karthik/Calculations
1
0
Fork 0
Code Issues Pull Requests repo.project_board Releases Wiki Activity

Adding a new script to calculate Dipole Trap characteristics

Browse Source
This commit is contained in:
Karthik 2023-01-11 18:54:23 +01:00
parent df395f5311
commit 435fbccbfa
3 changed files with 180 additions and 20 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
+Scripts/optimizingForSidebandEnhancement.m
View File

@ -173,7 +173,7 @@ OptionsStruct.RescalingFactorForSecondParameter = 1000;
OptionsStruct.YLabelString = 'Beam Waist (mW)';
OptionsStruct.RescalingFactorForQuantityOfInterest = 1e-10;
% OptionsStruct.ZLabelString = 'Enhancement Factor (\eta)';
OptionsStruct.ZLabelString = 'Loading rate (x 10^{9} atoms/s)';
OptionsStruct.ZLabelString = 'Loading rate (x 10^{10} atoms/s)';
OptionsStruct.TitleString = sprintf('Magnetic Gradient = %.0f (G/cm)', MOT2D.MagneticGradient * 100);
options = Helper.convertstruct2cell(OptionsStruct);
@ -189,7 +189,7 @@ SidebandBeam = Beams{cellfun(@(x) strcmpi(x.Alias, 'BlueSideban
SidebandBeam.Power = 0.2;
NumberOfPointsForFirstParam = 20; %iterations of the simulation
NumberOfPointsForSecondParam = 20;
DetuningArray = linspace(-1.0, -5.0, NumberOfPointsForFirstParam) * Helper.PhysicsConstants.BlueLinewidth;
DetuningArray = linspace(-0.5, -2.5, NumberOfPointsForFirstParam) * Helper.PhysicsConstants.BlueLinewidth;
BeamWaistArray = linspace(10, 25, NumberOfPointsForSecondParam) * 1e-03;
tStart = tic;
@ -229,7 +229,7 @@ OptionsStruct.RescalingFactorForSecondParameter = 1000;
OptionsStruct.YLabelString = 'Beam Waist (mW)';
OptionsStruct.RescalingFactorForQuantityOfInterest = 1e-10;
% OptionsStruct.ZLabelString = 'Enhancement Factor (\eta)';
OptionsStruct.ZLabelString = 'Loading rate (x 10^{9} atoms/s)';
OptionsStruct.ZLabelString = 'Loading rate (x 10^{10} atoms/s)';
OptionsStruct.TitleString = sprintf('Magnetic Gradient = %.0f (G/cm)', MOT2D.MagneticGradient * 100);
options = Helper.convertstruct2cell(OptionsStruct);

151
calculateDipoleTrapPotential.py Normal file
View File

@ -0,0 +1,151 @@
import math
import numpy as np
import matplotlib.pyplot as plt
from astropy import units as u, constants as ac
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)
axis = axis / math.sqrt(np.dot(axis, axis))
a = math.cos(theta / 2.0)
b, c, d = -axis * math.sin(theta / 2.0)
aa, bb, cc, dd = a * a, b * b, c * c, d * d
bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d
return np.array([[aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac)],
[2 * (bc - ad), aa + cc - bb - dd, 2 * (cd + ab)],
[2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc]])
# Rayleigh range
def z_R(w_0:np.ndarray, lamb:float)->np.ndarray:
return np.pi*w_0**2/lamb
# Beam Radius
def w(pos, w_0, lamb):
return w_0*np.sqrt(1+(pos*lamb/(np.pi*w_0**2))**2)
def trap_depth(w_1:"float|u.quantity.Quantity", w_2:"float|u.quantity.Quantity", P:"float|u.quantity.Quantity", alpha:float)->"float|u.quantity.Quantity":
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 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:
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))
return U
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 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])
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')
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
# 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
extent = 1e4 # range of spatial coordinates in one direction to calculate trap potential over
TrappingPotential = []
ComputedPotentials = []
TrapDepthLabels = []
gravity = False
astigmatism = False
tilt_gravity = True
theta = 0 # in degrees
tilt_axis = [1, 0, 0] # lab space coordinates are rotated about x-axis in reference frame of beam
for p in Powers:
Power = p*u.W # Single Beam Power
TrapDepth = trap_depth(w_x, w_z, Power, alpha=Polarizability)
TrapDepthInKelvin = (TrapDepth/ac.k_B).to(u.uK)
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)
x_Positions = np.arange(-extent, extent, 1)*u.um
y_Positions = np.arange(-extent, extent, 1)*u.um
z_Positions = np.arange(-extent, extent, 1)*u.um
Positions = np.vstack((x_Positions, y_Positions, z_Positions)) * projection_axis[:, np.newaxis]
if not gravity and not astigmatism:
TrappingPotential = single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, alpha = Polarizability)
TrappingPotential = TrappingPotential + np.zeros((3, len(TrappingPotential))) * TrappingPotential.unit
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
elif gravity and not astigmatism:
# Influence of Gravity
m = 164*u.u
gravity_axis = np.array([0, 0, 1])
if tilt_gravity:
R = rotation_matrix(tilt_axis, np.radians(theta))
gravity_axis = np.dot(R, gravity_axis)
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)
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)

43
test_MOTCaptureProcessSimulation.m
View File

@ -25,16 +25,16 @@ MOT2D = Simulator.TwoDimensionalMOT(options{:});
Beams = MOT2D.Beams;
%% - Run Simulation
MOT2D.NumberOfAtoms = 5000;
MOT2D.NumberOfAtoms = 10000;
MOT2D.SidebandBeam = true;
MOT2D.PushBeam = false;
CoolingBeam = Beams{cellfun(@(x) strcmpi(x.Alias, 'Blue'), Beams)};
CoolingBeam.Power = 0.2;
CoolingBeam.Waist = 16.67e-03;
CoolingBeam.Waist = 20e-03;
CoolingBeam.Detuning = -1.33*Helper.PhysicsConstants.BlueLinewidth;
SidebandBeam = Beams{cellfun(@(x) strcmpi(x.Alias, 'BlueSideband'), Beams)};
SidebandBeam.Power = 0.4;
SidebandBeam.Waist = 16.67e-03;
SidebandBeam.Power = 0.2;
SidebandBeam.Waist = 20e-03;
SidebandBeam.Detuning = -2.66*Helper.PhysicsConstants.BlueLinewidth;
PushBeam = Beams{cellfun(@(x) strcmpi(x.Alias, 'Push'), Beams)};
PushBeam.Power = 0.025;
@ -227,7 +227,7 @@ clear OptionsStruct
%% COOLING BEAM WAIST VS DETUNING
MOT2D.NumberOfAtoms = 20000;
MOT2D.MagneticGradient = 0.38;
MOT2D.MagneticGradient = 0.40;
MOT2D.SidebandBeam = false;
MOT2D.PushBeam = false;
CoolingBeam = Beams{cellfun(@(x) strcmpi(x.Alias, 'Blue'), Beams)};
@ -320,15 +320,24 @@ CoolingBeam = Beams{cellfun(@(x) strcmpi(x.Alias, 'Blue'), Beams)};
SaturationIntensity = CoolingBeam.SaturationIntensity;
SaturationParameter = 0.1 * (8 * Power) / (pi*BeamWaist^2 * SaturationIntensity); % two beams are reflected
n = 1000;
t = 2*pi*rand(n,1);
r = BeamRadius*sqrt(rand(n,1));
% xmin = -15e-03;
% xmax = 15e-03;
% x = xmin+rand(n,1)*(xmax-xmin);
x = r.*cos(t);
y = ones(n,1) * 2e-03;
z = r.*sin(t);
n = 10000;
xmin = -BeamRadius;
xmax = BeamRadius;
x = xmin+rand(n,1)*(xmax-xmin);
y = ones(n,1) * 0;
zmin = -BeamRadius;
zmax = BeamRadius;
z = zmin+rand(n,1)*(zmax-zmin);
% t = 2*pi*rand(n,1);
% r = BeamRadius*sqrt(rand(n,1));
% x = r.*cos(t);
% y = ones(n,1) * 0;
% z = r.*sin(t);
PositionVector = horzcat(x, y, z); %scatter3(zeros(n,1), y, z)
CoolingBeamLocalSaturationIntensity = @(x) MOT2D.calculateLocalSaturationIntensity(0.25 * SaturationParameter, x, Origin, WaveVectorEndPoint(BeamNumber,:), BeamRadius, BeamWaist);
IntensityProfile = zeros(n,1);
@ -337,8 +346,8 @@ for i=1:n
end
v = IntensityProfile; % Extract intensity value
rows = 100;
columns = 100;
rows = 35;
columns = 35;
Image = zeros(rows, columns);
for k = 1 : length(x)
row = ceil((x(k) - min(x)) * columns / (max(x) - min(x)));
@ -395,7 +404,7 @@ f_h.Units = 'pixels';
set(0,'units','pixels');
screensize = get(0,'ScreenSize');
f_h.Position = [[screensize(3)/3.5 screensize(4)/3.5] 750 600];
[xq,zq] = meshgrid(linspace(-BeamWaist, BeamWaist, n), linspace(-BeamWaist, BeamWaist, n));
[xq,zq] = meshgrid(linspace(-BeamRadius, BeamRadius, n), linspace(-BeamRadius, BeamRadius, n));
vq = griddata(x,z,v,xq,zq);
mesh(xq,zq,vq)
hold on