 5.86 * u.um, magnification = 0.5, eta = 0.5): def calculateAtomNumber(NCount, pixel_size, magnification, eta):
sigma = 8.468e-14 * (u.m)**(2) sigma = 8.468e-14 * (u.m)**(2)
return (1/eta * 1/sigma * NCount * pixel_size**2/magnification**2).decompose() return (1/eta * 1/sigma * NCount * pixel_size**2/magnification**2).decompose()
def meanThermalVelocity(T, m = 164*u.u): def meanThermalVelocity(T, m = DY_MASS):
return 4 * np.sqrt((ac.k_B * T) /(np.pi * m)) return 4 * np.sqrt((ac.k_B * T) /(np.pi * m))
def particleDensity(w_x, w_z, Power, N, T, m = 164*u.u): # For a thermal cloud def particleDensity(w_x, w_z, Power, N, T, m = DY_MASS): # For a thermal cloud
v_x = calculateTrapFrequency(w_x, w_z, Power, dir = 'x') v_x = calculateTrapFrequency(w_x, w_z, Power, dir = 'x')
v_y = calculateTrapFrequency(w_x, w_z, Power, dir = 'y') v_y = calculateTrapFrequency(w_x, w_z, Power, dir = 'y')
v_z = calculateTrapFrequency(w_x, w_z, Power, dir = 'z') v_z = calculateTrapFrequency(w_x, w_z, Power, dir = 'z')
return N * (2 * np.pi)**3 * (v_x * v_y * v_z) * (m / (2 * np.pi * ac.k_B * T))**(3/2) return N * (2 * np.pi)**3 * (v_x * v_y * v_z) * (m / (2 * np.pi * ac.k_B * T))**(3/2)
def calculateParticleDensityFromMeasurements(v_x, dv_x, v_y, dv_y, v_z, dv_z, w_x, w_z, T_x, T_y, dT_x, dT_y, modulation_depth, N, m = 164*u.u): def calculateParticleDensityFromMeasurements(v_x, dv_x, v_y, dv_y, v_z, dv_z, w_x, w_z, T_x, T_y, dT_x, dT_y, modulation_depth, N, m = DY_MASS):
alpha_x = [(v_x[0]/x)**(2/3) for x in v_x] alpha_x = [(v_x[0]/x)**(2/3) for x in v_x]
dalpha_x = [alpha_x[i] * np.sqrt((dv_x[0]/v_x[0])**2 + (dv_x[i]/v_x[i])**2) for i in range(len(v_x))] dalpha_x = [alpha_x[i] * np.sqrt((dv_x[0]/v_x[0])**2 + (dv_x[i]/v_x[i])**2) for i in range(len(v_x))]
alpha_y = [(v_z[0]/y)**2 for y in v_z] alpha_y = [(v_z[0]/y)**2 for y in v_z]
@ -118,7 +122,7 @@ def calculateParticleDensityFromMeasurements(v_x, dv_x, v_y, dv_y, v_z, dv_z, w_
return pd, dpd, avg_T, avg_dT, new_aspect_ratio return pd, dpd, avg_T, avg_dT, new_aspect_ratio
def thermaldeBroglieWavelength(T, m = 164*u.u): def thermaldeBroglieWavelength(T, m = DY_MASS):
return np.sqrt((2*np.pi*ac.hbar**2)/(m*ac.k_B*T)) return np.sqrt((2*np.pi*ac.hbar**2)/(m*ac.k_B*T))
def scatteringLength(B, FR_choice = 1, ABKG_choice = 1): def scatteringLength(B, FR_choice = 1, ABKG_choice = 1):
@ -161,7 +165,7 @@ def scatteringLength(B, FR_choice = 1, ABKG_choice = 1):
a_s = a_bkg * np.prod([(1 - resonancewB[j] / (B - resonanceB[j])) for j in range(len(resonanceB))]) a_s = a_bkg * np.prod([(1 - resonancewB[j] / (B - resonanceB[j])) for j in range(len(resonanceB))])
return a_s, a_bkg return a_s, a_bkg
def dipolarLength(mu = 9.93 * ac.muB, m = 164*u.u): def dipolarLength(mu = DY_DIPOLE_MOMENT, m = DY_MASS):
return (m * ac.mu0 * mu**2) / (12 * np.pi * ac.hbar**2) return (m * ac.mu0 * mu**2) / (12 * np.pi * ac.hbar**2)
def scatteringCrossSection(B): def scatteringCrossSection(B):
@ -213,19 +217,19 @@ def convert_modulation_depth_to_temperature(modulation_depth):
def gravitational_potential(positions, m): def gravitational_potential(positions, m):
return m * ac.g0 * positions return m * ac.g0 * positions
def single_gaussian_beam_potential(positions, waists, alpha = 184.4, P=1, wavelength=1.064*u.um): def single_gaussian_beam_potential(positions, waists, alpha = DY_POLARIZABILITY, P=1, wavelength=1.064*u.um):
A = 2*P/(np.pi*w(positions[1,:], waists[0], wavelength)*w(positions[1,:], waists[1], wavelength)) 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_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)) 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))
return U return U
def astigmatic_single_gaussian_beam_potential(positions, waists, del_y, alpha = 184.4, P=1, wavelength=1.064*u.um): def astigmatic_single_gaussian_beam_potential(positions, waists, del_y, alpha = DY_POLARIZABILITY, P=1, wavelength=1.064*u.um):
A = 2*P/(np.pi*w(positions[1,:] - (del_y/2), waists[0], wavelength)*w(positions[1,:] + (del_y/2), waists[1], wavelength)) A = 2*P/(np.pi*w(positions[1,:] - (del_y/2), waists[0], wavelength)*w(positions[1,:] + (del_y/2), waists[1], wavelength))
U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3) 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,:] - (del_y/2), waists[0], wavelength))**2 + (positions[2,:]/w(positions[1,:] + (del_y/2), waists[1], wavelength))**2)) U = - U_tilde * A * np.exp(-2 * ((positions[0,:]/w(positions[1,:] - (del_y/2), waists[0], wavelength))**2 + (positions[2,:]/w(positions[1,:] + (del_y/2), waists[1], wavelength))**2))
return U return U
def modulated_single_gaussian_beam_potential(positions, waists, alpha = 184.4, P=1, wavelength=1.064*u.um, mod_amp=1): def modulated_single_gaussian_beam_potential(positions, waists, alpha = DY_POLARIZABILITY, P=1, wavelength=1.064*u.um, mod_amp=1):
mod_amp = mod_amp * waists[0] mod_amp = mod_amp * waists[0]
n_points = len(positions[0,:]) n_points = len(positions[0,:])
dx, x_mod = modulation_function(mod_amp, n_points, func = 'arccos') dx, x_mod = modulation_function(mod_amp, n_points, func = 'arccos')
@ -237,7 +241,7 @@ def modulated_single_gaussian_beam_potential(positions, waists, alpha = 184.4, P
U = - U_tilde * A * 1/(2*mod_amp) * np.trapz(dU, dx = dx, axis = 0) U = - U_tilde * A * 1/(2*mod_amp) * np.trapz(dU, dx = dx, axis = 0)
return U return U
def harmonic_potential(pos, v, xoffset, yoffset, m = 164*u.u): def harmonic_potential(pos, v, xoffset, yoffset, m = DY_MASS):
U_Harmonic = ((0.5 * m * (2 * np.pi * v*u.Hz)**2 * (pos*u.um - xoffset*u.um)**2)/ac.k_B).to(u.uK) + yoffset*u.uK U_Harmonic = ((0.5 * m * (2 * np.pi * v*u.Hz)**2 * (pos*u.um - xoffset*u.um)**2)/ac.k_B).to(u.uK) + yoffset*u.uK
return U_Harmonic.value return U_Harmonic.value
@ -245,38 +249,60 @@ def gaussian_potential(pos, amp, waist, xoffset, yoffset):
U_Gaussian = amp * np.exp(-2 * ((pos + xoffset) / waist)**2) + yoffset U_Gaussian = amp * np.exp(-2 * ((pos + xoffset) / waist)**2) + yoffset
return U_Gaussian return U_Gaussian
def crossed_beam_potential(positions, theta, waists, P, alpha = 184.4, wavelength=1.064*u.um): def crossed_beam_potential(positions, waists, P, options, alpha = DY_POLARIZABILITY, wavelength=1.064*u.um):
beam_1_positions = positions delta = options['delta']
A_1 = 2*P[0]/(np.pi*w(beam_1_positions[1,:], waists[0][0], wavelength)*w(beam_1_positions[1,:], waists[0][1], wavelength))
foci_shift = options['foci_shift']
focus_shift_beam_1 = foci_shift[0]
focus_shift_beam_2 = foci_shift[1]
beam_disp = options['beam_disp']
beam_1_disp = (np.ones(np.shape(positions.T)) * np.array(beam_disp[0])).T * beam_disp[0].unit
beam_2_disp = (np.ones(np.shape(positions.T)) * np.array(beam_disp[1])).T * beam_disp[1].unit
beam_1_positions = positions + beam_1_disp
A_1 = 2*P[0]/(np.pi*w(beam_1_positions[1,:] + focus_shift_beam_1, waists[0][0], wavelength)*w(beam_1_positions[1,:] + focus_shift_beam_1, waists[0][1], wavelength))
U_1_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3) U_1_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
U_1 = - U_1_tilde * A_1 * np.exp(-2 * ((beam_1_positions[0,:]/w(beam_1_positions[1,:], waists[0][0], wavelength))**2 + (beam_1_positions[2,:]/w(beam_1_positions[1,:], waists[0][1], wavelength))**2)) U_1 = - U_1_tilde * A_1 * np.exp(-2 * ((beam_1_positions[0,:]/w(beam_1_positions[1,:] + focus_shift_beam_1, waists[0][0], wavelength))**2 + (beam_1_positions[2,:]/w(beam_1_positions[1,:] + focus_shift_beam_1, waists[0][1], wavelength))**2))
R = rotation_matrix([0, 0, 1], np.radians(theta)) R = rotation_matrix([0, 0, 1], np.radians(delta))
beam_2_positions = np.dot(R, beam_1_positions) beam_2_positions = np.dot(R, beam_1_positions) + beam_2_disp
A_2 = 2*P[1]/(np.pi*w(beam_2_positions[1,:], waists[1][0], wavelength)*w(beam_2_positions[1,:], waists[1][1], wavelength)) A_2 = 2*P[1]/(np.pi*w(beam_2_positions[1,:] + focus_shift_beam_2, waists[1][0], wavelength)*w(beam_2_positions[1,:] + focus_shift_beam_2, waists[1][1], wavelength))
U_2_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3) U_2_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
U_2 = - U_2_tilde * A_2 * np.exp(-2 * ((beam_2_positions[0,:]/w(beam_2_positions[1,:], waists[1][0], wavelength))**2 + (beam_2_positions[2,:]/w(beam_2_positions[1,:], waists[1][1], wavelength))**2)) U_2 = - U_2_tilde * A_2 * np.exp(-2 * ((beam_2_positions[0,:]/w(beam_2_positions[1,:] + focus_shift_beam_2, waists[1][0], wavelength))**2 + (beam_2_positions[2,:]/w(beam_2_positions[1,:] + focus_shift_beam_2, waists[1][1], wavelength))**2))
U = U_1 + U_2 U = U_1 + U_2
return U return U
def astigmatic_crossed_beam_potential(positions, theta, waists, P, del_y, alpha = 184.4, wavelength=1.064*u.um): def astigmatic_crossed_beam_potential(positions, waists, P, options, alpha = DY_POLARIZABILITY, wavelength=1.064*u.um):
delta = options['delta']
del_y = options['foci_disp_crossed']
del_y_1 = del_y[0] del_y_1 = del_y[0]
del_y_2 = del_y[1] del_y_2 = del_y[1]
beam_1_positions = positions
A_1 = 2*P[0]/(np.pi*w(beam_1_positions[1,:] - (del_y_1/2), waists[0][0], wavelength)*w(beam_1_positions[1,:] + (del_y_1/2), waists[0][1], wavelength))
U_1_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
U_1 = - U_1_tilde * A_1 * np.exp(-2 * ((beam_1_positions[0,:]/w(beam_1_positions[1,:] - (del_y_1/2), waists[0][0], wavelength))**2 + (beam_1_positions[2,:]/w(beam_1_positions[1,:] + (del_y_1/2), waists[0][1], wavelength))**2))
R = rotation_matrix([0, 0, 1], np.radians(theta)) foci_shift = options['foci_shift']
beam_2_positions = np.dot(R, beam_1_positions) focus_shift_beam_1 = foci_shift[0]
A_2 = 2*P[1]/(np.pi*w(beam_2_positions[1,:] - (del_y_2/2), waists[1][0], wavelength)*w(beam_2_positions[1,:] + (del_y_2/2), waists[1][1], wavelength)) focus_shift_beam_2 = foci_shift[1]
beam_disp = options['beam_disp']
beam_1_disp = (np.ones(np.shape(positions.T)) * np.array(beam_disp[0])).T * beam_disp[0].unit
beam_2_disp = (np.ones(np.shape(positions.T)) * np.array(beam_disp[1])).T * beam_disp[1].unit
beam_1_positions = positions + beam_1_disp
A_1 = 2*P[0]/(np.pi*w(beam_1_positions[1,:] - (del_y_1/2) + focus_shift_beam_1, waists[0][0], wavelength)*w(beam_1_positions[1,:] + (del_y_1/2) + focus_shift_beam_1, waists[0][1], wavelength))
U_1_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
U_1 = - U_1_tilde * A_1 * np.exp(-2 * ((beam_1_positions[0,:]/w(beam_1_positions[1,:] - (del_y_1/2) + focus_shift_beam_1, waists[0][0], wavelength))**2 + (beam_1_positions[2,:]/w(beam_1_positions[1,:] + (del_y_1/2) + focus_shift_beam_1, waists[0][1], wavelength))**2))
R = rotation_matrix([0, 0, 1], np.radians(delta))
beam_2_positions = np.dot(R, beam_1_positions) + beam_2_disp
A_2 = 2*P[1]/(np.pi*w(beam_2_positions[1,:] - (del_y_2/2) + focus_shift_beam_2, waists[1][0], wavelength)*w(beam_2_positions[1,:] + (del_y_2/2) + focus_shift_beam_2, waists[1][1], wavelength))
U_2_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3) U_2_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
U_2 = - U_2_tilde * A_2 * np.exp(-2 * ((beam_2_positions[0,:]/w(beam_2_positions[1,:] - (del_y_2/2), waists[1][0], wavelength))**2 + (beam_2_positions[2,:]/w(beam_2_positions[1,:] + (del_y_2/2), waists[1][1], wavelength))**2)) U_2 = - U_2_tilde * A_2 * np.exp(-2 * ((beam_2_positions[0,:]/w(beam_2_positions[1,:] - (del_y_2/2) + focus_shift_beam_2, waists[1][0], wavelength))**2 + (beam_2_positions[2,:]/w(beam_2_positions[1,:] + (del_y_2/2) + focus_shift_beam_2, waists[1][1], wavelength))**2))
U = U_1 + U_2 U = U_1 + U_2
@ -286,10 +312,10 @@ def astigmatic_crossed_beam_potential(positions, theta, waists, P, del_y, alpha
# COMPUTE/EXTRACT TRAP POTENTIAL AND PARAMETERS # # COMPUTE/EXTRACT TRAP POTENTIAL AND PARAMETERS #
##################################################################### #####################################################################
def trap_depth(w_1, w_2, P, alpha = 184.4): def trap_depth(w_1, w_2, P, alpha = DY_POLARIZABILITY):
return 2*P/(np.pi*w_1*w_2) * (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3) return 2*P/(np.pi*w_1*w_2) * (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
def calculateTrapFrequency(w_x, w_z, Power, dir = 'x', m = 164*u.u): def calculateTrapFrequency(w_x, w_z, Power, dir = 'x', m = DY_MASS):
TrapDepth = trap_depth(w_x, w_z, Power) TrapDepth = trap_depth(w_x, w_z, Power)
TrapFrequency = np.nan TrapFrequency = np.nan
if dir == 'x': if dir == 'x':
@ -301,7 +327,7 @@ def calculateTrapFrequency(w_x, w_z, Power, dir = 'x', m = 164*u.u):
TrapFrequency = ((1/(2 * np.pi)) * np.sqrt(4 * TrapDepth/ (m*w_z**2))).decompose() TrapFrequency = ((1/(2 * np.pi)) * np.sqrt(4 * TrapDepth/ (m*w_z**2))).decompose()
return round(TrapFrequency.value, 2)*u.Hz return round(TrapFrequency.value, 2)*u.Hz
def calculateCrossedBeamTrapFrequency(delta, Waists, Powers, dir = 'x', m = 164*u.u, wavelength=1.064*u.um): def calculateCrossedBeamTrapFrequency(delta, Waists, Powers, dir = 'x', m = DY_MASS, wavelength=1.064*u.um):
TrapDepth_1 = trap_depth(Waists[0][0], Waists[1][0], Powers[0]) TrapDepth_1 = trap_depth(Waists[0][0], Waists[1][0], Powers[0])
TrapDepth_2 = trap_depth(Waists[0][1], Waists[1][1], Powers[1]) TrapDepth_2 = trap_depth(Waists[0][1], Waists[1][1], Powers[1])
@ -392,7 +418,7 @@ def computeTrapPotential(w_x, w_z, Power, options):
if gravity and not astigmatism: if gravity and not astigmatism:
# Influence of Gravity # Influence of Gravity
m = 164*u.u m = DY_MASS
gravity_axis = np.array([0, 0, 1]) gravity_axis = np.array([0, 0, 1])
tilt_gravity = options['tilt_gravity'] tilt_gravity = options['tilt_gravity']
theta = options['theta'] theta = options['theta']
@ -407,24 +433,24 @@ def computeTrapPotential(w_x, w_z, Power, options):
elif not gravity and astigmatism: elif not gravity and astigmatism:
# Influence of Astigmatism # Influence of Astigmatism
disp_foci = options['disp_foci'] foci_disp_single = options['foci_disp_single']
TrappingPotential = astigmatic_single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, del_y = disp_foci) TrappingPotential = astigmatic_single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, del_y = foci_disp_single)
TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis]) TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis])
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK) TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
elif gravity and astigmatism: elif gravity and astigmatism:
# Influence of Gravity and Astigmatism # Influence of Gravity and Astigmatism
m = 164*u.u m = DY_MASS
gravity_axis = np.array([0, 0, 1]) gravity_axis = np.array([0, 0, 1])
tilt_gravity = options['tilt_gravity'] tilt_gravity = options['tilt_gravity']
theta = options['theta'] theta = options['theta']
tilt_axis = options['tilt_axis'] tilt_axis = options['tilt_axis']
disp_foci = options['disp_foci'] foci_disp_single = options['foci_disp_single']
if tilt_gravity: if tilt_gravity:
R = rotation_matrix(tilt_axis, np.radians(theta)) R = rotation_matrix(tilt_axis, np.radians(theta))
gravity_axis = np.dot(R, gravity_axis) gravity_axis = np.dot(R, gravity_axis)
gravity_axis_positions = np.vstack((x_Positions, y_Positions, z_Positions)) * gravity_axis[:, np.newaxis] gravity_axis_positions = np.vstack((x_Positions, y_Positions, z_Positions)) * gravity_axis[:, np.newaxis]
TrappingPotential = astigmatic_single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, del_y = disp_foci) TrappingPotential = astigmatic_single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, del_y = foci_disp_single)
TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis]) + gravitational_potential(gravity_axis_positions, m) TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis]) + gravitational_potential(gravity_axis_positions, m)
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK) TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
@ -472,15 +498,14 @@ def computeTrapPotential(w_x, w_z, Power, options):
return Positions, IdealTrappingPotential, TrappingPotential, TrapDepthsInKelvin, CalculatedTrapFrequencies, ExtractedTrapFrequencies return Positions, IdealTrappingPotential, TrappingPotential, TrapDepthsInKelvin, CalculatedTrapFrequencies, ExtractedTrapFrequencies
else: else:
delta = options['delta']
waists = np.vstack((np.asarray([w_x[0].value, w_z[0].value])*u.um, np.asarray([w_x[1].value, w_z[1].value])*u.um)) waists = np.vstack((np.asarray([w_x[0].value, w_z[0].value])*u.um, np.asarray([w_x[1].value, w_z[1].value])*u.um))
IdealTrappingPotential = crossed_beam_potential(Positions, delta, waists, P = Power) IdealTrappingPotential = crossed_beam_potential(Positions, waists, Power, options)
IdealTrappingPotential = IdealTrappingPotential * (np.ones((3, len(IdealTrappingPotential))) * projection_axis[:, np.newaxis]) IdealTrappingPotential = IdealTrappingPotential * (np.ones((3, len(IdealTrappingPotential))) * projection_axis[:, np.newaxis])
IdealTrappingPotential = (IdealTrappingPotential/ac.k_B).to(u.uK) IdealTrappingPotential = (IdealTrappingPotential/ac.k_B).to(u.uK)
if gravity and not astigmatism: if gravity and not astigmatism:
# Influence of Gravity # Influence of Gravity
m = 164*u.u m = DY_MASS
gravity_axis = np.array([0, 0, 1]) gravity_axis = np.array([0, 0, 1])
tilt_gravity = options['tilt_gravity'] tilt_gravity = options['tilt_gravity']
theta = options['theta'] theta = options['theta']
@ -489,37 +514,73 @@ def computeTrapPotential(w_x, w_z, Power, options):
R = rotation_matrix(tilt_axis, np.radians(theta)) R = rotation_matrix(tilt_axis, np.radians(theta))
gravity_axis = np.dot(R, gravity_axis) gravity_axis = np.dot(R, gravity_axis)
gravity_axis_positions = np.vstack((x_Positions, y_Positions, z_Positions)) * gravity_axis[:, np.newaxis] gravity_axis_positions = np.vstack((x_Positions, y_Positions, z_Positions)) * gravity_axis[:, np.newaxis]
TrappingPotential = crossed_beam_potential(Positions, delta, waists, P = Power) TrappingPotential = crossed_beam_potential(Positions, waists, Power, options)
TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis]) + gravitational_potential(gravity_axis_positions, m) TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis]) + gravitational_potential(gravity_axis_positions, m)
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK) TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
elif not gravity and astigmatism: elif not gravity and astigmatism:
# Influence of Astigmatism # Influence of Astigmatism
disp_foci = options['disp_foci_crossed'] TrappingPotential = astigmatic_crossed_beam_potential(Positions, waists, Power, options)
TrappingPotential = astigmatic_crossed_beam_potential(Positions, delta, waists, P = Power, del_y = disp_foci)
TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis]) TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis])
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK) TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
elif gravity and astigmatism: elif gravity and astigmatism:
# Influence of Gravity and Astigmatism # Influence of Gravity and Astigmatism
m = 164*u.u m = DY_MASS
gravity_axis = np.array([0, 0, 1]) gravity_axis = np.array([0, 0, 1])
tilt_gravity = options['tilt_gravity'] tilt_gravity = options['tilt_gravity']
theta = options['theta'] theta = options['theta']
tilt_axis = options['tilt_axis'] tilt_axis = options['tilt_axis']
disp_foci = options['disp_foci_crossed']
if tilt_gravity: if tilt_gravity:
R = rotation_matrix(tilt_axis, np.radians(theta)) R = rotation_matrix(tilt_axis, np.radians(theta))
gravity_axis = np.dot(R, gravity_axis) gravity_axis = np.dot(R, gravity_axis)
gravity_axis_positions = np.vstack((x_Positions, y_Positions, z_Positions)) * gravity_axis[:, np.newaxis] gravity_axis_positions = np.vstack((x_Positions, y_Positions, z_Positions)) * gravity_axis[:, np.newaxis]
TrappingPotential = astigmatic_crossed_beam_potential(Positions, delta, waists, P = Power, del_y = disp_foci) TrappingPotential = astigmatic_crossed_beam_potential(Positions, waists, Power, options)
TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis]) + gravitational_potential(gravity_axis_positions, m) TrappingPotential = TrappingPotential * (np.ones((3, len(TrappingPotential))) * projection_axis[:, np.newaxis]) + gravitational_potential(gravity_axis_positions, m)
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK) TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
else: else:
TrappingPotential = IdealTrappingPotential TrappingPotential = IdealTrappingPotential
return Positions, TrappingPotential infls = np.where(np.diff(np.sign(np.gradient(np.gradient(TrappingPotential[axis].value)))))[0]
try:
if TrappingPotential[axis][0] > TrappingPotential[axis][-1]:
EffectiveTrapDepthInKelvin = max(TrappingPotential[axis][infls[1]:-1]) - min(TrappingPotential[axis][infls[0]:infls[1]])
elif TrappingPotential[axis][0] < TrappingPotential[axis][-1]:
EffectiveTrapDepthInKelvin = max(TrappingPotential[axis][0:infls[0]]) - min(TrappingPotential[axis][infls[0]:infls[1]])
else:
EffectiveTrapDepthInKelvin = IdealTrapDepthInKelvin
except:
EffectiveTrapDepthInKelvin = np.nan
TrapDepthsInKelvin = [IdealTrapDepthInKelvin, EffectiveTrapDepthInKelvin]
v_x = calculateCrossedBeamTrapFrequency(options['delta'], [w_x, w_z], Power, dir = 'x')
v_y = calculateCrossedBeamTrapFrequency(options['delta'], [w_x, w_z], Power, dir = 'y')
v_z = calculateCrossedBeamTrapFrequency(options['delta'], [w_x, w_z], Power, dir = 'z')
CalculatedTrapFrequencies = [v_x, v_y, v_z]
v, dv, popt, pcov = extractTrapFrequency(Positions, IdealTrappingPotential, axis)
if np.isinf(v):
v = np.nan
if np.isinf(dv):
dv = np.nan
IdealTrapFrequency = [v, dv]
if options['extract_trap_frequencies']:
v, dv, popt, pcov = extractTrapFrequency(Positions, TrappingPotential, axis)
if np.isinf(v):
v = np.nan
if np.isinf(dv):
dv = np.nan
TrapFrequency = [v, dv]
ExtractedTrapFrequencies = [IdealTrapFrequency, TrapFrequency]
else:
ExtractedTrapFrequencies = [IdealTrapFrequency]
return Positions, IdealTrappingPotential, TrappingPotential, TrapDepthsInKelvin, CalculatedTrapFrequencies, ExtractedTrapFrequencies
def extractWaist(Positions, TrappingPotential): def extractWaist(Positions, TrappingPotential):
tmp_pos = Positions.value tmp_pos = Positions.value
@ -538,7 +599,7 @@ def extractWaist(Positions, TrappingPotential):
popt, pcov = curve_fit(gaussian_potential, xdata, Potential, p0) popt, pcov = curve_fit(gaussian_potential, xdata, Potential, p0)
return popt, pcov return popt, pcov
def computeIntensityProfileAndPotentials(Power, waists, wavelength, options, alpha = 184.4): def computeIntensityProfileAndPotentials(Power, waists, wavelength, options, alpha = DY_POLARIZABILITY):
w_x = waists[0] w_x = waists[0]
w_z = waists[1] w_z = waists[1]
extent = options['extent'] extent = options['extent']
@ -939,4 +1000,3 @@ def plotCollisionRatesAndPSD(Gamma_elastic, PSD, modulation_depth, new_aspect_ra
##################################################################### #####################################################################
#Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability