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MAJOR UPDATE: Complete refactoring of the MOT simulation code to better reflect OOP.

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Karthik 2021-07-14 20:23:00 +02:00
parent 149d59f7c4
commit a9b7045c57
62 changed files with 1231 additions and 1529 deletions
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0
MOT Capture Process Simulation/+Helper/ImageSelection.class → +Helper/ImageSelection.class
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0
MOT Capture Process Simulation/+Helper/ImageSelection.java → +Helper/ImageSelection.java
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14
MOT Capture Process Simulation/+Helper/PhysicsConstants.m → +Helper/PhysicsConstants.m
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@ -28,14 +28,14 @@ classdef PhysicsConstants < handle
BlueWavelength = 421.291e-9;
BlueLandegFactor = 1.22;
BlueLifetime = 4.94e-9;
BlueLinewidth = 2.02e8;
OrangeWavelength = 626.086e-9;
OrangeLandegFactor = 1.29;
OrangeLifetime = 1.2e-6;
OrangeLinewidth = 8.5e5;
PushBeamLifetime = 1.2e-6;
BlueLinewidth = 1/4.94e-9;
RedWavelength = 626.086e-9;
RedLandegFactor = 1.29;
RedLifetime = 1.2e-6;
RedLinewidth = 1/1.2e-6;
PushBeamWaveLength = 626.086e-9;
PushBeamLinewidth = 8.5e5;
PushBeamLifetime = 1.2e-6;
PushBeamLinewidth = 1/1.2e-6;
end
methods

0
MOT Capture Process Simulation/+Helper/bringFiguresWithTagInForeground.m → +Helper/bringFiguresWithTagInForeground.m
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0
MOT Capture Process Simulation/+Helper/calculateDistanceFromPointToLine.m → +Helper/calculateDistanceFromPointToLine.m
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0
MOT Capture Process Simulation/+Helper/convertstruct2cell.m → +Helper/convertstruct2cell.m
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0
MOT Capture Process Simulation/+Helper/findAllZeroCrossings.m → +Helper/findAllZeroCrossings.m
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0
MOT Capture Process Simulation/+Helper/getFigureByTag.m → +Helper/getFigureByTag.m
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0
MOT Capture Process Simulation/+Helper/ode5.m → +Helper/ode5.m
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0
MOT Capture Process Simulation/+Helper/onenoteccdata.m → +Helper/onenoteccdata.m
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0
MOT Capture Process Simulation/+Helper/parforNotifications.m → +Helper/parforNotifications.m
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0
MOT Capture Process Simulation/+Helper/screencapture.m → +Helper/screencapture.m
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3
MOT Capture Process Simulation/+Plotting/plotAngularDistributionForDifferentBeta.m → +Plotter/plotAngularDistributionForDifferentBeta.m
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@ -15,8 +15,6 @@ function plotAngularDistributionForDifferentBeta(obj, Beta)
hold on
obj.reinitializeSimulator();
SimulationBeta = obj.Beta;
if ~ismember(SimulationBeta, Beta)
@ -38,7 +36,6 @@ function plotAngularDistributionForDifferentBeta(obj, Beta)
theta = linspace(0.0001,pi/2,1000);
J = zeros(1,length(theta));
obj.Beta = Beta(i);
obj.NozzleLength = (2 * obj.NozzleRadius) / Beta(i);
for j=1:length(theta)

6
MOT Capture Process Simulation/+Plotting/plotCaptureVelocityVsAngle.m → +Plotter/plotCaptureVelocityVsAngle.m
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@ -1,10 +1,10 @@
function plotCaptureVelocityVsAngle(obj)
function plotCaptureVelocityVsAngle(OvenObj, MOTObj)
theta = linspace(0, obj.NozzleExitDivergence, 1000);
theta = linspace(0, OvenObj.ExitDivergence, 1000);
CaptureVelocity = zeros(length(theta),3);
for i=1:length(theta)
CaptureVelocity(i,:) = obj.calculateCaptureVelocity([-obj.OvenDistance,0,0], [cos(theta(i)),0,sin(theta(i))]);
CaptureVelocity(i,:) = MOTObj.calculateCaptureVelocity(OvenObj, [-OvenObj.OvenDistance,0,0], [cos(theta(i)),0,sin(theta(i))]);
end
f_h = Helper.getFigureByTag('Capture Velocity');

0
MOT Capture Process Simulation/+Plotting/plotConfidenceIntervalRegion.m → +Plotter/plotConfidenceIntervalRegion.m
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85
+Plotter/plotDynamicalQuantities.m Normal file
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@ -0,0 +1,85 @@
function plotDynamicalQuantities(OvenObj, MOTObj, MaximumVelocity, IncidentAtomDirection, IncidentAtomPosition, varargin)
p = inputParser;
p.KeepUnmatched = true;
addRequired(p, 'OvenObject' , @isobject);
addRequired(p, 'MOTObject' , @isobject);
addRequired(p, 'MaximumVelocity' , @(x) assert(isnumeric(x) && isscalar(x)));
addRequired(p, 'IncidentAtomDirection' , @(x) assert(isnumeric(x) && isscalar(x)));
addRequired(p, 'IncidentAtomPosition' , @(x) assert(isnumeric(x) && isscalar(x)));
addParameter(p, 'PlotPositions' , false, @islogical);
addParameter(p, 'PlotVelocities' , false, @islogical);
p.parse(OvenObj, MOTObj, MaximumVelocity, IncidentAtomDirection, IncidentAtomPosition, varargin{:})
MaximumVelocity = p.Results.MaximumVelocity;
IncidentAtomDirection = p.Results.IncidentAtomDirection;
IncidentAtomPosition = p.Results.IncidentAtomDirection;
PlotPositions = p.Results.PlotPositions;
PlotVelocities = p.Results.PlotVelocities;
f_h = Helper.getFigureByTag('Trajectories Plot');
set(groot,'CurrentFigure',f_h);
a_h = get(f_h, 'CurrentAxes');
if ~isempty(get(a_h, 'Children'))
clf(f_h);
end
f_h.Name = 'Trajectories Plot';
f_h.Units = 'pixels';
set(0,'units','pixels');
screensize = get(0,'ScreenSize');
f_h.Position = [[screensize(3)/50 screensize(4)/3.5] 1870 600];
N = MOTObj.NumberOfAtoms;
Theta = IncidentAtomDirection;
z = IncidentAtomPosition;
L = OvenObj.OvenDistance * 2;
T = MOTObj.SimulationTime;
tau = MOTObj.TimeStep;
Y = linspace(0,MaximumVelocity,N);
DynamicalQuantities = zeros(length(Y),int64(T/tau),6);
for i=1:length(Y)
x =-L/2;
vx = Y(i)*cos(Theta);
vz = Y(i)*sin(Theta);
r = [x,0,z];
v = [vx,0,vz];
DynamicalQuantities(i,:,:) = MOTObj.solver(r, v);
end
LabelStringArrayForPositions = {'x (mm)', 'y (mm)', 'z (mm)'};
LabelStringArrayForVelocities = {'v_x (m/s)', 'v_y (m/s)', 'v_z (m/s)'};
colors = { [0, 0.4470, 0.7410], [0.8500, 0.3250, 0.0980], [0.4940, 0.1840, 0.5560]};
t = linspace(0, T, T/tau) * 1e+3;
for i=1:length(Y)
for j = 1:3
if PlotPositions
subplot(1, 3, j)
hold on
plot(t, DynamicalQuantities(i,:,j) * 1e+3,'Color', colors{j},'linewidth',1.3)
hXLabel = xlabel('Time (ms)');
hYLabel = ylabel(LabelStringArrayForPositions{j});
hold off
set([hXLabel, hYLabel], 'FontSize', 14);
elseif PlotVelocities
subplot(1, 3, j)
hold on
plot(t, DynamicalQuantities(i,:,j+3),'Color', colors{j},'linewidth',1.3)
hXLabel = xlabel('Time (ms)');
hYLabel = ylabel(LabelStringArrayForVelocities{j});
hold off
set([hXLabel, hYLabel], 'FontSize', 14);
end
end
end
hold off
hTitle = sgtitle(sprintf("Magnetic gradient = %.2f T/m", MOTObj.MagneticGradient));
set(hTitle, 'FontSize', 18);
Helper.bringFiguresWithTagInForeground();
end

11
MOT Capture Process Simulation/+Plotting/plotFreeMolecularFluxVsTemp.m → +Plotter/plotFreeMolecularFluxVsTemp.m
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@ -20,19 +20,18 @@ function plotFreeMolecularFluxVsTemp(obj, Temperature)
obj.OvenTemperature = Temperature(i);
flux = zeros(1,length(beta));
for j=1:length(beta)
obj.Beta = beta(j);
obj.NozzleLength = (2 * obj.NozzleRadius) / beta(j);
[ReducedClausingFactor, ~] = obj.calculateReducedClausingFactor();
flux(j) = ReducedClausingFactor * obj.calculateFreeMolecularRegimeFlux();
end
plot(beta, flux, 'DisplayName', sprintf('T = %.1f ℃', Temperature(i)), 'Linewidth', 1.5)
end
set(gca,'yscale','log')
obj.reinitializeSimulator();
[ReducedClausingFactor, ~] = obj.calculateReducedClausingFactor();
obj.restoreDefaults();
xline(obj.Beta, 'k--','Linewidth', 0.5);
fmf = ReducedClausingFactor * obj.calculateFreeMolecularRegimeFlux();
fmf = obj.ReducedClausingFactor * obj.calculateFreeMolecularRegimeFlux();
yline(fmf, 'k--', 'Linewidth', 1.5);
textstring = [sprintf('%1.e',fmf) ' atoms/s for ' '$$ \beta $$ = ' num2str(obj.Beta, '%.2f') sprintf(' @ %.2f K', obj.OvenTemperatureinKelvin)];
txt = text((obj.Beta + 0.05*obj.Beta), (max(fmf) + 0.2*fmf), textstring, 'Interpreter','latex');

14
MOT Capture Process Simulation/+Plotting/plotInitialVeloctiySamplingVsAngle.m → +Plotter/plotInitialVeloctiySamplingVsAngle.m
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@ -1,8 +1,6 @@
function plotInitialVeloctiySamplingVsAngle(obj, NumberOfBins)
function plotInitialVeloctiySamplingVsAngle(obj, MOTObj, NumberOfBins)
n = obj.NumberOfAtoms;
obj.setInitialConditions();
VelocitySamples = initialVelocitySampling(obj);
VelocitySamples = obj.initialVelocitySampling(MOTObj);
Speeds = zeros(length(VelocitySamples),1);
Angles = zeros(length(VelocitySamples),1);
@ -19,8 +17,8 @@ function plotInitialVeloctiySamplingVsAngle(obj, NumberOfBins)
* obj.OvenTemperatureinKelvin)));
c = integral(VelocityDistribution, 0, obj.VelocityCutoff);
AnglesArray = linspace(0, obj.NozzleExitDivergence,1000);
AngleBinSize = obj.NozzleExitDivergence / NumberOfBins;
AnglesArray = linspace(0, obj.ExitDivergence,1000);
AngleBinSize = obj.ExitDivergence / NumberOfBins;
dtheta = AnglesArray(2)-AnglesArray(1);
AngularDistribution = zeros(1,length(AnglesArray));
d = 0;
@ -57,8 +55,8 @@ function plotInitialVeloctiySamplingVsAngle(obj, NumberOfBins)
histogram(Angles .* 1e+03, NumberOfBins,'FaceAlpha',0.4, 'EdgeAlpha',0.4)
hold on
plot(AnglesArray .* 1e+03, (n/d * AngleBinSize .* AngularDistribution),'--', 'Linewidth',1.5)
xline(obj.NozzleExitDivergence.* 1e+03, 'k--', 'Linewidth', 1.5);
text((obj.NozzleExitDivergence - 0.5 * obj.NozzleExitDivergence).* 1e+03, max(h_1.Values) - 0.45 * max(h_1.Values), 'Maximum Allowed Divergence ----------->');
xline(obj.ExitDivergence.* 1e+03, 'k--', 'Linewidth', 1.5);
text((obj.ExitDivergence - 0.5 * obj.ExitDivergence).* 1e+03, max(h_1.Values) - 0.45 * max(h_1.Values), 'Maximum Allowed Divergence ----------->');
hXLabel_2 = xlabel('\theta (mrad)');
hYLabel_2 = ylabel('Counts');
hold off

0
MOT Capture Process Simulation/+Plotting/plotMeanFreePathAndVapourPressureVsTemp.m → +Plotter/plotMeanFreePathAndVapourPressureVsTemp.m
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19
MOT Capture Process Simulation/+Plotting/plotPhaseSpaceWithAccelerationField.m → +Plotter/plotPhaseSpaceWithAccelerationField.m
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@ -1,5 +1,4 @@
function plotPhaseSpaceWithAccelerationField(obj, MinimumVelocity, MaximumVelocity, NumberOfBins, IncidentAtomDirection, IncidentAtomPosition)
function plotPhaseSpaceWithAccelerationField(OvenObj, MOTObj, MinimumVelocity, MaximumVelocity, NumberOfBins, IncidentAtomDirection, IncidentAtomPosition)
f_h = Helper.getFigureByTag('Phase Space Plot');
set(groot,'CurrentFigure',f_h);
a_h = get(f_h, 'CurrentAxes');
@ -13,22 +12,22 @@ function plotPhaseSpaceWithAccelerationField(obj, MinimumVelocity, MaximumVeloci
screensize = get(0,'ScreenSize');
f_h.Position = [[screensize(3)/3.5 screensize(4)/3.5] 750 600];
N = obj.NumberOfAtoms;
L = obj.OvenDistance * 2;
N = MOTObj.NumberOfAtoms;
L = OvenObj.OvenDistance * 2;
Theta = IncidentAtomDirection;
z = IncidentAtomPosition;
T = obj.SimulationTime;
tau = obj.TimeStep;
T = MOTObj.SimulationTime;
tau = MOTObj.TimeStep;
[X,Y] = meshgrid(-L/2:L/NumberOfBins:L/2,-MaximumVelocity:2*MaximumVelocity/NumberOfBins:MaximumVelocity);
a=zeros(NumberOfBins+1,NumberOfBins+1,3);
obj.setInitialConditions();
MOTObj.restoreDefaults();
for i=1:length(X)
for j=1:length(Y)
a(i,j,:) = obj.calculateTotalAcceleration([X(1,i), 0, z], [Y(j,1)*cos(Theta),0,Y(j,1)*sin(Theta)]);
a(i,j,:) = MOTObj.calculateTotalAcceleration([X(1,i), 0, z], [Y(j,1)*cos(Theta),0,Y(j,1)*sin(Theta)]);
end
end
for i=1:length(X)
@ -57,7 +56,7 @@ function plotPhaseSpaceWithAccelerationField(obj, MinimumVelocity, MaximumVeloci
vz = Y(i)*sin(Theta);
r = [x,0,z];
v = [vx,0,vz];
DynamicalQuantities(i,:,:) = obj.solver(r, v);
DynamicalQuantities(i,:,:) = MOTObj.solver(r, v);
end
hold on
@ -70,7 +69,7 @@ function plotPhaseSpaceWithAccelerationField(obj, MinimumVelocity, MaximumVeloci
hXLabel = xlabel('Position: Along the x-axis (m)');
hYLabel = ylabel('Velocity (m/s)');
hTitle = sgtitle(sprintf("Magnetic gradient = %.2f T/m", obj.MagneticGradient));
hTitle = sgtitle(sprintf("Magnetic gradient = %.3f T/m", MOTObj.MagneticGradient));
set([hXLabel, hYLabel] , ...
'FontSize' , 14 );
set( hTitle , ...

0
MOT Capture Process Simulation/+Plotting/plotPositionAndVelocitySampling.m → +Plotter/plotPositionAndVelocitySampling.m
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0
MOT Capture Process Simulation/+Plotting/plotResultForOneParameterScan.m → +Plotter/plotResultForOneParameterScan.m
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0
MOT Capture Process Simulation/+Plotting/plotResultForTwoParameterScan.m → +Plotter/plotResultForTwoParameterScan.m
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0
MOT Capture Process Simulation/+Plotting/visualizeMagneticField.m → +Plotter/visualizeMagneticField.m
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203
+Simulator/@Beams/Beams.m Normal file
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@ -0,0 +1,203 @@
classdef Beams < handle & matlab.mixin.Copyable
properties (Access = private)
BlueBeamDefault = struct('Alias', 'Blue', ...
'Power', 400e-3, ...
'Detuning', -1.39*Helper.PhysicsConstants.BlueLinewidth, ...
'Radius', 16.67e-3, ...
'Waist', 15e-3, ...
'WaveNumber',2*pi/Helper.PhysicsConstants.BlueWavelength, ...
'Linewidth', Helper.PhysicsConstants.BlueLinewidth, ...
'SaturationIntensity', 0.1 * (2 * pi^2 / 3) * ...
((Helper.PhysicsConstants.PlanckConstantReduced * ...
Helper.PhysicsConstants.SpeedOfLight * ...
Helper.PhysicsConstants.BlueLinewidth) / (Helper.PhysicsConstants.BlueWavelength)^3));
BlueSidebandBeamDefault = struct('Alias', 'BlueSideband', ...
'Power', 200e-3, ...
'Detuning', -3*Helper.PhysicsConstants.BlueLinewidth, ...
'Radius', 16.67e-3, ...
'Waist', 10e-3, ...
'WaveNumber',2*pi/Helper.PhysicsConstants.BlueWavelength, ...
'Linewidth', Helper.PhysicsConstants.BlueLinewidth, ...
'SaturationIntensity', 0.1 * (2 * pi^2 / 3) * ...
((Helper.PhysicsConstants.PlanckConstantReduced * ...
Helper.PhysicsConstants.SpeedOfLight * ...
Helper.PhysicsConstants.BlueLinewidth) / (Helper.PhysicsConstants.BlueWavelength)^3));
PushBeamDefault = struct('Alias', 'Push', ...
'Power', 10e-3 , ...
'Detuning', 0*Helper.PhysicsConstants.RedLinewidth, ...
'Radius', 1.2e-03, ...
'Waist', 20.001e-3, ...
'WaveNumber',2*pi/Helper.PhysicsConstants.RedWavelength, ...
'Linewidth', Helper.PhysicsConstants.RedLinewidth, ...
'SaturationIntensity', 0.1 * (2 * pi^2 / 3) * ...
((Helper.PhysicsConstants.PlanckConstantReduced * ...
Helper.PhysicsConstants.SpeedOfLight * ...
Helper.PhysicsConstants.RedLinewidth) / (Helper.PhysicsConstants.RedWavelength)^3));
RedBeamDefault = struct('Alias', 'Red', ...
'Power', 100e-3 , ...
'Detuning', -1*Helper.PhysicsConstants.RedLinewidth, ...
'Radius', 1.2e-3, ...
'Waist', 12e-3 , ...
'WaveNumber',2*pi/Helper.PhysicsConstants.RedWavelength, ...
'Linewidth', Helper.PhysicsConstants.RedLinewidth, ...
'SaturationIntensity', 0.1 * (2 * pi^2 / 3) * ...
((Helper.PhysicsConstants.PlanckConstantReduced * ...
Helper.PhysicsConstants.SpeedOfLight * ...
Helper.PhysicsConstants.RedLinewidth) / (Helper.PhysicsConstants.RedWavelength)^3));
end
properties
Alias
Power;
Detuning;
Radius;
Waist;
WaveNumber;
SaturationIntensity;
Linewidth;
end
properties (Dependent)
SaturationParameter;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- Methods
methods
%% Class Constructor
function this = Beams(BeamName)
input = inputParser;
addRequired(input,'BeamName', @ischar);
parse(input, BeamName);
this.Alias = input.Results.BeamName;
switch this.Alias
case this.BlueBeamDefault.Alias
this.Power = this.BlueBeamDefault.Power;
this.Detuning = this.BlueBeamDefault.Detuning;
this.Radius = this.BlueBeamDefault.Radius;
this.Waist = this.BlueBeamDefault.Waist;
this.WaveNumber = this.BlueBeamDefault.WaveNumber;
this.Linewidth = this.BlueBeamDefault.Linewidth;
this.SaturationIntensity = this.BlueBeamDefault.SaturationIntensity;
case this.BlueSidebandBeamDefault.Alias
this.Power = this.BlueSidebandBeamDefault.Power;
this.Detuning = this.BlueSidebandBeamDefault.Detuning;
this.Radius = this.BlueSidebandBeamDefault.Radius;
this.Waist = this.BlueSidebandBeamDefault.Waist;
this.WaveNumber = this.BlueSidebandBeamDefault.WaveNumber;
this.Linewidth = this.BlueSidebandBeamDefault.Linewidth;
this.SaturationIntensity = this.BlueSidebandBeamDefault.SaturationIntensity;
case this.PushBeamDefault.Alias
this.Power = this.PushBeamDefault.Power;
this.Detuning = this.PushBeamDefault.Detuning;
this.Radius = this.PushBeamDefault.Radius;
this.Waist = this.PushBeamDefault.Waist;
this.WaveNumber = this.PushBeamDefault.WaveNumber;
this.Linewidth = this.PushBeamDefault.Linewidth;
this.SaturationIntensity = this.PushBeamDefault.SaturationIntensity;
case this.RedBeamDefault.Alias
this.Power = this.RedBeamDefault.Power;
this.Detuning = this.RedBeamDefault.Detuning;
this.Radius = this.RedBeamDefault.Radius;
this.Waist = this.RedBeamDefault.Waist;
this.WaveNumber = this.RedBeamDefault.WaveNumber;
this.Linewidth = this.RedBeamDefault.Linewidth;
this.SaturationIntensity = this.RedBeamDefault.SaturationIntensity;
otherwise
error('No such beam!')
end
end
end % - lifecycle
methods
function set.Power(this,val)
this.Power = val;
end
function ret = get.Power(this)
ret = this.Power;
end
function set.Detuning(this, val)
this.Detuning = val;
end
function ret = get.Detuning(this)
ret = this.Detuning;
end
function set.Radius(this, val)
this.Radius = val;
end
function ret = get.Radius(this)
ret = this.Radius;
end
function set.Waist(this, val)
this.Waist = val;
end
function ret = get.Waist(this)
ret = this.Waist;
end
function set.WaveNumber(this, val)
this.WaveNumber = val;
end
function ret = get.WaveNumber(this)
ret = this.WaveNumber;
end
function set.SaturationIntensity(this, val)
this.SaturationIntensity = val;
end
function ret = get.SaturationIntensity(this)
ret = this.SaturationIntensity;
end
function set.Linewidth(this, val)
this.Linewidth = val;
end
function ret = get.Linewidth(this)
ret = this.Linewidth;
end
end % - setters and getters
methods
function ret = get.SaturationParameter(this)
ret = 0.1 * (4 * this.Power) / (pi*this.Waist^2 * this.SaturationIntensity); % two beams are reflected
end
end % - getters for dependent properties
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- Methods
methods(Access = protected)
function cp = copyElement(this)
% Shallow copy object
cp = copyElement@matlab.mixin.Copyable(this);
% Forces the setter to redefine the function handles to the new copied object
pl = properties(this);
for k = 1:length(pl)
sc = superclasses(this.(pl{k}));
if any(contains(sc,{'matlab.mixin.Copyable'}))
cp.(pl{k}) = this.(pl{k}).copy();
end
end
end
end
methods (Static)
% Creates an Instance of Class, ensures singleton behaviour (that there
% can only be one Instance of this class
function singleObj = getInstance(BeamName)
% Creates an Instance of Class, ensures singleton behaviour
persistent localObj;
if isempty(localObj) || ~isvalid(localObj)
localObj = Simulator.Beams(BeamName);
end
singleObj = localObj;
end
end
end

173
+Simulator/@MOTCaptureProcess/MOTCaptureProcess.m Normal file
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@ -0,0 +1,173 @@
classdef MOTCaptureProcess < handle & matlab.mixin.Copyable
properties (Access = public)
SimulationMode; % MOT type
TimeStep;
SimulationTime;
NumberOfAtoms;
%Flags
SpontaneousEmission;
Sideband;
PushBeam;
ZeemanSlowerBeam;
Gravity;
BackgroundCollision;
DebugMode;
DoSave;
SaveDirectory;
end
properties
Beams = {}; %Contains beam objects
end % - public
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- Methods
methods
%% Class Destructor (Clears object)
function this = MOTCaptureProcess(varargin)
p = inputParser;
p.KeepUnmatched = true;
addParameter(p, 'SimulationMode', '2D',...
@(x) any(strcmpi(x,{'2D','3D', 'Full'})));
addParameter(p, 'NumberOfAtoms', 5000,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'TimeStep', 10e-06,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'SimulationTime', 3e-03,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'SpontaneousEmission', false,...
@islogical);
addParameter(p, 'Sideband', false,...
@islogical);
addParameter(p, 'PushBeam', false,...
@islogical);
addParameter(p, 'ZeemanSlowerBeam', false,...
@islogical);
addParameter(p, 'Gravity', false,...
@islogical);
addParameter(p, 'BackgroundCollision', false,...
@islogical);
addParameter(p, 'DebugMode', false,...
@islogical);
addParameter(p, 'SaveData', false,...
@islogical);
addParameter(p, 'SaveDirectory', pwd,...
@ischar);
p.parse(varargin{:});
this.SimulationMode = p.Results.SimulationMode;
this.NumberOfAtoms = p.Results.NumberOfAtoms;
this.TimeStep = p.Results.TimeStep;
this.SimulationTime = p.Results.SimulationTime;
this.SpontaneousEmission = p.Results.SpontaneousEmission;
this.Sideband = p.Results.Sideband;
this.PushBeam = p.Results.PushBeam;
this.ZeemanSlowerBeam = p.Results.ZeemanSlowerBeam;
this.Gravity = p.Results.Gravity;
this.BackgroundCollision = p.Results.BackgroundCollision;
this.DebugMode = p.Results.DebugMode;
this.DoSave = p.Results.SaveData;
this.SaveDirectory = p.Results.SaveDirectory;
switch this.SimulationMode
case "2D"
this.Beams{1} = Simulator.Beams('Blue');
this.Beams{2} = Simulator.Beams('BlueSideband');
this.Beams{3} = Simulator.Beams('Push');
case "3D"
this.Beams{1} = Simulator.Beams('Red');
% Development In progress
case "Full"
% Development In progress
end
end
end % - lifecycle
methods
function set.TimeStep(this, val)
assert(val > 1e-06, 'Not time efficient to compute for time steps smaller than 1 microsecond!');
this.TimeStep = val;
end
function ret = get.TimeStep(this)
ret = this.TimeStep;
end
function set.SimulationTime(this, val)
% assert(val <= 5e-03, 'Not time efficient to compute for time spans longer than 5 milliseconds!');
this.SimulationTime = val;
end
function ret = get.SimulationTime(this)
ret = this.SimulationTime;
end
function set.NumberOfAtoms(this, val)
assert(val <= 20000, 'Not time efficient to compute for atom numbers larger than 20,000!');
this.NumberOfAtoms = val;
end
function ret = get.NumberOfAtoms(this)
ret = this.NumberOfAtoms;
end
function set.DebugMode(this, val)
this.DebugMode = val;
end
function ret = get.DebugMode(this)
ret = this.DebugMode;
end
function set.DoSave(this, val)
this.DoSave = val;
end
function ret = get.DoSave(this)
ret = this.DoSave;
end
function set.SaveDirectory(this, val)
this.SaveDirectory = val;
end
function ret = get.SaveDirectory(this)
ret = this.SaveDirectory;
end
end % - setters and getters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- Methods
methods(Access = protected)
function cp = copyElement(this)
% Shallow copy object
cp = copyElement@matlab.mixin.Copyable(this);
% Forces the setter to redefine the function handles to the new copied object
pl = properties(this);
for k = 1:length(pl)
sc = superclasses(this.(pl{k}));
if any(contains(sc,{'matlab.mixin.Copyable'}))
cp.(pl{k}) = this.(pl{k}).copy();
end
end
end
end
methods (Static)
% Creates an Instance of Class, ensures singleton behaviour (that there
% can only be one Instance of this class
function singleObj = getInstance(varargin)
% Creates an Instance of Class, ensures singleton behaviour
persistent localObj;
if isempty(localObj) || ~isvalid(localObj)
localObj = Simulator.MOTCaptureProcess(varargin{:});
end
singleObj = localObj;
end
end
end

177
+Simulator/@Oven/Oven.m Normal file
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@ -0,0 +1,177 @@
classdef Oven < Simulator.MOTCaptureProcess & matlab.mixin.Copyable
properties (Access = private)
OvenDefaults = struct('NozzleLength', 60e-3, ...
'NozzleRadius', 2.60e-3, ...
'OvenTemperature', 1000);
end
properties (Access = public)
NozzleLength;
NozzleRadius;
OvenTemperature;
VelocityCutoff;
ClausingFactor;
ReducedClausingFactor;
ReducedFlux;
end
properties (Dependent)
ExitDivergence;
Beta;
OvenDistance;
OvenTemperatureinKelvin;
AverageVelocity;
AtomicBeamDensity;
MeanFreePath;
CollisionTime;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- Methods
methods
function this = Oven(varargin)
this@Simulator.MOTCaptureProcess('SimulationMode', '2D', varargin{:});
this.NozzleLength = this.OvenDefaults.NozzleLength;
this.NozzleRadius = this.OvenDefaults.NozzleRadius;
this.OvenTemperature = this.OvenDefaults.OvenTemperature;
this.ClausingFactor = this.calculateClausingFactor();
[this.ReducedClausingFactor, ~] = this.calculateReducedClausingFactor();
end
function restoreDefaults(this)
this.NozzleLength = this.OvenDefaults.NozzleLength;
this.NozzleRadius = this.OvenDefaults.NozzleRadius;
this.OvenTemperature = this.OvenDefaults.OvenTemperature;
this.ClausingFactor = this.calculateClausingFactor();
[this.ReducedClausingFactor, ~] = this.calculateReducedClausingFactor();
end
end % - lifecycle
methods
function set.NozzleLength(this,val)
this.NozzleLength = val;
end
function ret = get.NozzleLength(this)
ret = this.NozzleLength;
end
function set.NozzleRadius(this,val)
this.NozzleRadius = val;
end
function ret = get.NozzleRadius(this)
ret = this.NozzleRadius;
end
function set.OvenTemperature(this,val)
this.OvenTemperature = val;
end
function ret = get.OvenTemperature(this)
ret = this.OvenTemperature;
end
function set.VelocityCutoff(this,val)
this.VelocityCutoff = val;
end
function ret = get.VelocityCutoff(this)
ret = this.VelocityCutoff;
end
function set.ClausingFactor(this,val)
this.ClausingFactor = val;
end
function ret = get.ClausingFactor(this)
ret = this.ClausingFactor;
end
function set.ReducedClausingFactor(this,val)
this.ReducedClausingFactor = val;
end
function ret = get.ReducedClausingFactor(this)
ret = this.ReducedClausingFactor;
end
function set.ReducedFlux(this,val)
this.ReducedFlux = val;
end
function ret = get.ReducedFlux(this)
ret = this.ReducedFlux;
end
end % - setters and getters
methods
function ret = get.Beta(this)
ret = 2 * (this.NozzleRadius/this.NozzleLength);
end
function ret = get.OvenDistance(this)
ApertureCut = max(2.5e-3,this.NozzleRadius);
ret = (25+12.5)*1e-3 + (this.NozzleRadius + ApertureCut) / tan(15/360 * 2 * pi);
end
function ret = get.ExitDivergence(this)
Theta_Nozzle = atan((this.NozzleRadius + 0.035/sqrt(2))/this.OvenDistance); % The angle of capture region towards the oven nozzle
Theta_Aperture = 15/360*2*pi; % The limitation angle of the second aperture in the oven
ret = min(Theta_Nozzle,Theta_Aperture);
end
function ret = get.OvenTemperatureinKelvin(this)
ret = this.OvenTemperature + Helper.PhysicsConstants.ZeroKelvin;
end
function ret = get.AverageVelocity(this)
%See Background collision probability section in Barbiero
ret = sqrt((8 * pi * Helper.PhysicsConstants.BoltzmannConstant*this.OvenTemperatureinKelvin)/ (9 * Helper.PhysicsConstants.Dy164Mass));
end
function ret = get.AtomicBeamDensity(this)
%See Background collision probability section in Barbiero
ret = this.calculateFreeMolecularRegimeFlux() / (this.AverageVelocity * pi * (this.Beta*this.NozzleLength/2)^2);
end
function ret = get.MeanFreePath(this)
% Cross section = pi ( 2 * Van-der-waals radius of Dy)^2;
% Van-der-waals radius of Dy = 281e-12
%See Expected atomic flux section and Background collision probability section in Barbiero
ret = 1/(sqrt(2) * ( pi * (2*281e-12)^2) * this.AtomicBeamDensity);
end
function ret = get.CollisionTime(this)
ret = 3 * this.MeanFreePath/this.AverageVelocity; %See Background collision probability section in Barbiero
end
end % - getters for dependent properties
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- Methods
methods(Access = protected)
function cp = copyElement(this)
% Shallow copy object
cp = copyElement@matlab.mixin.Copyable(this);
% Forces the setter to redefine the function handles to the new copied object
pl = properties(this);
for k = 1:length(pl)
sc = superclasses(this.(pl{k}));
if any(contains(sc,{'matlab.mixin.Copyable'}))
cp.(pl{k}) = this.(pl{k}).copy();
end
end
end
end
methods (Static)
% Creates an Instance of Class, ensures singleton behaviour (that there
% can only be one Instance of this class
function singleObj = getInstance(varargin)
% Creates an Instance of Class, ensures singleton behaviour
persistent localObj;
if isempty(localObj) || ~isvalid(localObj)
localObj = Simulator.Oven();
end
singleObj = localObj;
end
end
end

0
MOT Capture Process Simulation/@MOTSimulator/angularDistributionFunction.m → +Simulator/@Oven/angularDistributionFunction.m
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0
MOT Capture Process Simulation/@MOTSimulator/calculateClausingFactor.m → +Simulator/@Oven/calculateClausingFactor.m
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0
MOT Capture Process Simulation/@MOTSimulator/calculateFreeMolecularRegimeFlux.m → +Simulator/@Oven/calculateFreeMolecularRegimeFlux.m
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2
MOT Capture Process Simulation/@MOTSimulator/calculateReducedClausingFactor.m → +Simulator/@Oven/calculateReducedClausingFactor.m
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@ -9,7 +9,7 @@ function [ReducedClausingFactor, NormalizationConstantForAngularDistribution] =
ReducedClausingFactor = 0; % We have to calculate the probability of an atom coming out of the oven subject to the physical constraint
parfor p = 1:length(ThetaArray) % that the angle of divergence is not more than the angle subtended at the mouth of the nozzle
if ThetaArray(p) <= this.NozzleExitDivergence
if ThetaArray(p) <= this.ExitDivergence
ReducedClausingFactor = ReducedClausingFactor + (2 * pi * sin(ThetaArray(p)) * AngularDistribution(p) * (ThetaArray(2)-ThetaArray(1)));
end
end

7
+Simulator/@Oven/initialPositionSampling.m Normal file
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@ -0,0 +1,7 @@
function ret = initialPositionSampling(this)
n = this.NumberOfAtoms;
phi = 2 * pi * rand(n,1);
rho = this.Beta * 0.5 * this.NozzleLength * sqrt(rand(n,1));
ret = [-this.OvenDistance * ones(n,1), rho.*cos(phi), rho.*sin(phi)];
end

59
+Simulator/@Oven/initialVelocitySampling.m Normal file
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@ -0,0 +1,59 @@
function ret = initialVelocitySampling(this, MOTObj)
n = this.NumberOfAtoms;
% Calculate Calculate Capture velocity --> Introduce velocity cutoff
MOTObj.CaptureVelocity = 1.05 * MOTObj.calculateCaptureVelocity(this, [-this.OvenDistance,0,0], [1,0,0]);
this.VelocityCutoff = MOTObj.CaptureVelocity(1); % Should be the magnitude of the 3-D velocity vector but since here the obtained capture
% velocity is only along the x-axis, we take the first term which is the x-component of the velocity.
[ReducedClausingFactor, NormalizationConstantForAngularDistribution] = this.calculateReducedClausingFactor();
this.ReducedClausingFactor = ReducedClausingFactor;
VelocityDistribution = @(velocity) sqrt(2 / pi) * sqrt(Helper.PhysicsConstants.Dy164Mass/(Helper.PhysicsConstants.BoltzmannConstant * this.OvenTemperatureinKelvin))^3 ...
* velocity.^3 .* exp(-velocity.^2 .* (Helper.PhysicsConstants.Dy164Mass / (2 * Helper.PhysicsConstants.BoltzmannConstant ...
* this.OvenTemperatureinKelvin)));
c = integral(VelocityDistribution, 0, this.VelocityCutoff);
this.ReducedFlux = c * this.ReducedClausingFactor * this.calculateFreeMolecularRegimeFlux();
ret = zeros(n,3);
SampledVelocityMagnitude = zeros(n,1);
SampledPolarAngle = zeros(n,1);
SampledAzimuthalAngle = zeros(n,1);
MostProbableVelocity = sqrt((3 * Helper.PhysicsConstants.BoltzmannConstant * this.OvenTemperature) / Helper.PhysicsConstants.Dy164Mass); % For v * f(v) distribution
if MostProbableVelocity > this.VelocityCutoff
MaximumVelocityAllowed = this.VelocityCutoff;
else
MaximumVelocityAllowed = MostProbableVelocity;
end
NormalizationConstantForVelocityDistribution = this.velocityDistributionFunction(MaximumVelocityAllowed);
parfor i = 1:n
% Rejection Sampling of speed
y = rand(1);
x = this.VelocityCutoff * rand(1);
while y > ((NormalizationConstantForVelocityDistribution)^-1 * this.velocityDistributionFunction(x)) %As long as this loop condition is satisfied, reject the corresponding x value
y = rand(1);
x = this.VelocityCutoff * rand(1);
end
SampledVelocityMagnitude(i) = x; % When loop condition is not satisfied, accept x value and store as sample
% Rejection Sampling of polar angle
w = rand(1);
z = this.ExitDivergence * rand(1);
while w > ((NormalizationConstantForAngularDistribution)^-1 * 2 * pi * this.angularDistributionFunction(z) * sin(z)) %As long as this loop condition is satisfied, reject the corresponding x value
w = rand(1);
z = this.ExitDivergence * rand(1);
end
SampledPolarAngle(i) = z; %When loop condition is not satisfied, accept x value and store as sample
% Sampling of azimuthal angle
SampledAzimuthalAngle(i)= 2 * pi * rand(1);
ret(i,:)=[SampledVelocityMagnitude(i)*cos(SampledPolarAngle(i)), SampledVelocityMagnitude(i)*sin(SampledPolarAngle(i))*cos(SampledAzimuthalAngle(i)), ...
SampledVelocityMagnitude(i)*sin(SampledPolarAngle(i))*sin(SampledAzimuthalAngle(i))];
end

0
MOT Capture Process Simulation/@MOTSimulator/velocityDistributionFunction.m → +Simulator/@Oven/velocityDistributionFunction.m
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169
+Simulator/@TwoDimensionalMOT/TwoDimensionalMOT.m Normal file
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@ -0,0 +1,169 @@
classdef TwoDimensionalMOT < Simulator.MOTCaptureProcess & matlab.mixin.Copyable
properties (Access = private)
MagneticGradienDefault = 0.425; % T/m
ExitDivergenceDefault = 16e-3;
DistanceBetweenPushBeamAnd3DMOTCenterDefault = 0;
PushBeamDistanceDefault = 0.32;
end
properties (Access = public)
TotalPower;
LandegFactor;
MagneticSubLevel;
MagneticGradient;
CaptureVelocity;
ExitDivergence;
DistanceBetweenPushBeamAnd3DMOTCenter;
PushBeamDistance;
TimeSpentInInteractionRegion;
ParticleDynamicalQuantities;
InitialParameters;
end
methods
function this = TwoDimensionalMOT(varargin)
this@Simulator.MOTCaptureProcess('SimulationMode', '2D', varargin{:});
p = inputParser;
p.KeepUnmatched = true;
addParameter(p, 'TotalPower', 0.8,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'LandegFactor', 1,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'MagneticSubLevel', 1,...
@(x) assert(isnumeric(x) && isscalar(x)));
addParameter(p, 'MagneticGradient', 0.38,...
@(x) assert(isnumeric(x) && isscalar(x)));
p.parse(varargin{:});
this.TotalPower = p.Results.TotalPower;
this.LandegFactor = p.Results.LandegFactor;
this.MagneticSubLevel = p.Results.MagneticSubLevel;
this.MagneticGradient = p.Results.MagneticGradient;
this.ExitDivergence = this.ExitDivergenceDefault;
this.DistanceBetweenPushBeamAnd3DMOTCenter = this.DistanceBetweenPushBeamAnd3DMOTCenterDefault;
this.PushBeamDistance = this.PushBeamDistanceDefault;
this.InitialParameters = struct;
this.InitialParameters.TotalPower = this.TotalPower;
this.InitialParameters.LandegFactor = this.LandegFactor;
this.InitialParameters.MagneticSubLevel= this.MagneticSubLevel;
this.InitialParameters.MagneticGradient= this.MagneticGradient;
end
function restoreDefaults(this)
this.TotalPower = this.InitialParameters.TotalPower;
this.LandegFactor = this.InitialParameters.LandegFactor;
this.MagneticSubLevel = this.InitialParameters.MagneticSubLevel;
this.MagneticGradient = this.InitialParameters.MagneticGradient;
this.ExitDivergence = this.ExitDivergenceDefault;
this.DistanceBetweenPushBeamAnd3DMOTCenter = this.DistanceBetweenPushBeamAnd3DMOTCenterDefault;
this.PushBeamDistance = this.PushBeamDistanceDefault;
end
end % - lifecycle
methods
function set.TotalPower(this,val)
this.TotalPower = val;
end
function ret = get.TotalPower(this)
ret = this.TotalPower;
end
function set.LandegFactor(this,val)
this.LandegFactor = val;
end
function ret = get.LandegFactor(this)
ret = this.LandegFactor;
end
function set.MagneticSubLevel(this,val)
this.MagneticSubLevel = val;
end
function ret = get.MagneticSubLevel(this)
ret = this.MagneticSubLevel;
end
function set.MagneticGradient(this,val)
this.MagneticGradient = val;
end
function ret = get.MagneticGradient(this)
ret = this.MagneticGradient;
end
function set.CaptureVelocity(this,val)
this.CaptureVelocity = val;
end
function ret = get.CaptureVelocity(this)
ret = this.CaptureVelocity;
end
function set.ExitDivergence(this,val)
this.ExitDivergence = val;
end
function ret = get.ExitDivergence(this)
ret = this.ExitDivergence;
end
function set.DistanceBetweenPushBeamAnd3DMOTCenter(this,val)
this.DistanceBetweenPushBeamAnd3DMOTCenter = val;
end
function ret = get.DistanceBetweenPushBeamAnd3DMOTCenter(this)
ret = this.DistanceBetweenPushBeamAnd3DMOTCenter;
end
function set.PushBeamDistance(this,val)
this.PushBeamDistance = val;
end
function ret = get.PushBeamDistance(this)
ret = this.PushBeamDistance;
end
function set.TimeSpentInInteractionRegion(this,val)
this.TimeSpentInInteractionRegion = val;
end
function ret = get.TimeSpentInInteractionRegion(this)
ret = this.TimeSpentInInteractionRegion;
end
function set.ParticleDynamicalQuantities(this,val)
this.ParticleDynamicalQuantities = val;
end
function ret = get.ParticleDynamicalQuantities(this)
ret = this.ParticleDynamicalQuantities;
end
function set.InitialParameters(this,val)
this.InitialParameters = val;
end
function ret = get.InitialParameters(this)
ret = this.InitialParameters;
end
end % - setters and getters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- Methods
methods(Access = protected)
function cp = copyElement(this)
% Shallow copy object
cp = copyElement@matlab.mixin.Copyable(this);
% Forces the setter to redefine the function handles to the new copied object
pl = properties(this);
for k = 1:length(pl)
sc = superclasses(this.(pl{k}));
if any(contains(sc,{'matlab.mixin.Copyable'}))
cp.(pl{k}) = this.(pl{k}).copy();
end
end
end
end
methods (Static)
% Creates an Instance of Class, ensures singleton behaviour (that there
% can only be one Instance of this class
function singleObj = getInstance(varargin)
% Creates an Instance of Class, ensures singleton behaviour
persistent localObj;
if isempty(localObj) || ~isvalid(localObj)
localObj = Simulator.TwoDimensionalMOT(varargin{:});
end
singleObj = localObj;
end
end
end

35
+Simulator/@TwoDimensionalMOT/accelerationDueToPushBeam.m Normal file
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@ -0,0 +1,35 @@
function ret = accelerationDueToPushBeam(this, PositionVector, VelocityVector)
% is the distance between the chamber center and the cross point of push beam and z-axis (along the gravity)
WaveVectorEndPoint = [0, 1, this.DistanceBetweenPushBeamAnd3DMOTCenter/this.PushBeamDistance];
WaveVectorEndPoint = WaveVectorEndPoint./norm(WaveVectorEndPoint);
Origin=[0,0,0];
PushBeamObj = this.Beams{cellfun(@(x) strcmpi(x.Alias, 'Push'), this.Beams)};
PushBeamDetuning = PushBeamObj.Detuning;
PushBeamRadius = PushBeamObj.Radius;
PushBeamWaist = PushBeamObj.Waist;
PushBeamWaveNumber = PushBeamObj.WaveNumber;
PushBeamLinewidth = PushBeamObj.Linewidth;
PushBeamSaturationParameter = 0.25 * PushBeamObj.SaturationParameter;
SaturationIntensity = this.calculateLocalSaturationIntensity(PushBeamSaturationParameter, PositionVector, Origin, WaveVectorEndPoint, PushBeamRadius, PushBeamWaist);
DopplerShift = dot(WaveVectorEndPoint(:), VelocityVector) * PushBeamWaveNumber;
Detuning = PushBeamDetuning - DopplerShift;
s_push = SaturationIntensity/(1 + SaturationIntensity + (4 * (Detuning./PushBeamLinewidth).^2));
a_sat = (Helper.PhysicsConstants.PlanckConstantReduced * PushBeamWaveNumber * WaveVectorEndPoint(:)/Helper.PhysicsConstants.Dy164Mass).*(PushBeamLinewidth * 0.5);
a_push = a_sat .* (s_push/(1+s_push));
if this.SpontaneousEmission
a_scatter = this.accelerationDueToSpontaneousEmissionProcess(s_push, s_push, PushBeamLinewidth, PushBeamWaveNumber);
else
a_scatter = [0,0,0];
end
a_total = a_push + a_scatter;
ret = a_total(1:3);
end

0
MOT Capture Process Simulation/@MOTSimulator/accelerationDueToSpontaneousEmissionProcess.m → +Simulator/@TwoDimensionalMOT/accelerationDueToSpontaneousEmissionProcess.m
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7
MOT Capture Process Simulation/@MOTSimulator/bootstrapErrorEstimation.m → +Simulator/@TwoDimensionalMOT/bootstrapErrorEstimation.m
View File

@ -1,5 +1,4 @@
function [LoadingRate, StandardError, ConfidenceInterval] = bootstrapErrorEstimation(this, NumberOfLoadedAtoms)
function [LoadingRate, StandardError, ConfidenceInterval] = bootstrapErrorEstimation(this, ovenObj, NumberOfLoadedAtoms)
n = this.NumberOfAtoms;
NumberOfTimeSteps = int64(this.SimulationTime/this.TimeStep);
@ -16,14 +15,14 @@ function [LoadingRate, StandardError, ConfidenceInterval] = bootstrapErrorEstima
MeanLoadingRatioInEachSample(SampleNumber) = mean(BoostrapSample) / n; % Empirical bootstrap distribution of sample means
end
LoadingRate = mean(MeanLoadingRatioInEachSample) * this.ReducedFlux;
LoadingRate = mean(MeanLoadingRatioInEachSample) * ovenObj.ReducedFlux;
Variance = 0; % Bootstrap Estimate of Variance
for SampleNumber = 1:NumberOfBootsrapSamples
Variance = Variance + (MeanLoadingRatioInEachSample(SampleNumber) - mean(MeanLoadingRatioInEachSample))^2;
end
StandardError = sqrt((1 / (NumberOfBootsrapSamples-1)) * Variance) * this.ReducedFlux;
StandardError = sqrt((1 / (NumberOfBootsrapSamples-1)) * Variance) * ovenObj.ReducedFlux;
ts = tinv([0.025 0.975],NumberOfBootsrapSamples-1); % T-Score
ConfidenceInterval = LoadingRate + ts*StandardError; % 95% Confidence Intervals

22
+Simulator/@TwoDimensionalMOT/calculateCaptureVelocity.m Normal file
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@ -0,0 +1,22 @@
function ret = calculateCaptureVelocity(this, ovenObj, PositionVector, VelocityVector)
VelocityUnitVector = VelocityVector./norm(VelocityVector);
UpperLimit = 500;
LowerLimit = 0;
for Index = 1:500
InitialVelocity = (0.5 * (UpperLimit + LowerLimit)) * VelocityUnitVector;
ParticleDynamicalQuantities = this.solver(PositionVector, InitialVelocity);
FinalPositionVector = ParticleDynamicalQuantities(end, 1:3);
if rssq(FinalPositionVector) <= ovenObj.OvenDistance
LowerLimit = 0.5 * (UpperLimit + LowerLimit);
else
UpperLimit = 0.5 * (UpperLimit + LowerLimit);
end
if UpperLimit - LowerLimit < 1
ret = (0.5 * (UpperLimit + LowerLimit)) * VelocityUnitVector;
break;
end
end
end

29
+Simulator/@TwoDimensionalMOT/calculateLoadingRate.m Normal file
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@ -0,0 +1,29 @@
function [LoadingRate, StandardError, ConfidenceInterval] = calculateLoadingRate(this, ovenObj)
n = this.NumberOfAtoms;
DynamicalQuantities = this.ParticleDynamicalQuantities;
NumberOfTimeSteps = int64(this.SimulationTime/this.TimeStep);
NumberOfLoadedAtoms = zeros(1, NumberOfTimeSteps);
CollisionEvents = zeros(1, n);
% Include the stochastic process of background collisions
for AtomIndex = 1:n
this.TimeSpentInInteractionRegion(AtomIndex) = this.computeTimeSpentInInteractionRegion(squeeze(DynamicalQuantities(AtomIndex,:,1:3)));
CollisionEvents(AtomIndex) = this.computeCollisionProbability(ovenObj, this.TimeSpentInInteractionRegion(AtomIndex));
end
% Count the number of loaded atoms subject to conditions
for TimeIndex = 1:NumberOfTimeSteps
if TimeIndex ~= 1
NumberOfLoadedAtoms(TimeIndex) = NumberOfLoadedAtoms(TimeIndex-1);
end
for AtomIndex = 1:n
Position = squeeze(DynamicalQuantities(AtomIndex, TimeIndex, 1:3))';
Velocity = squeeze(DynamicalQuantities(AtomIndex, TimeIndex, 4:6))';
if this.exitCondition(ovenObj, Position, Velocity, CollisionEvents(AtomIndex))
NumberOfLoadedAtoms(TimeIndex) = NumberOfLoadedAtoms(TimeIndex) + 1;
end
end
end
[LoadingRate, StandardError, ConfidenceInterval] = this.bootstrapErrorEstimation(ovenObj, NumberOfLoadedAtoms);
end

0
MOT Capture Process Simulation/@MOTSimulator/calculateLocalSaturationIntensity.m → +Simulator/@TwoDimensionalMOT/calculateLocalSaturationIntensity.m
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49
MOT Capture Process Simulation/@MOTSimulator/calculateTotalAcceleration.m → +Simulator/@TwoDimensionalMOT/calculateTotalAcceleration.m
View File

@ -1,5 +1,18 @@
function ret = calculateTotalAcceleration(this, PositionVector, VelocityVector)
CoolingBeamObj = this.Beams{cellfun(@(x) strcmpi(x.Alias, 'Blue'), this.Beams)};
CoolingBeamDetuning = CoolingBeamObj.Detuning;
CoolingBeamRadius = CoolingBeamObj.Radius;
CoolingBeamWaist = CoolingBeamObj.Waist;
CoolingBeamWaveNumber = CoolingBeamObj.WaveNumber;
CoolingBeamLinewidth = CoolingBeamObj.Linewidth;
CoolingBeamSaturationParameter = CoolingBeamObj.SaturationParameter;
SidebandBeamObj = this.Beams{cellfun(@(x) strcmpi(x.Alias, 'BlueSideband'), this.Beams)};
SidebandDetuning = SidebandBeamObj.Detuning;
SidebandBeamRadius = SidebandBeamObj.Radius;
SidebandBeamWaist = SidebandBeamObj.Waist;
SidebandSaturationParameter = SidebandBeamObj.SaturationParameter;
WaveVectorEndPoint = zeros(2,3);
WaveVectorEndPoint(1,:) = [1,0,1];
WaveVectorEndPoint(1,:) = WaveVectorEndPoint(1,1:3)/norm(WaveVectorEndPoint(1,:));
@ -10,11 +23,11 @@ function ret = calculateTotalAcceleration(this, PositionVector, VelocityVector)
Origin = [0,0,0];
% Calculate the Saturation Intensity at the specified point along its Gaussian Profile
CoolingBeamLocalSaturationIntensity = [this.calculateLocalSaturationIntensity(0.25 * this.CoolingBeamSaturationParameter, PositionVector, Origin, WaveVectorEndPoint(1,:), this.CoolingBeamRadius, this.CoolingBeamWaist), ...
this.calculateLocalSaturationIntensity(0.25 * this.CoolingBeamSaturationParameter, PositionVector, Origin, WaveVectorEndPoint(2,:), this.CoolingBeamRadius, this.CoolingBeamWaist)];
CoolingBeamLocalSaturationIntensity = [this.calculateLocalSaturationIntensity(0.25 * CoolingBeamSaturationParameter, PositionVector, Origin, WaveVectorEndPoint(1,:), CoolingBeamRadius, CoolingBeamWaist), ...
this.calculateLocalSaturationIntensity(0.25 * CoolingBeamSaturationParameter, PositionVector, Origin, WaveVectorEndPoint(2,:), CoolingBeamRadius, CoolingBeamWaist)];
SidebandLocalSaturationIntensity = [this.calculateLocalSaturationIntensity(0.25 * this.SidebandSaturationParameter, PositionVector, Origin, WaveVectorEndPoint(1,:), this.SidebandBeamRadius, this.SidebandBeamWaist), ...
this.calculateLocalSaturationIntensity(0.25 * this.SidebandSaturationParameter, PositionVector, Origin, WaveVectorEndPoint(2,:), this.SidebandBeamRadius, this.SidebandBeamWaist)];
SidebandLocalSaturationIntensity = [this.calculateLocalSaturationIntensity(0.25 * SidebandSaturationParameter, PositionVector, Origin, WaveVectorEndPoint(1,:), SidebandBeamRadius, SidebandBeamWaist), ...
this.calculateLocalSaturationIntensity(0.25 * SidebandSaturationParameter, PositionVector, Origin, WaveVectorEndPoint(2,:), SidebandBeamRadius, SidebandBeamWaist)];
TotalAcceleration = zeros(1,3);
@ -29,25 +42,25 @@ function ret = calculateTotalAcceleration(this, PositionVector, VelocityVector)
ZeemanShift = this.LandegFactor * this.MagneticSubLevel * (Helper.PhysicsConstants.BohrMagneton / Helper.PhysicsConstants.PlanckConstantReduced) * B;
DopplerShift = dot(WaveVectorEndPoint(i,:), VelocityVector) * this.CoolingBeamWaveNumber;
DopplerShift = dot(WaveVectorEndPoint(i,:), VelocityVector) * CoolingBeamWaveNumber;
Delta_Cooling(i*2-1) = this.CoolingBeamDetuning + DopplerShift + (ZeemanShift * Sigma(i));
Delta_Cooling(i*2) = this.CoolingBeamDetuning - DopplerShift - (ZeemanShift * Sigma(i));
Delta_Cooling(i*2-1) = CoolingBeamDetuning + DopplerShift + (ZeemanShift * Sigma(i));
Delta_Cooling(i*2) = CoolingBeamDetuning - DopplerShift - (ZeemanShift * Sigma(i));
if this.Sideband
Delta_Sideband(i*2-1) = this.SidebandDetuning + DopplerShift + (ZeemanShift * Sigma(i));
Delta_Sideband(i*2) = this.SidebandDetuning - DopplerShift - (ZeemanShift * Sigma(i));
Delta_Sideband(i*2-1) = SidebandDetuning + DopplerShift + (ZeemanShift * Sigma(i));
Delta_Sideband(i*2) = SidebandDetuning - DopplerShift - (ZeemanShift * Sigma(i));
end
end
SaturationParameter = [0,0,0,0,0,0,0,0];
for i = 1:2
SaturationParameter(2*i-1) = CoolingBeamLocalSaturationIntensity(i) /(1 + 4 * (Delta_Cooling(2*i-1)/this.CoolingBeamLinewidth)^2);
SaturationParameter(2*i) = CoolingBeamLocalSaturationIntensity(i) /(1 + 4 * (Delta_Cooling(2*i) /this.CoolingBeamLinewidth)^2);
SaturationParameter(2*i-1) = CoolingBeamLocalSaturationIntensity(i) /(1 + 4 * (Delta_Cooling(2*i-1)/CoolingBeamLinewidth)^2);
SaturationParameter(2*i) = CoolingBeamLocalSaturationIntensity(i) /(1 + 4 * (Delta_Cooling(2*i) /CoolingBeamLinewidth)^2);
if this.Sideband
SaturationParameter(2*i-1+4) = SidebandLocalSaturationIntensity(i) /(1 + 4 * (Delta_Sideband(2*i-1)/this.CoolingBeamLinewidth)^2);
SaturationParameter(2*i+4) = SidebandLocalSaturationIntensity(i) /(1 + 4 * (Delta_Sideband(2*i)/this.CoolingBeamLinewidth)^2);
SaturationParameter(2*i-1+4) = SidebandLocalSaturationIntensity(i) /(1 + 4 * (Delta_Sideband(2*i-1)/CoolingBeamLinewidth)^2);
SaturationParameter(2*i+4) = SidebandLocalSaturationIntensity(i) /(1 + 4 * (Delta_Sideband(2*i)/CoolingBeamLinewidth)^2);
end
end
@ -55,13 +68,13 @@ function ret = calculateTotalAcceleration(this, PositionVector, VelocityVector)
for i = 1:2
a_sat = (Helper.PhysicsConstants.PlanckConstantReduced * this.CoolingBeamWaveNumber * WaveVectorEndPoint(i,1:3)/Helper.PhysicsConstants.Dy164Mass).*(this.CoolingBeamLinewidth * 0.5);
a_sat = (Helper.PhysicsConstants.PlanckConstantReduced * CoolingBeamWaveNumber * WaveVectorEndPoint(i,1:3)/Helper.PhysicsConstants.Dy164Mass).*(CoolingBeamLinewidth * 0.5);
a_1 = a_sat .* (SaturationParameter(2*i-1)/(1 + TotalSaturationParameter));
a_2 = a_sat .* (SaturationParameter(2*i) /(1 + TotalSaturationParameter));
if this.SpontaneousEmission
a_scattering = this.accelerationDueToSpontaneousEmissionProcess(SaturationParameter(2*i-1), TotalSaturationParameter, this.CoolingBeamLinewidth, this.CoolingBeamWaveNumber) + ...
this.accelerationDueToSpontaneousEmissionProcess(SaturationParameter(2*i), TotalSaturationParameter, this.CoolingBeamLinewidth, this.CoolingBeamWaveNumber);
a_scattering = this.accelerationDueToSpontaneousEmissionProcess(SaturationParameter(2*i-1), TotalSaturationParameter, CoolingBeamLinewidth, CoolingBeamWaveNumber) + ...
this.accelerationDueToSpontaneousEmissionProcess(SaturationParameter(2*i), TotalSaturationParameter, CoolingBeamLinewidth, CoolingBeamWaveNumber);
else
a_scattering = [0,0,0];
end
@ -72,8 +85,8 @@ function ret = calculateTotalAcceleration(this, PositionVector, VelocityVector)
if this.SpontaneousEmission
a_scattering = a_scattering + ...
this.accelerationDueToSpontaneousEmissionProcess(SaturationParameter(2*i-1+4), TotalSaturationParameter, this.CoolingBeamLinewidth, this.CoolingBeamWaveNumber) + ...
this.accelerationDueToSpontaneousEmissionProcess(SaturationParameter(2*i+4), TotalSaturationParameter, this.CoolingBeamLinewidth, this.CoolingBeamWaveNumber);
this.accelerationDueToSpontaneousEmissionProcess(SaturationParameter(2*i-1+4), TotalSaturationParameter, CoolingBeamLinewidth, CoolingBeamWaveNumber) + ...
this.accelerationDueToSpontaneousEmissionProcess(SaturationParameter(2*i+4), TotalSaturationParameter, CoolingBeamLinewidth, CoolingBeamWaveNumber);
else
a_scattering = [0,0,0];
end

4
MOT Capture Process Simulation/@MOTSimulator/computeCollisionProbability.m → +Simulator/@TwoDimensionalMOT/computeCollisionProbability.m
View File

@ -1,6 +1,6 @@
function ret = computeCollisionProbability(this)
function ret = computeCollisionProbability(this, ovenObj, tau_2D)
collision = rand(1);
CollisionProbability = 1 - exp(-this.TimeSpentInInteractionRegion/this.CollisionTime);
CollisionProbability = 1 - exp(-tau_2D/ovenObj.CollisionTime);
if this.BackgroundCollision && collision <= CollisionProbability
ret = true;
else

4
MOT Capture Process Simulation/@MOTSimulator/computeTimeSpentInInteractionRegion.m → +Simulator/@TwoDimensionalMOT/computeTimeSpentInInteractionRegion.m
View File

@ -5,12 +5,12 @@ function T = computeTimeSpentInInteractionRegion(this, r)
% T : gives the distribution of time spent in the interaction region
% USAGE:
% T = this.computeTimeSpentInInteractionRegion(r)
T = 0;
CoolingBeamObj = this.Beams{cellfun(@(x) strcmpi(x.Alias, 'Blue'), this.Beams)};
NumberOfTimeSteps = int64(this.SimulationTime/this.TimeStep);
for n = 1:(NumberOfTimeSteps - 1)
dr = Helper.calculateDistanceFromPointToLine(r(n+1, :), [0 0 0], [0 0 1]);
if dr < this.CoolingBeamRadius
if dr < CoolingBeamObj.Radius
A = 1;
else
A = 0;

4
MOT Capture Process Simulation/@MOTSimulator/exitCondition.m → +Simulator/@TwoDimensionalMOT/exitCondition.m
View File

@ -1,9 +1,9 @@
function ret = exitCondition(this, PositionVector, VelocityVector, CollisionEvent)
function ret = exitCondition(this, ovenObj, PositionVector, VelocityVector, CollisionEvent)
d = Helper.calculateDistanceFromPointToLine(PositionVector, [0 0 0], [0 1 0]);
y = PositionVector(2);
DivergenceAngle = (d/abs(y));
%DivergenceAngle = atan(norm(cross(PositionVector, )) / norm(dot(PositionVector, [0 1 0])));
if (y >= 0) && (DivergenceAngle <= this.MOTExitDivergence) && (abs(VelocityVector(2))<=this.VelocityCutoff) && ~CollisionEvent
if (y >= 0) && (DivergenceAngle <= this.ExitDivergence) && (abs(VelocityVector(2))<=ovenObj.VelocityCutoff) && ~CollisionEvent
ret = true;
else
ret = false;

8
+Simulator/@TwoDimensionalMOT/magneticFieldForMOT.m Normal file
View File

@ -0,0 +1,8 @@
function ret = magneticFieldForMOT(this, r)
ret = zeros(1,4);
alpha = this.MagneticGradient;
ret(1) = r(3)*alpha;
ret(2) = 0;
ret(3) = r(1)*alpha;
ret(4) = sqrt(ret(1)^2+ret(2)^2+ret(3)^2);
end

10
MOT Capture Process Simulation/@MOTSimulator/runSimulation.m → +Simulator/@TwoDimensionalMOT/runSimulation.m
View File

@ -1,14 +1,14 @@
function [LoadingRate, StandardError, ConfidenceInterval] = runSimulation(this)
function [LoadingRate, StandardError, ConfidenceInterval] = runSimulation(this, ovenObj)
%% - Sampling for initial positions and velocities
% - sampling the position distribution
Positions = this.initialPositionSampling();
Positions = ovenObj.initialPositionSampling();
% - sampling the velocity distribution
Velocities = this.initialVelocitySampling();
Velocities = ovenObj.initialVelocitySampling(this);
%% Solve ODE
progressbar = Helper.parforNotifications();
progressbar.PB_start(this.NumberOfAtoms,'Message',['Simulating capture process for ' num2str(this.NumberOfAtoms,'%.0f') ' atoms:']);
progressbar.PB_start(this.NumberOfAtoms,'Message',['Simulating 2-D MOT capture process for ' num2str(this.NumberOfAtoms,'%.0f') ' atoms:']);
% calculate the final position of the atoms
DynamicalQuantities = zeros(this.NumberOfAtoms,int64(this.SimulationTime/this.TimeStep),6);
@ -20,5 +20,5 @@ function [LoadingRate, StandardError, ConfidenceInterval] = runSimulation(this)
this.ParticleDynamicalQuantities = DynamicalQuantities;
%% Calculate the Loading Rate
[LoadingRate, StandardError, ConfidenceInterval] = this.calculateLoadingRate();
[LoadingRate, StandardError, ConfidenceInterval] = this.calculateLoadingRate(ovenObj);
end

1
MOT Capture Process Simulation/@MOTSimulator/solver.m → +Simulator/@TwoDimensionalMOT/solver.m
View File

@ -1,5 +1,4 @@
function ParticleDynamicalQuantities = solver(this, InitialPosition, InitialVelocity)
if this.Gravity
g = [0,0,-Helper.PhysicsConstants.GravitationalAcceleration];
else

107
MOT Capture Process Simulation/+Plotting/plotDynamicalQuantities.m
View File

@ -1,107 +0,0 @@
function plotDynamicalQuantities(obj, MaximumVelocity, IncidentAtomDirection, IncidentAtomPosition)
f_h = Helper.getFigureByTag('Trajectories Plot');
set(groot,'CurrentFigure',f_h);
a_h = get(f_h, 'CurrentAxes');
if ~isempty(get(a_h, 'Children'))
clf(f_h);
end
f_h.Name = 'Trajectories Plot';
f_h.Units = 'pixels';
set(0,'units','pixels');
screensize = get(0,'ScreenSize');
f_h.Position = [[screensize(3)/50 screensize(4)/10] 1870 850];
N = obj.NumberOfAtoms;
Theta = IncidentAtomDirection;
z = IncidentAtomPosition;
obj.setInitialConditions();
L = obj.OvenDistance * 2;
T = obj.SimulationTime;
tau = obj.TimeStep;
Y = linspace(0,MaximumVelocity,N);
DynamicalQuantities = zeros(length(Y),int64(T/tau),6);
for i=1:length(Y)
x =-L/2;
vx = Y(i)*cos(Theta);
vz = Y(i)*sin(Theta);
r = [x,0,z];
v = [vx,0,vz];
DynamicalQuantities(i,:,:) = obj.solver(r, v);
end
t = linspace(0, T, T/tau) * 1e+3;
for i=1:length(Y)
subplot(3, 3, 1)
hold on
plot(t, DynamicalQuantities(i,:,1) * 1e+3,'r','linewidth',1.3)
hXLabel_1 = xlabel('Time (ms)');
hYLabel_1 = ylabel('x (mm)');
hold off
subplot(3, 3, 2)
hold on
plot(t, DynamicalQuantities(i,:,2) * 1e+3,'g','linewidth',1.3)
hXLabel_2 = xlabel('Time (ms)');
hYLabel_2 = ylabel('y (mm)');
hold off
subplot(3, 3, 3)
hold on
plot(t, DynamicalQuantities(i,:,3) * 1e+3,'b','linewidth',1.3)
hXLabel_3 = xlabel('Time (ms)');
hYLabel_3 = ylabel('z (m/s)');
hold off
subplot(3, 3, 4)
hold on
plot(t, DynamicalQuantities(i,:,4),'r','linewidth',1.3)
hXLabel_4 = xlabel('Time (ms)');
hYLabel_4 = ylabel('v_x (m/s)');
hold off
subplot(3, 3, 5)
hold on
plot(t, DynamicalQuantities(i,:,5),'g','linewidth',1.3)
hXLabel_5 = xlabel('Time (ms)');
hYLabel_5 = ylabel('v_y (m/s)');
hold off
subplot(3, 3, 6)
hold on
plot(t, DynamicalQuantities(i,:,6),'b','linewidth',1.3)
hXLabel_6 = xlabel('Time (ms)');
hYLabel_6 = ylabel('v_z (m/s)');
hold off
subplot(3, 3, 7)
hold on
plot(DynamicalQuantities(i,:,1), DynamicalQuantities(i,:,4),'r','linewidth',1.3)
hXLabel_7 = xlabel('x (mm)');
hYLabel_7 = ylabel('v_x (m/s)');
xlim([-L/2 L/2])
hold off
subplot(3, 3, 8)
hold on
plot(DynamicalQuantities(i,:,2), DynamicalQuantities(i,:,5),'g','linewidth',1.3)
hXLabel_8 = xlabel('y (mm)');
hYLabel_8 = ylabel('v_y (m/s)');
xlim([-1 1] * 1e-04)
hold off
subplot(3, 3, 9)
hold on
plot(DynamicalQuantities(i,:,3), DynamicalQuantities(i,:,6),'b','linewidth',1.3)
hXLabel_9 = xlabel('z (mm)');
hYLabel_9 = ylabel('v_z (m/s)');
xlim([-1 1] * 1e-04)
hold off
end
hold off
hTitle = sgtitle(sprintf("Magnetic gradient = %.2f T/m", obj.MagneticGradient));
set([hXLabel_1, hXLabel_2, hXLabel_3, hXLabel_4, hXLabel_5, hXLabel_6, hXLabel_7, hXLabel_8, hXLabel_9,...
hYLabel_1, hYLabel_2, hYLabel_3, hYLabel_4, hYLabel_5, hYLabel_6, hYLabel_7, hYLabel_8, hYLabel_9], ...
'FontSize' , 14 );
set( hTitle , ...
'FontSize' , 18 );
Helper.bringFiguresWithTagInForeground();
end

654
MOT Capture Process Simulation/@MOTSimulator/MOTSimulator.m
View File

@ -1,654 +0,0 @@
classdef MOTSimulator < handle & matlab.mixin.Copyable
properties (Access = public)
SimulationMode; % MOT type
TimeStep;
SimulationTime;
NumberOfAtoms;
ParticleDynamicalQuantities;
NozzleLength;
NozzleRadius;
Beta;
ApertureCut;
OvenDistance;
OvenTemperature;
MagneticGradient;
NozzleExitDivergence;
MOTExitDivergence;
MOTDistance;
BluePower;
BlueDetuning;
BlueBeamRadius;
BlueBeamWaist;
BlueWaveNumber;
BlueSaturationIntensity;
OrangePower;
OrangeDetuning;
OrangeBeamRadius;
OrangeBeamWaist;
OrangeWaveNumber;
OrangeSaturationIntensity;
CoolingBeamPower;
CoolingBeamWaveNumber;
CoolingBeamLinewidth;
CoolingBeamDetuning;
CoolingBeamRadius;
CoolingBeamWaist;
CoolingBeamSaturationIntensity;
SidebandPower;
SidebandDetuning;
SidebandBeamRadius;
SidebandBeamWaist;
SidebandBeamSaturationIntensity;
PushBeamPower;
PushBeamWaveNumber;
PushBeamLinewidth;
PushBeamDetuning;
PushBeamRadius;
PushBeamWaist;
PushBeamDistance;
DistanceBetweenPushBeamAnd3DMOTCenter;
PushBeamSaturationIntensity;
ZeemanSlowerBeamPower;
ZeemanSlowerBeamDetuning;
ZeemanSlowerBeamRadius;
ZeemanSlowerBeamWaist;
ZeemanSlowerBeamSaturationIntensity;
TotalPower;
LandegFactor;
MagneticSubLevel;
CaptureVelocity;
VelocityCutoff;
ClausingFactor;
ReducedClausingFactor;
ReducedFlux;
TimeSpentInInteractionRegion;
%Flags
SpontaneousEmission;
Sideband;
PushBeam;
ZeemanSlowerBeam;
Gravity;
BackgroundCollision;
DebugMode;
DoSave;
SaveDirectory;
Results;
end
properties (SetAccess = private, GetAccess = public)
SimulationParameters
end
properties (Dependent, SetAccess = private)
CoolingBeamSaturationParameter;
SidebandSaturationParameter;
PushBeamSaturationParameter;
ZeemanSlowerBeamSaturationParameter;
OvenTemperatureinKelvin;
AverageVelocity;
AtomicBeamDensity;
MeanFreePath;
CollisionTime;
end
methods
function s = MOTSimulator(varargin)
p = inputParser;
p.KeepUnmatched = true;
addParameter(p, 'SimulationMode', '2D',...
@(x) any(strcmpi(x,{'2D','3D'})));
addParameter(p, 'TimeStep', 10e-06,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'SimulationTime', 3e-03,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'SpontaneousEmission', false,...
@islogical);
addParameter(p, 'Sideband', false,...
@islogical);
addParameter(p, 'PushBeam', false,...
@islogical);
addParameter(p, 'ZeemanSlowerBeam', false,...
@islogical);
addParameter(p, 'Gravity', false,...
@islogical);
addParameter(p, 'BackgroundCollision', false,...
@islogical);
addParameter(p, 'DebugMode', false,...
@islogical);
addParameter(p, 'SaveData', false,...
@islogical);
addParameter(p, 'SaveDirectory', pwd,...
@ischar);
p.parse(varargin{:});
s.SimulationMode = p.Results.SimulationMode;
s.TimeStep = p.Results.TimeStep;
s.SimulationTime = p.Results.SimulationTime;
s.SpontaneousEmission = p.Results.SpontaneousEmission;
s.Sideband = p.Results.Sideband;
s.PushBeam = p.Results.PushBeam;
s.ZeemanSlowerBeam = p.Results.ZeemanSlowerBeam;
s.Gravity = p.Results.Gravity;
s.BackgroundCollision = p.Results.BackgroundCollision;
s.DebugMode = p.Results.DebugMode;
s.DoSave = p.Results.SaveData;
s.SaveDirectory = p.Results.SaveDirectory;
s.reinitializeSimulator();
poolobj = gcp('nocreate'); % Check if pool is open
if isempty(poolobj)
parpool;
end
end
end % - lifecycle
methods
function set.TimeStep(this, val)
assert(val > 1e-06, 'Not time efficient to compute for time steps smaller than 1 microsecond!');
this.TimeStep = val;
end
function ret = get.TimeStep(this)
ret = this.TimeStep;
end
function set.SimulationTime(this, val)
% assert(val <= 5e-03, 'Not time efficient to compute for time spans longer than 5 milliseconds!');
this.SimulationTime = val;
end
function ret = get.SimulationTime(this)
ret = this.SimulationTime;
end
function set.NumberOfAtoms(this, val)
assert(val <= 20000, 'Not time efficient to compute for atom numbers larger than 20,000!');
this.NumberOfAtoms = val;
end
function ret = get.NumberOfAtoms(this)
ret = this.NumberOfAtoms;
end
function set.ParticleDynamicalQuantities(this,val)
this.ParticleDynamicalQuantities = val;
end
function ret = get.ParticleDynamicalQuantities(this)
ret = this.ParticleDynamicalQuantities;
end
function set.NozzleLength(this,val)
this.NozzleLength = val;
end
function ret = get.NozzleLength(this)
ret = this.NozzleLength;
end
function set.NozzleRadius(this,val)
this.NozzleRadius = val;
end
function ret = get.NozzleRadius(this)
ret = this.NozzleRadius;
end
function set.Beta(this,val)
this.Beta = val;
end
function ret = get.Beta(this)
ret = this.Beta;
end
function set.ApertureCut(this,val)
this.ApertureCut = val;
end
function ret = get.ApertureCut(this)
ret = this.ApertureCut;
end
function set.OvenDistance(this,val)
this.OvenDistance = val;
end
function ret = get.OvenDistance(this)
ret = this.OvenDistance;
end
function set.OvenTemperature(this,val)
this.OvenTemperature = val;
end
function ret = get.OvenTemperature(this)
ret = this.OvenTemperature;
end
function set.MagneticGradient(this,val)
this.MagneticGradient = val;
end
function ret = get.MagneticGradient(this)
ret = this.MagneticGradient;
end
function set.NozzleExitDivergence(this,val)
this.NozzleExitDivergence = val;
end
function ret = get.NozzleExitDivergence(this)
ret = this.NozzleExitDivergence;
end
function set.MOTExitDivergence(this,val)
this.MOTExitDivergence = val;
end
function ret = get.MOTExitDivergence(this)
ret = this.MOTExitDivergence;
end
function set.MOTDistance(this,val)
this.MOTDistance = val;
end
function ret = get.MOTDistance(this)
ret = this.MOTDistance;
end
function set.BluePower(this,val)
this.BluePower = val;
end
function ret = get.BluePower(this)
ret = this.BluePower;
end
function set.BlueDetuning(this, val)
this.BlueDetuning = val;
end
function ret = get.BlueDetuning(this)
ret = this.BlueDetuning;
end
function set.BlueBeamRadius(this, val)
this.BlueBeamRadius = val;
end
function ret = get.BlueBeamRadius(this)
ret = this.BlueBeamRadius;
end
function set.BlueBeamWaist(this, val)
this.BlueBeamWaist = val;
end
function ret = get.BlueBeamWaist(this)
ret = this.BlueBeamWaist;
end
function set.BlueWaveNumber(this, val)
this.BlueWaveNumber = val;
end
function ret = get.BlueWaveNumber(this)
ret = this.BlueWaveNumber;
end
function set.BlueSaturationIntensity(this, val)
this.BlueSaturationIntensity = val;
end
function ret = get.BlueSaturationIntensity(this)
ret = this.BlueSaturationIntensity;
end
function set.OrangePower(this,val)
this.OrangePower = val;
end
function ret = get.OrangePower(this)
ret = this.OrangePower;
end
function set.OrangeDetuning(this, val)
this.OrangeDetuning = val;
end
function ret = get.OrangeDetuning(this)
ret = this.OrangeDetuning;
end
function set.OrangeBeamRadius(this, val)
this.OrangeBeamRadius = val;
end
function ret = get.OrangeBeamRadius(this)
ret = this.OrangeBeamRadius;
end
function set.OrangeBeamWaist(this, val)
this.OrangeBeamWaist = val;
end
function ret = get.OrangeBeamWaist(this)
ret = this.OrangeBeamWaist;
end
function set.OrangeWaveNumber(this, val)
this.OrangeWaveNumber = val;
end
function ret = get.OrangeWaveNumber(this)
ret = this.OrangeWaveNumber;
end
function set.OrangeSaturationIntensity(this, val)
this.OrangeSaturationIntensity = val;
end
function ret = get.OrangeSaturationIntensity(this)
ret = this.OrangeSaturationIntensity;
end
function set.CoolingBeamPower(this,val)
this.CoolingBeamPower = val;
end
function ret = get.CoolingBeamPower(this)
ret = this.CoolingBeamPower;
end
function set.CoolingBeamDetuning(this, val)
this.CoolingBeamDetuning = val;
end
function ret = get.CoolingBeamDetuning(this)
ret = this.CoolingBeamDetuning;
end
function set.CoolingBeamRadius(this, val)
this.CoolingBeamRadius = val;
end
function ret = get.CoolingBeamRadius(this)
ret = this.CoolingBeamRadius;
end
function set.CoolingBeamWaist(this, val)
this.CoolingBeamWaist = val;
end
function ret = get.CoolingBeamWaist(this)
ret = this.CoolingBeamWaist;
end
function set.CoolingBeamWaveNumber(this, val)
this.CoolingBeamWaveNumber = val;
end
function ret = get.CoolingBeamWaveNumber(this)
ret = this.CoolingBeamWaveNumber;
end
function set.CoolingBeamLinewidth(this, val)
this.CoolingBeamLinewidth = val;
end
function ret = get.CoolingBeamLinewidth(this)
ret = this.CoolingBeamLinewidth;
end
function set.CoolingBeamSaturationIntensity(this, val)
this.CoolingBeamSaturationIntensity = val;
end
function ret = get.CoolingBeamSaturationIntensity(this)
ret = this.CoolingBeamSaturationIntensity;
end
function set.SidebandPower(this,val)
this.SidebandPower = val;
end
function ret = get.SidebandPower(this)
ret = this.SidebandPower;
end
function set.SidebandDetuning(this, val)
this.SidebandDetuning = val;
end
function ret = get.SidebandDetuning(this)
ret = this.SidebandDetuning;
end
function set.SidebandBeamRadius(this, val)
this.SidebandBeamRadius = val;
end
function ret = get.SidebandBeamRadius(this)
ret = this.SidebandBeamRadius;
end
function set.SidebandBeamWaist(this, val)
this.SidebandBeamWaist = val;
end
function ret = get.SidebandBeamWaist(this)
ret = this.SidebandBeamWaist;
end
function set.SidebandBeamSaturationIntensity(this, val)
this.SidebandBeamSaturationIntensity = val;
end
function ret = get.SidebandBeamSaturationIntensity(this)
ret = this.SidebandBeamSaturationIntensity;
end
function set.PushBeamPower(this,val)
this.PushBeamPower = val;
end
function ret = get.PushBeamPower(this)
ret = this.PushBeamPower;
end
function set.PushBeamDetuning(this, val)
this.PushBeamDetuning = val;
end
function ret = get.PushBeamDetuning(this)
ret = this.PushBeamDetuning;
end
function set.PushBeamRadius(this, val)
this.PushBeamRadius = val;
end
function ret = get.PushBeamRadius(this)
ret = this.PushBeamRadius;
end
function set.PushBeamWaist(this, val)
this.PushBeamWaist = val;
end
function ret = get.PushBeamWaist(this)
ret = this.PushBeamWaist;
end
function set.PushBeamWaveNumber(this, val)
this.PushBeamWaveNumber= val;
end
function ret = get.PushBeamWaveNumber(this)
ret = this.PushBeamWaveNumber;
end
function set.PushBeamLinewidth(this, val)
this.PushBeamLinewidth = val;
end
function ret = get.PushBeamLinewidth(this)
ret = this.PushBeamLinewidth;
end
function set.PushBeamDistance(this, val)
this.PushBeamDistance = val;
end
function ret = get.PushBeamDistance(this)
ret = this.PushBeamDistance;
end
function set.DistanceBetweenPushBeamAnd3DMOTCenter(this, val)
this.DistanceBetweenPushBeamAnd3DMOTCenter = val;
end
function ret = get.DistanceBetweenPushBeamAnd3DMOTCenter(this)
ret = this.DistanceBetweenPushBeamAnd3DMOTCenter;
end
function set.PushBeamSaturationIntensity(this, val)
this.PushBeamSaturationIntensity = val;
end
function ret = get.PushBeamSaturationIntensity(this)
ret = this.PushBeamSaturationIntensity;
end
function set.ZeemanSlowerBeamPower(this,val)
this.ZeemanSlowerBeamPower = val;
end
function ret = get.ZeemanSlowerBeamPower(this)
ret = this.ZeemanSlowerBeamPower;
end
function set.ZeemanSlowerBeamDetuning(this, val)
this.ZeemanSlowerBeamDetuning = val;
end
function ret = get.ZeemanSlowerBeamDetuning(this)
ret = this.ZeemanSlowerBeamDetuning;
end
function set.ZeemanSlowerBeamRadius(this, val)
this.ZeemanSlowerBeamRadius = val;
end
function ret = get.ZeemanSlowerBeamRadius(this)
ret = this.ZeemanSlowerBeamRadius;
end
function set.ZeemanSlowerBeamWaist(this, val)
this.ZeemanSlowerBeamWaist = val;
end
function ret = get.ZeemanSlowerBeamWaist(this)
ret = this.ZeemanSlowerBeamWaist;
end
function set.ZeemanSlowerBeamSaturationIntensity(this, val)
this.ZeemanSlowerBeamSaturationIntensity = val;
end
function ret = get.ZeemanSlowerBeamSaturationIntensity(this)
ret = this.ZeemanSlowerBeamSaturationIntensity;
end
function set.TotalPower(this,val)
this.TotalPower = val;
end
function ret = get.TotalPower(this)
ret = this.TotalPower;
end
function set.LandegFactor(this,val)
this.LandegFactor = val;
end
function ret = get.LandegFactor(this)
ret = this.LandegFactor;
end
function set.MagneticSubLevel(this,val)
this.MagneticSubLevel = val;
end
function ret = get.MagneticSubLevel(this)
ret = this.MagneticSubLevel;
end
function set.CaptureVelocity(this,val)
this.CaptureVelocity = val;
end
function ret = get.CaptureVelocity(this)
ret = this.CaptureVelocity;
end
function set.VelocityCutoff(this,val)
this.VelocityCutoff = val;
end
function ret = get.VelocityCutoff(this)
ret = this.VelocityCutoff;
end
function set.ClausingFactor(this,val)
this.ClausingFactor = val;
end
function ret = get.ClausingFactor(this)
ret = this.ClausingFactor;
end
function set.ReducedClausingFactor(this,val)
this.ReducedClausingFactor = val;
end
function ret = get.ReducedClausingFactor(this)
ret = this.ReducedClausingFactor;
end
function set.ReducedFlux(this,val)
this.ReducedFlux = val;
end
function ret = get.ReducedFlux(this)
ret = this.ReducedFlux;
end
function set.TimeSpentInInteractionRegion(this,val)
this.TimeSpentInInteractionRegion = val;
end
function ret = get.TimeSpentInInteractionRegion(this)
ret = this.TimeSpentInInteractionRegion;
end
function set.DebugMode(this, val)
this.DebugMode = val;
end
function ret = get.DebugMode(this)
ret = this.DebugMode;
end
function set.DoSave(this, val)
this.DoSave = val;
end
function ret = get.DoSave(this)
ret = this.DoSave;
end
function set.SaveDirectory(this, val)
this.SaveDirectory = val;
end
function ret = get.SaveDirectory(this)
ret = this.SaveDirectory;
end
function set.Results(this, val)
this.Results = val;
end
function ret = get.Results(this)
ret = this.Results;
end
end % - setters and getters
methods
function ret = get.CoolingBeamSaturationParameter(this)
ret = 0.1 * (4 * this.CoolingBeamPower) / (pi*this.CoolingBeamWaist^2 * this.CoolingBeamSaturationIntensity); % two beams are reflected
end
function ret = get.SidebandSaturationParameter(this)
ret = 0.1 * (4 * this.SidebandPower) / (pi*this.SidebandBeamWaist^2 * this.SidebandBeamSaturationIntensity);
end
function ret = get.PushBeamSaturationParameter(this)
ret = 0.1 * this.PushBeamPower/(pi * this.PushBeamWaist^2 * this.PushBeamSaturationIntensity);
end
function ret = get.ZeemanSlowerBeamSaturationParameter(this)
ret = 0.1 * this.ZeemanSlowerBeamPower / (pi * this.ZeemanSlowerBeamWaist^2 * this.ZeemanSlowerBeamSaturationIntensity);
end
function ret = get.OvenTemperatureinKelvin(this)
ret = this.OvenTemperature + Helper.PhysicsConstants.ZeroKelvin;
end
function ret = get.AverageVelocity(this)
%See Background collision probability section in Barbiero
ret = sqrt((8 * pi *Helper.PhysicsConstants.BoltzmannConstant*this.OvenTemperatureinKelvin)/ (9 * Helper.PhysicsConstants.Dy164Mass));
end
function ret = get.AtomicBeamDensity(this)
%See Background collision probability section in Barbiero
ret = this.calculateFreeMolecularRegimeFlux() / (this.AverageVelocity * pi * (this.Beta*this.NozzleLength/2)^2);
end
function ret = get.MeanFreePath(this)
% Cross section = pi ( 2 * Van-der-waals radius of Dy)^2;
% Van-der-waals radius of Dy = 281e-12
%See Expected atomic flux section and Background collision probability section in Barbiero
ret = 1/(sqrt(2) * ( pi * (2*281e-12)^2) * this.AtomicBeamDensity);
end
function ret = get.CollisionTime(this)
ret = 3 * this.MeanFreePath/this.AverageVelocity; %See Background collision probability section in Barbiero
end
end % - getters for dependent properties
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
methods(Access = protected)
function cp = copyElement(this)
% Shallow copy object
cp = copyElement@matlab.mixin.Copyable(this);
% Forces the setter to redefine the function handles to the new copied object
% cp.potentialType = this.potentialType;
pl = properties(this);
for k = 1:length(pl)
sc = superclasses(this.(pl{k}));
if any(contains(sc,{'matlab.mixin.Copyable'}))
cp.(pl{k}) = this.(pl{k}).copy();
end
end
end
end
methods (Static)
% Creates an Instance of Class, ensures singleton behaviour (that there
% can only be one Instance of this class
function singleObj = getInstance(varargin)
% Creates an Instance of Class, ensures singleton behaviour
persistent localObj;
if isempty(localObj) || ~isvalid(localObj)
localObj = MOTSimulator(varargin{:});
end
singleObj = localObj;
end
end
end

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MOT Capture Process Simulation/@MOTSimulator/accelerationDueToPushBeam.m
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function ret = accelerationDueToPushBeam(this, PositionVector, VelocityVector)
% is the distance between the chamber center and the cross point of push beam and z-axis (along the gravity)
WaveVectorEndPoint = [0, 1, this.DistanceBetweenPushBeamAnd3DMOTCenter/this.PushBeamDistance];
WaveVectorEndPoint = WaveVectorEndPoint./norm(WaveVectorEndPoint);
Origin=[0,0,0];
SaturationIntensity = this.calculateLocalSaturationIntensity(this.PushBeamSaturationParameter, PositionVector, Origin, WaveVectorEndPoint, this.PushBeamRadius, this.PushBeamWaist);
DopplerShift = dot(WaveVectorEndPoint(:), VelocityVector) * this.PushBeamWaveNumber;
Detuning = this.PushBeamDetuning - DopplerShift;
s_push = SaturationIntensity/(1 + SaturationIntensity + (4 * (Detuning./this.PushBeamLinewidth).^2));
a_sat = (Helper.PhysicsConstants.PlanckConstantReduced * this.PushBeamWaveNumber * WaveVectorEndPoint(:)/Helper.PhysicsConstants.Dy164Mass).*(this.PushBeamLinewidth * 0.5);
a_push = a_sat .* (s_push/(1+s_push));
if this.SpontaneousEmission
a_scatter = this.accelerationDueToSpontaneousEmissionProcess(s_push, s_push, this.PushBeamLinewidth, this.PushBeamWaveNumber);
else
a_scatter = [0,0,0];
end
a_total = a_push + a_scatter;
ret = a_total(1:3);
end

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MOT Capture Process Simulation/@MOTSimulator/calculateCaptureVelocity.m
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function ret = calculateCaptureVelocity(this, PositionVector, VelocityVector)
switch this.SimulationMode
case "2D"
VelocityUnitVector = VelocityVector./norm(VelocityVector);
UpperLimit = 500;
LowerLimit = 0;
for Index = 1:500
InitialVelocity = (0.5 * (UpperLimit + LowerLimit)) * VelocityUnitVector;
ParticleDynamicalQuantities = this.solver(PositionVector, InitialVelocity);
FinalPositionVector = ParticleDynamicalQuantities(end, 1:3);
if rssq(FinalPositionVector) <= this.OvenDistance
LowerLimit = 0.5 * (UpperLimit + LowerLimit);
else
UpperLimit = 0.5 * (UpperLimit + LowerLimit);
end
if UpperLimit - LowerLimit < 1
ret = (0.5 * (UpperLimit + LowerLimit)) * VelocityUnitVector;
break;
end
end
case "3D"
% Development In progress
end
end

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MOT Capture Process Simulation/@MOTSimulator/calculateLoadingRate.m
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function [LoadingRate, StandardError, ConfidenceInterval] = calculateLoadingRate(this)
switch this.SimulationMode
case "2D"
n = this.NumberOfAtoms;
DynamicalQuantities = this.ParticleDynamicalQuantities;
NumberOfTimeSteps = int64(this.SimulationTime/this.TimeStep);
NumberOfLoadedAtoms = zeros(1, NumberOfTimeSteps);
TimeCounts = zeros(1, n);
CollisionEvents = zeros(1, n);
% Include the stochastic process of background collisions
for AtomIndex = 1:n
TimeCounts(AtomIndex) = this.computeTimeSpentInInteractionRegion(squeeze(DynamicalQuantities(AtomIndex,:,1:3)));
end
this.TimeSpentInInteractionRegion = mean(TimeCounts);
for AtomIndex = 1:n
CollisionEvents(AtomIndex) = this.computeCollisionProbability();
end
% Count the number of loaded atoms subject to conditions
for TimeIndex = 1:NumberOfTimeSteps
if TimeIndex ~= 1
NumberOfLoadedAtoms(TimeIndex) = NumberOfLoadedAtoms(TimeIndex-1);
end
for AtomIndex = 1:n
Position = squeeze(DynamicalQuantities(AtomIndex, TimeIndex, 1:3))';
Velocity = squeeze(DynamicalQuantities(AtomIndex, TimeIndex, 4:6))';
if this.exitCondition(Position, Velocity, CollisionEvents(AtomIndex))
NumberOfLoadedAtoms(TimeIndex) = NumberOfLoadedAtoms(TimeIndex) + 1;
end
end
end
[LoadingRate, StandardError, ConfidenceInterval] = this.bootstrapErrorEstimation(NumberOfLoadedAtoms);
case "3D"
% Development In progress
end
end

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MOT Capture Process Simulation/@MOTSimulator/doOneParameterScan.m
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function [LoadingRateArray, StandardErrorArray, ConfidenceIntervalArray] = doOneParameterScan(this, ParameterName, ParameterArray, varargin)
p = inputParser;
p.KeepUnmatched = true;
addRequired(p, 'ClassObject' , @isobject);
addRequired(p, 'ParameterName' , @ischar);
addRequired(p, 'ParameterArray' , @isvector);
addParameter(p, 'ChangeRelatedParameter', false, @islogical);
addParameter(p, 'RelatedParameterName', 'none', @ischar);
addParameter(p, 'RelatedParameterArray', length(ParameterArray), @isvector);
addParameter(p, 'ChangeInitialConditions', false, @islogical);
addParameter(p, 'ParameterNameArray', {}, @iscell);
addParameter(p, 'ParameterValueArray', {}, @iscell);
p.parse(this, ParameterName, ParameterArray, varargin{:})
ParameterName = p.Results.ParameterName;
ParameterArray = p.Results.ParameterArray;
ChangeRelatedParameter = p.Results.ChangeRelatedParameter;
RelatedParameterName = p.Results.RelatedParameterName;
RelatedParameterArray = p.Results.RelatedParameterArray;
ChangeInitialConditions = p.Results.ChangeInitialConditions;
ParameterNameArray = p.Results.ParameterNameArray;
ParameterValueArray = p.Results.ParameterValueArray;
NumberOfPointsForParam = length(ParameterArray);
LoadingRateArray = zeros(1,NumberOfPointsForParam);
StandardErrorArray = zeros(1,NumberOfPointsForParam);
ConfidenceIntervalArray = zeros(NumberOfPointsForParam, 2);
for i=1:NumberOfPointsForParam
eval(sprintf('OptionsStruct.%s = %d;', ParameterName, ParameterArray(i)));
if ChangeRelatedParameter
eval(sprintf('OptionsStruct.%s = %d;', RelatedParameterName, RelatedParameterArray(i)));
end
if ChangeInitialConditions
for j = 1:length(ParameterNameArray)
eval(sprintf('OptionsStruct.%s = %d;', ParameterNameArray{j}, ParameterValueArray{j}));
end
end
options = Helper.convertstruct2cell(OptionsStruct);
this.setInitialConditions(options{:});
tic
[LoadingRate, StandardError, ConfidenceInterval] = this.runSimulation();
LoadingRateArray(i) = LoadingRate;
StandardErrorArray(i) = StandardError;
ConfidenceIntervalArray(i,1) = ConfidenceInterval(1);
ConfidenceIntervalArray(i,2) = ConfidenceInterval(2);
end
if this.DoSave
LoadingRate = struct;
LoadingRate.Values = LoadingRateArray;
LoadingRate.Errors = StandardErrorArray;
LoadingRate.CI = ConfidenceIntervalArray;
this.Results = LoadingRate;
SaveFolder = [this.SaveDirectory filesep 'Results'];
Filename = ['OneParameterScan_' datestr(now,'yyyymmdd_HHMM')];
eval([sprintf('%s_Object', Filename) ' = this;']);
mkdir(SaveFolder);
save([SaveFolder filesep Filename], sprintf('%s_Object', Filename));
end
end

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MOT Capture Process Simulation/@MOTSimulator/doTwoParameterScan.m
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function [LoadingRateArray, StandardErrorArray, ConfidenceIntervalArray] = doTwoParameterScan(this, FirstParameterName, FirstParameterArray, ...
SecondParameterName, SecondParameterArray, varargin)
p = inputParser;
p.KeepUnmatched = true;
addRequired(p, 'ClassObject' , @isobject);
addRequired(p, 'FirstParameterName' , @ischar);
addRequired(p, 'FirstParameterArray' , @isvector);
addRequired(p, 'SecondParameterName' , @ischar);
addRequired(p, 'SecondParameterArray', @isvector);
addParameter(p, 'ChangeRelatedParameter', false, @islogical);
addParameter(p, 'Order', 1, @(x) assert(isnumeric(x) && isscalar(x) && (x > 0) && (x < 3)));
addParameter(p, 'RelatedParameterName', 'none', @ischar);
addParameter(p, 'RelatedParameterArray', length(FirstParameterArray), @isvector);
addParameter(p, 'ChangeInitialConditions', false, @islogical);
addParameter(p, 'ParameterNameArray', {}, @iscell);
addParameter(p, 'ParameterValueArray', {}, @iscell);
p.parse(this, FirstParameterName, FirstParameterArray, ...
SecondParameterName, SecondParameterArray, varargin{:})
FirstParameterName = p.Results.FirstParameterName;
FirstParameterArray = p.Results.FirstParameterArray;
SecondParameterName = p.Results.SecondParameterName;
SecondParameterArray = p.Results.SecondParameterArray;
ChangeRelatedParameter = p.Results.ChangeRelatedParameter;
Order = p.Results.Order;
RelatedParameterName = p.Results.RelatedParameterName;
RelatedParameterArray = p.Results.RelatedParameterArray;
ChangeInitialConditions = p.Results.ChangeInitialConditions;
ParameterNameArray = p.Results.ParameterNameArray;
ParameterValueArray = p.Results.ParameterValueArray;
NumberOfPointsForFirstParam = length(FirstParameterArray);
NumberOfPointsForSecondParam = length(SecondParameterArray);
LoadingRateArray = zeros(NumberOfPointsForFirstParam, NumberOfPointsForSecondParam);
StandardErrorArray = zeros(NumberOfPointsForFirstParam, NumberOfPointsForSecondParam);
ConfidenceIntervalArray = zeros(NumberOfPointsForFirstParam, NumberOfPointsForSecondParam, 2);
for i=1:NumberOfPointsForFirstParam
eval(sprintf('OptionsStruct.%s = %d;', FirstParameterName, FirstParameterArray(i)));
if ChangeRelatedParameter && Order == 1
eval(sprintf('OptionsStruct.%s = %d;', RelatedParameterName, RelatedParameterArray(i)));
end
for j=1:NumberOfPointsForSecondParam
eval(sprintf('OptionsStruct.%s = %d;', SecondParameterName, SecondParameterArray(j)));
if ChangeRelatedParameter && Order == 2
eval(sprintf('OptionsStruct.%s = %d;', RelatedParameterName, RelatedParameterArray(j)));
end
if ChangeInitialConditions
for k = 1:length(ParameterNameArray)
eval(sprintf('OptionsStruct.%s = %d;', ParameterNameArray{k}, ParameterValueArray{k}));
end
end
options = Helper.convertstruct2cell(OptionsStruct);
this.setInitialConditions(options{:});
tic
[LoadingRate, StandardError, ConfidenceInterval] = this.runSimulation();
LoadingRateArray(i, j) = LoadingRate;
StandardErrorArray(i, j) = StandardError;
ConfidenceIntervalArray(i, j, 1) = ConfidenceInterval(1);
ConfidenceIntervalArray(i, j, 2) = ConfidenceInterval(2);
end
end
if this.DoSave
LoadingRate = struct;
LoadingRate.Values = LoadingRateArray;
LoadingRate.Errors = StandardErrorArray;
LoadingRate.CI = ConfidenceIntervalArray;
this.Results = LoadingRate;
SaveFolder = [this.SaveDirectory filesep 'Results'];
Filename = ['TwoParameterScan_' datestr(now,'yyyymmdd_HHMM')];
eval([sprintf('%s_Object', Filename) ' = this;']);
mkdir(SaveFolder);
save([SaveFolder filesep Filename], sprintf('%s_Object', Filename));
end
end

12
MOT Capture Process Simulation/@MOTSimulator/initialPositionSampling.m
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function ret = initialPositionSampling(this)
switch this.SimulationMode
case "2D"
n = this.NumberOfAtoms;
phi = 2 * pi * rand(n,1);
rho = this.Beta * 0.5 * this.NozzleLength * sqrt(rand(n,1));
ret = [-this.OvenDistance * ones(n,1), rho.*cos(phi), rho.*sin(phi)];
case "3D"
% Development In progress
end
end

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MOT Capture Process Simulation/@MOTSimulator/initialVelocitySampling.m
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function ret = initialVelocitySampling(this)
switch this.SimulationMode
case "2D"
n = this.NumberOfAtoms;
% Calculate Calculate Capture velocity --> Introduce velocity cutoff
this.CaptureVelocity = 1.05 * this.calculateCaptureVelocity([-this.OvenDistance,0,0], [1,0,0]);
this.VelocityCutoff = this.CaptureVelocity(1); % Should be the magnitude of the 3-D velocity vector but since here the obtained capture
% velocity is only along the x-axis, we take the first term which is the x-component of the velocity.
[ReducedClausingFactor, NormalizationConstantForAngularDistribution] = this.calculateReducedClausingFactor();
this.ReducedClausingFactor = ReducedClausingFactor;
VelocityDistribution = @(velocity) sqrt(2 / pi) * sqrt(Helper.PhysicsConstants.Dy164Mass/(Helper.PhysicsConstants.BoltzmannConstant * this.OvenTemperatureinKelvin))^3 ...
* velocity.^3 .* exp(-velocity.^2 .* (Helper.PhysicsConstants.Dy164Mass / (2 * Helper.PhysicsConstants.BoltzmannConstant ...
* this.OvenTemperatureinKelvin)));
c = integral(VelocityDistribution, 0, this.VelocityCutoff);
this.ReducedFlux = c * this.ReducedClausingFactor * this.calculateFreeMolecularRegimeFlux();
ret = zeros(n,3);
SampledVelocityMagnitude = zeros(n,1);
SampledPolarAngle = zeros(n,1);
SampledAzimuthalAngle = zeros(n,1);
MostProbableVelocity = sqrt((3 * Helper.PhysicsConstants.BoltzmannConstant * this.OvenTemperature) / Helper.PhysicsConstants.Dy164Mass); % For v * f(v) distribution
if MostProbableVelocity > this.VelocityCutoff
MaximumVelocityAllowed = this.VelocityCutoff;
else
MaximumVelocityAllowed = MostProbableVelocity;
end
NormalizationConstantForVelocityDistribution = this.velocityDistributionFunction(MaximumVelocityAllowed);
parfor i = 1:n
% Rejection Sampling of speed
y = rand(1);
x = this.VelocityCutoff * rand(1);
while y > ((NormalizationConstantForVelocityDistribution)^-1 * this.velocityDistributionFunction(x)) %As long as this loop condition is satisfied, reject the corresponding x value
y = rand(1);
x = this.VelocityCutoff * rand(1);
end
SampledVelocityMagnitude(i) = x; % When loop condition is not satisfied, accept x value and store as sample
% Rejection Sampling of polar angle
w = rand(1);
z = this.NozzleExitDivergence * rand(1);
while w > ((NormalizationConstantForAngularDistribution)^-1 * 2 * pi * this.angularDistributionFunction(z) * sin(z)) %As long as this loop condition is satisfied, reject the corresponding x value
w = rand(1);
z = this.NozzleExitDivergence * rand(1);
end
SampledPolarAngle(i) = z; %When loop condition is not satisfied, accept x value and store as sample
% Sampling of azimuthal angle
SampledAzimuthalAngle(i)= 2 * pi * rand(1);
ret(i,:)=[SampledVelocityMagnitude(i)*cos(SampledPolarAngle(i)), SampledVelocityMagnitude(i)*sin(SampledPolarAngle(i))*cos(SampledAzimuthalAngle(i)), ...
SampledVelocityMagnitude(i)*sin(SampledPolarAngle(i))*sin(SampledAzimuthalAngle(i))];
end
case "3D"
% Development In progress
end
end

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MOT Capture Process Simulation/@MOTSimulator/magneticFieldForMOT.m
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function ret = magneticFieldForMOT(this, r)
switch this.SimulationMode
case '2D'
ret = zeros(1,4);
alpha = this.MagneticGradient;
ret(1) = r(3)*alpha;
ret(2) = 0;
ret(3) = r(1)*alpha;
ret(4) = sqrt(ret(1)^2+ret(2)^2+ret(3)^2);
case '3D'
% Development in progress
end
end

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MOT Capture Process Simulation/@MOTSimulator/reinitializeSimulator.m
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function reinitializeSimulator(this)
%% PHYSICAL CONSTANTS
pc = Helper.PhysicsConstants;
%% SIMULATION PARAMETERS
this.NozzleLength = 60e-3;
this.NozzleRadius = 2.60e-3;
this.Beta = 2 * (this.NozzleRadius/this.NozzleLength);
this.ApertureCut = max(2.5e-3,this.NozzleRadius);
this.OvenDistance = (25+12.5)*1e-3 + (this.NozzleRadius + this.ApertureCut) / tan(15/360 * 2 * pi);
% Distance between the nozzle and the 2-D MOT chamber center
% 25 is the beam radius/sqrt(2)
% 12.5 is the radius of the oven
% 15 eg is the angle between the 2-D MOT chamber center and the nozzle
this.OvenTemperature = 1000; % Temperature in Celsius
this.MOTDistance = 0.32; % Distance between the 2-D MOT the 3-D MOT
this.BlueWaveNumber = 2*pi/pc.BlueWavelength;
this.BlueSaturationIntensity = 0.1 * (2 * pi^2 / 3) * ((pc.PlanckConstantReduced * pc.SpeedOfLight * pc.BlueLinewidth) / (pc.BlueWavelength)^3);
this.OrangeWaveNumber = 2*pi/pc.OrangeWavelength;
this.OrangeSaturationIntensity = 0.1 * (2 * pi^2 / 3) * ((pc.PlanckConstantReduced * pc.SpeedOfLight * pc.OrangeLinewidth) / (pc.OrangeWavelength)^3);
this.BlueBeamRadius = min(0.035/2,sqrt(2)/2*this.OvenDistance); % Diameter of CF40 flange = 0.035
Theta_Nozzle = atan((this.NozzleRadius+this.BlueBeamRadius*sqrt(2))/this.OvenDistance); % The angle of capture region towards the oven nozzle
Theta_Aperture = 15/360*2*pi; % The limitation angle of the second aperture in the oven
this.NozzleExitDivergence = min(Theta_Nozzle,Theta_Aperture);
this.MOTExitDivergence = 16e-3; % The limitation angle between 2D-MOT and 3D-MOT
this.TotalPower = 0.6;
this.OrangeBeamRadius = 1.2e-3;
this.PushBeamRadius = 1.2e-3;
this.PushBeamDistance = 0.32;
this.PushBeamLinewidth = Helper.PhysicsConstants.OrangeLinewidth;
this.PushBeamWaveNumber = this.OrangeWaveNumber;
this.PushBeamSaturationIntensity = this.OrangeSaturationIntensity;
this.ZeemanSlowerBeamRadius = 0.035;
this.ZeemanSlowerBeamSaturationIntensity = this.BlueSaturationIntensity;
this.DistanceBetweenPushBeamAnd3DMOTCenter = 0;
end

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MOT Capture Process Simulation/@MOTSimulator/setInitialConditions.m
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function setInitialConditions(this, varargin)
p = inputParser;
p.KeepUnmatched = true;
addParameter(p, 'NumberOfAtoms', 5000,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'BluePower', this.TotalPower,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'BlueDetuning', -1.39*Helper.PhysicsConstants.BlueLinewidth,...
@(x) assert(isnumeric(x) && isscalar(x)));
addParameter(p, 'BlueBeamWaist', 16.6667e-3,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'SidebandPower', 0.5*this.TotalPower,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'SidebandDetuning', -4.5*Helper.PhysicsConstants.BlueLinewidth,...
@(x) assert(isnumeric(x) && isscalar(x)));
addParameter(p, 'SidebandBeamWaist', 15e-3,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'PushBeamPower', 100e-3,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'PushBeamDetuning', -5*Helper.PhysicsConstants.OrangeLinewidth,...
@(x) assert(isnumeric(x) && isscalar(x)));
addParameter(p, 'PushBeamWaist', 0.81e-3,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'OrangePower', 70e-3,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'OrangeDetuning', -1*Helper.PhysicsConstants.OrangeLinewidth,...
@(x) assert(isnumeric(x) && isscalar(x)));
addParameter(p, 'OrangeBeamWaist', 12e-3,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'ZeemanSlowerBeamPower', 200e-3,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'ZeemanSlowerBeamDetuning', -7*Helper.PhysicsConstants.BlueLinewidth,...
@(x) assert(isnumeric(x) && isscalar(x)));
addParameter(p, 'ZeemanSlowerBeamWaist', 7e-3,...
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
addParameter(p, 'MagneticGradient', 0.425,... % T/m
@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
p.parse(varargin{:});
this.NumberOfAtoms = p.Results.NumberOfAtoms;
this.BluePower = p.Results.BluePower;
this.BlueDetuning = p.Results.BlueDetuning;
this.BlueBeamWaist = p.Results.BlueBeamWaist;
this.SidebandPower = p.Results.SidebandPower;
this.SidebandDetuning = p.Results.SidebandDetuning;
this.SidebandBeamWaist = p.Results.SidebandBeamWaist;
this.PushBeamPower = p.Results.PushBeamPower;
this.PushBeamDetuning = p.Results.PushBeamDetuning;
this.PushBeamWaist = p.Results.PushBeamWaist;
this.OrangePower = p.Results.OrangePower;
this.OrangeDetuning = p.Results.OrangeDetuning;
this.OrangeBeamWaist = p.Results.OrangeBeamWaist;
this.ZeemanSlowerBeamPower = p.Results.ZeemanSlowerBeamPower;
this.ZeemanSlowerBeamDetuning = p.Results.ZeemanSlowerBeamDetuning;
this.ZeemanSlowerBeamWaist = p.Results.ZeemanSlowerBeamWaist;
this.MagneticGradient = p.Results.MagneticGradient;
%% Set general parameters according to simulation mode
switch this.SimulationMode
case "2D"
this.CoolingBeamPower = this.BluePower;
this.CoolingBeamWaist = this.BlueBeamWaist;
this.CoolingBeamLinewidth = Helper.PhysicsConstants.BlueLinewidth;
this.CoolingBeamWaveNumber = this.BlueWaveNumber;
this.CoolingBeamDetuning = this.BlueDetuning;
this.CoolingBeamRadius = this.BlueBeamRadius;
this.CoolingBeamWaist = this.BlueBeamWaist;
this.CoolingBeamSaturationIntensity = this.BlueSaturationIntensity;
this.SidebandBeamRadius = this.BlueBeamRadius;
this.SidebandBeamSaturationIntensity = this.BlueSaturationIntensity;
this.LandegFactor = Helper.PhysicsConstants.BlueLandegFactor;
this.MagneticSubLevel = 1;
case "3D"
% Development In progress
end
%% - store in struct
this.SimulationParameters = struct;
this.SimulationParameters.SimulationMode = this.SimulationMode;
this.SimulationParameters.TimeStep = this.TimeStep;
this.SimulationParameters.SimulationTime = this.SimulationTime;
this.SimulationParameters.NumberOfAtoms = this.NumberOfAtoms;
this.SimulationParameters.NozzleLength = this.NozzleLength;
this.SimulationParameters.NozzleRadius = this.NozzleRadius;
this.SimulationParameters.Beta = this.Beta;
this.SimulationParameters.ApertureCut = this.ApertureCut;
this.SimulationParameters.OvenDistance = this.OvenDistance;
this.SimulationParameters.OvenTemperature = this.OvenTemperature;
this.SimulationParameters.MagneticGradient = this.MagneticGradient;
this.SimulationParameters.NozzleExitDivergence = this.NozzleExitDivergence;
this.SimulationParameters.MOTExitDivergence = this.MOTExitDivergence;
this.SimulationParameters.MOTDistance = this.MOTDistance;
this.SimulationParameters.BluePower = this.BluePower;
this.SimulationParameters.BlueDetuning = this.BlueDetuning;
this.SimulationParameters.BlueBeamRadius = this.BlueBeamRadius;
this.SimulationParameters.BlueBeamWaist = this.BlueBeamWaist;
this.SimulationParameters.BlueSaturationIntensity = this.BlueSaturationIntensity;
this.SimulationParameters.OrangePower = this.OrangePower;
this.SimulationParameters.OrangeDetuning = this.OrangeDetuning;
this.SimulationParameters.OrangeBeamRadius = this.OrangeBeamRadius;
this.SimulationParameters.OrangeBeamWaist = this.OrangeBeamWaist;
this.SimulationParameters.OrangeSaturationIntensity = this.OrangeSaturationIntensity;
this.SimulationParameters.SidebandPower = this.SidebandPower;
this.SimulationParameters.SidebandDetuning = this.SidebandDetuning;
this.SimulationParameters.SidebandBeamRadius = this.SidebandBeamRadius;
this.SimulationParameters.SidebandBeamWaist = this.SidebandBeamWaist;
this.SimulationParameters.SidebandBeamSaturationIntensity = this.SidebandBeamSaturationIntensity;
this.SimulationParameters.PushBeamPower = this.PushBeamPower;
this.SimulationParameters.PushBeamDetuning = this.PushBeamDetuning;
this.SimulationParameters.PushBeamRadius = this.PushBeamRadius;
this.SimulationParameters.PushBeamWaist = this.PushBeamWaist;
this.SimulationParameters.PushBeamDistance = this.PushBeamDistance;
this.SimulationParameters.DistanceBetweenPushBeamAnd3DMOTCenter = this.DistanceBetweenPushBeamAnd3DMOTCenter;
this.SimulationParameters.PushBeamSaturationIntensity = this.PushBeamSaturationIntensity;
this.SimulationParameters.TotalPower = this.TotalPower;
this.SimulationParameters.LandegFactor = this.LandegFactor;
this.SimulationParameters.MagneticSubLevel = this.MagneticSubLevel;
this.SimulationParameters.CoolingBeamSaturationParameter = this.CoolingBeamSaturationParameter;
this.SimulationParameters.SidebandSaturationParameter = this.SidebandSaturationParameter;
this.SimulationParameters.PushBeamSaturationParameter = this.PushBeamSaturationParameter;
this.SimulationParameters.OvenTemperatureinKelvin = this.OvenTemperatureinKelvin;
this.SimulationParameters.AverageVelocity = this.AverageVelocity;
this.SimulationParameters.AtomicBeamDensity = this.AtomicBeamDensity;
this.SimulationParameters.MeanFreePath = this.MeanFreePath;
this.SimulationParameters.CollisionTime = this.CollisionTime;
if strcmpi(this.SimulationMode, '3D')
this.SimulationParameters.ZeemanSlowerBeamPower = this.ZeemanSlowerBeamPower;
this.SimulationParameters.ZeemanSlowerBeamDetuning = this.ZeemanSlowerBeamDetuning;
this.SimulationParameters.ZeemanSlowerBeamRadius = this.ZeemanSlowerBeamRadius;
this.SimulationParameters.ZeemanSlowerBeamBeamWaist = this.ZeemanSlowerBeamWaist;
this.SimulationParameters.ZeemanSlowerBeamSaturationIntensity = this.ZeemanSlowerBeamSaturationIntensity;
this.SimulationParameters.ZeemanSlowerBeamSaturationParameter = this.ZeemanSlowerBeamSaturationParameter;
end
end

188
MOT Capture Process Simulation/test_MOTSimulator.m
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%% - Create solver object with specified options
clc
%%
OptionsStruct = struct;
OptionsStruct.SimulationMode = '2D';
OptionsStruct.TimeStep = 50e-06; % in s
OptionsStruct.SimulationTime = 4e-03; % in s
OptionsStruct.SpontaneousEmission = true;
OptionsStruct.Sideband = false;
OptionsStruct.PushBeam = false;
OptionsStruct.Gravity = false;
OptionsStruct.BackgroundCollision = true;
OptionsStruct.SaveData = false;
OptionsStruct.SaveDirectory = 'C:\DY LAB\MOT Simulation Project\Calculations\Code\MOT Capture Process Simulation';
options = Helper.convertstruct2cell(OptionsStruct);
Simulator = MOTSimulator(options{:});
clear OptionsStruct
%% - Set Initial Conditions: Run with default values
Simulator.setInitialConditions();
%% - Set Initial Conditions: Set manually
OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 5000;
OptionsStruct.BluePower = 0.2; % in W
OptionsStruct.BlueDetuning = -1.5 * Helper.PhysicsConstants.BlueLinewidth; % in Hz
OptionsStruct.BlueBeamWaist = 0.016; % in m
OptionsStruct.SidebandPower = 0.2;
OptionsStruct.SidebandDetuning = -3 * Helper.PhysicsConstants.BlueLinewidth; % in Hz
OptionsStruct.SidebandBeamWaist = 0.010; % in m
OptionsStruct.PushBeamPower = 0.010; % in W
OptionsStruct.PushBeamDetuning = 0; % in Hz
OptionsStruct.PushBeamWaist = 0.005; % in m
options = Helper.convertstruct2cell(OptionsStruct);
Simulator.setInitialConditions(options{:});
clear OptionsStruct
%% - Run Simulation
[LoadingRate, ~] = Simulator.runSimulation();
%% - Plot initial distribution
Simulator.setInitialConditions();
% - sampling the position distribution
InitialPositions = Simulator.initialPositionSampling();
% - sampling the velocity distribution
InitialVelocities = Simulator.initialVelocitySampling();
NumberOfBins = 100;
Plotting.plotPositionAndVelocitySampling(NumberOfBins, InitialPositions, InitialVelocities);
%% - Plot distributions of magnitude and direction of initial velocities
NumberOfBins = 50;
Plotting.plotInitialVeloctiySamplingVsAngle(Simulator, NumberOfBins)
%% - Plot Magnetic Field
XAxisRange = [-5 5];
YAxisRange = [-5 5];
ZAxisRange = [-5 5];
Plotting.visualizeMagneticField(Simulator, XAxisRange, YAxisRange, ZAxisRange)
%% - Plot MFP & VP for different temperatures
TemperatureinCelsius = linspace(750,1100,2000); % Temperature in Celsius
Plotting.plotMeanFreePathAndVapourPressureVsTemp(TemperatureinCelsius)
%% - Plot the Free Molecular Flux for different temperatures
Temperature = [950, 1000, 1050]; % Temperature
Plotting.plotFreeMolecularFluxVsTemp(Simulator,Temperature)
%% - Plot Angular Distribution for different Beta
Beta = [0.5, 0.1 , 0.05, 0.02, 0.01]; %Beta = 2 * radius / length of the tube
Plotting.plotAngularDistributionForDifferentBeta(Simulator, Beta)
%% - Plot Capture Velocity
Simulator.setInitialConditions();
Plotting.plotCaptureVelocityVsAngle(Simulator);
%% - Plot Phase Space
Simulator.NumberOfAtoms = 100;
MinimumVelocity = 0;
MaximumVelocity = 150;
NumberOfBins = 200; %Along each axis
IncidentAtomDirection = 0*2*pi/360;
IncidentAtomPosition = 0;
Plotting.plotPhaseSpaceWithAccelerationField(Simulator, MinimumVelocity, MaximumVelocity, NumberOfBins, IncidentAtomDirection, IncidentAtomPosition)
%% - Plot trajectories along the 3 directions
Simulator.NumberOfAtoms = 100;
MaximumVelocity = 150;
IncidentAtomDirection = 0*2*pi/360;
IncidentAtomPosition = 0;
Plotting.plotDynamicalQuantities(Simulator, MaximumVelocity, IncidentAtomDirection, IncidentAtomPosition);
%% - Scan parameters
% ONE-PARAMETER SCAN
NumberOfPointsForParam = 5; %iterations of the simulation
% Scan Cooling Beam Power
PowerArray = linspace(0.1, 1.0, NumberOfPointsForParam) * Simulator.TotalPower;
% Scan Cooling Beam Detuning
% DetuningArray = linspace(-0.5,-10, NumberOfPointsForParam) * Helper.PhysicsConstants.BlueLinewidth;
OptionsStruct = struct;
OptionsStruct.ChangeInitialConditions = true;
OptionsStruct.ParameterNameArray = {'NumberOfAtoms'};
OptionsStruct.ParameterValueArray = {5000};
options = Helper.convertstruct2cell(OptionsStruct);
tStart = tic;
[LoadingRateArray, StandardErrorArray, ConfidenceIntervalArray] = Simulator.doOneParameterScan('BluePower', PowerArray, options{:});
tEnd = toc(tStart);
fprintf('Total Computational Time: %0.1f seconds. \n', tEnd);
clear OptionsStruct
% - Plot results
ParameterArray = PowerArray;
QuantityOfInterestArray = LoadingRateArray;
OptionsStruct = struct;
OptionsStruct.RescalingFactorForParameter = 1000;
OptionsStruct.XLabelString = 'Cooling Beam Power (mW)';
OptionsStruct.RescalingFactorForYQuantity = 1e-11;
OptionsStruct.ErrorsForYQuantity = true;
OptionsStruct.ErrorsArray = StandardErrorArray;
OptionsStruct.CIForYQuantity = true;
OptionsStruct.CIArray = ConfidenceIntervalArray;
OptionsStruct.RemoveOutliers = true;
OptionsStruct.YLabelString = 'Loading rate (x 10^{11} atoms/s)';
OptionsStruct.TitleString = sprintf('Magnetic Gradient = %.0f (G/cm)', Simulator.MagneticGradient * 100);
options = Helper.convertstruct2cell(OptionsStruct);
Plotting.plotResultForOneParameterScan(ParameterArray, QuantityOfInterestArray, options{:})
clear OptionsStruct
%% TWO-PARAMETER SCAN
NumberOfPointsForParam = 10; %iterations of the simulation
NumberOfPointsForSecondParam = 10;
% Scan Sideband Detuning and Power Ratio
DetuningArray = linspace(-0.5,-10, NumberOfPointsForParam) * Helper.PhysicsConstants.BlueLinewidth;
SidebandPowerArray = linspace(0.1,0.9, NumberOfPointsForSecondParam) * Simulator.TotalPower;
BluePowerArray = Simulator.TotalPower - SidebandPowerArray;
OptionsStruct = struct;
OptionsStruct.ChangeRelatedParameter = true;
OptionsStruct.Order = 2; %Change after first parameter = 1, Change after second parameter = 2
OptionsStruct.RelatedParameterName = 'BluePower';
OptionsStruct.RelatedParameterArray = BluePowerArray;
OptionsStruct.ChangeInitialConditions = true;
OptionsStruct.ParameterNameArray = {'NumberOfAtoms'};
OptionsStruct.ParameterValueArray = {5000};
options = Helper.convertstruct2cell(OptionsStruct);
tStart = tic;
[LoadingRateArray, StandardErrorArray, ConfidenceInterval] = Simulator.doTwoParameterScan('SidebandDetuning', DetuningArray, 'SidebandPower', SidebandPowerArray, options{:});
tEnd = toc(tStart);
fprintf('Total Computational Time: %0.1f seconds. \n', tEnd);
clear OptionsStruct
% - Plot results
FirstParameterArray = DetuningArray;
SecondParameterArray = SidebandPowerArray;
QuantityOfInterestArray = LoadingRateArray;
OptionsStruct = struct;
OptionsStruct.RescalingFactorForFirstParameter = (Helper.PhysicsConstants.BlueLinewidth)^-1;
OptionsStruct.XLabelString = 'Sideband Detuning (\Delta/\Gamma)';
OptionsStruct.RescalingFactorForSecondParameter = 1000;
OptionsStruct.YLabelString = 'Sideband Power (mW)';
OptionsStruct.RescalingFactorForQuantityOfInterest = 1e-10;
OptionsStruct.ZLabelString = 'Loading rate (x 10^{10} atoms/s)';
OptionsStruct.TitleString = sprintf('Magnetic Gradient = %.0f (G/cm)', Simulator.MagneticGradient * 100);
options = Helper.convertstruct2cell(OptionsStruct);
Plotting.plotResultForTwoParameterScan(FirstParameterArray, SecondParameterArray, QuantityOfInterestArray, options{:})
clear OptionsStruct

188
test_MOTCaptureProcessSimulation.m Normal file
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%% This script is testing the functionalities of the MOT Capture Process Simulation Classes
%
% Important: Run only sectionwise!!
%% - Testing the MOTCaptureProcess-Class
% - Create MOTCaptureProcess object with specified options
% - Automatically creates Beams objects
OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 10000;
OptionsStruct.TimeStep = 50e-06; % in s
OptionsStruct.SimulationTime = 4e-03; % in s
OptionsStruct.SpontaneousEmission = true;
OptionsStruct.Sideband = false;
OptionsStruct.PushBeam = true;
OptionsStruct.Gravity = true;
OptionsStruct.BackgroundCollision = true;
OptionsStruct.SaveData = false;
OptionsStruct.SaveDirectory = 'C:\DY LAB\MOT Simulation Project\Calculations\Code\MOT Capture Process Simulation';
options = Helper.convertstruct2cell(OptionsStruct);
clear OptionsStruct
Oven = Simulator.Oven(options{:});
MOT2D = Simulator.TwoDimensionalMOT(options{:});
Beams = MOT2D.Beams;
%% - Run Simulation
poolobj = gcp('nocreate'); % Check if pool is open
if isempty(poolobj)
parpool;
end
[LoadingRate, ~] = MOT2D.runSimulation(Oven);
%% - Plot initial distribution
% - sampling the position distribution
InitialPositions = Oven.initialPositionSampling();
% - sampling the velocity distribution
InitialVelocities = Oven.initialVelocitySampling(MOT2D);
NumberOfBins = 100;
Plotter.plotPositionAndVelocitySampling(NumberOfBins, InitialPositions, InitialVelocities);
%% - Plot distributions of magnitude and direction of initial velocities
NumberOfBins = 50;
Plotter.plotInitialVeloctiySamplingVsAngle(Oven, MOT2D, NumberOfBins)
%% - Plot Magnetic Field
XAxisRange = [-5 5];
YAxisRange = [-5 5];
ZAxisRange = [-5 5];
Plotter.visualizeMagneticField(MOT2D, XAxisRange, YAxisRange, ZAxisRange)
%% - Plot MFP & VP for different temperatures
TemperatureinCelsius = linspace(750,1100,2000); % Temperature in Celsius
Plotter.plotMeanFreePathAndVapourPressureVsTemp(TemperatureinCelsius)
%% - Plot the Free Molecular Flux for different temperatures
Temperature = [950, 1000, 1050]; % Temperature
Plotter.plotFreeMolecularFluxVsTemp(Oven,Temperature)
%% - Plot Angular Distribution for different Beta
Beta = [0.5, 0.1 , 0.05, 0.02, 0.01]; %Beta = 2 * radius / length of the tube
Plotter.plotAngularDistributionForDifferentBeta(Oven, Beta)
%% - Plot Capture Velocity
Plotter.plotCaptureVelocityVsAngle(Oven, MOT2D); % Takes a long time to plot!
%% - Plot Phase Space with Acceleration Field
MOT2D.Sideband = false;
MOT2D.NumberOfAtoms = 50;
MinimumVelocity = 0;
MaximumVelocity = 150;
NumberOfBins = 200; %Along each axis
IncidentAtomDirection = 0*2*pi/360;
IncidentAtomPosition = 0;
Plotter.plotPhaseSpaceWithAccelerationField(Oven, MOT2D, MinimumVelocity, MaximumVelocity, NumberOfBins, IncidentAtomDirection, IncidentAtomPosition)
%% - Plot Trajectories along the 3 directions
MOT2D.NumberOfAtoms = 100;
MaximumVelocity = 150;
IncidentAtomDirection = 0*2*pi/360;
IncidentAtomPosition = 0;
%% - Positions
Plotter.plotDynamicalQuantities(Oven, MOT2D, MaximumVelocity, IncidentAtomDirection, IncidentAtomPosition, 'PlotPositions', true);
%% - Velocities
Plotter.plotDynamicalQuantities(Oven, MOT2D, MaximumVelocity, IncidentAtomDirection, IncidentAtomPosition, 'PlotVelocities', true);
%% - Scan parameters: One-Parameter Scan
MOT2D.NumberOfAtoms = 5000;
MOT2D.TotalPower = 0.4;
CoolingBeam = Beams{cellfun(@(x) strcmpi(x.Alias, 'Blue'), Beams)};
NumberOfPointsForFirstParam = 5; %iterations of the simulation
% Scan Cooling Beam Power
PowerArray = linspace(0.1, 1.0, NumberOfPointsForFirstParam) * MOT2D.TotalPower;
% Scan Cooling Beam Detuning
% DetuningArray = linspace(-0.5,-10, NumberOfPointsForParam) * Helper.PhysicsConstants.BlueLinewidth;
LoadingRateArray = zeros(1,NumberOfPointsForFirstParam);
StandardErrorArray = zeros(1,NumberOfPointsForFirstParam);
ConfidenceIntervalArray = zeros(NumberOfPointsForFirstParam, 2);
tStart = tic;
for i=1:NumberOfPointsForFirstParam
CoolingBeam.Power = PowerArray(i);
[LoadingRateArray(i), StandardErrorArray(i), ConfidenceIntervalArray(i, :)] = MOT2D.runSimulation(Oven);
end
tEnd = toc(tStart);
fprintf('Total Computational Time: %0.1f seconds. \n', tEnd);
clear OptionsStruct
% - Plot results
ParameterArray = PowerArray;
QuantityOfInterestArray = LoadingRateArray;
OptionsStruct = struct;
OptionsStruct.RescalingFactorForParameter = 1000;
OptionsStruct.XLabelString = 'Cooling Beam Power (mW)';
OptionsStruct.RescalingFactorForYQuantity = 1e-10;
OptionsStruct.ErrorsForYQuantity = true;
OptionsStruct.ErrorsArray = StandardErrorArray;
OptionsStruct.CIForYQuantity = true;
OptionsStruct.CIArray = ConfidenceIntervalArray;
OptionsStruct.RemoveOutliers = true;
OptionsStruct.YLabelString = 'Loading rate (x 10^{10} atoms/s)';
OptionsStruct.TitleString = sprintf('Magnetic Gradient = %.0f (G/cm)', MOT2D.MagneticGradient * 100);
options = Helper.convertstruct2cell(OptionsStruct);
Plotter.plotResultForOneParameterScan(ParameterArray, QuantityOfInterestArray, options{:})
clear OptionsStruct
%% - Scan parameters: Two-Parameter Scan
MOT2D.NumberOfAtoms = 5000;
MOT2D.TotalPower = 0.6;
MOT2D.Sideband = true;
SidebandBeam = Beams{cellfun(@(x) strcmpi(x.Alias, 'BlueSideband'), Beams)};
NumberOfPointsForFirstParam = 10; %iterations of the simulation
NumberOfPointsForSecondParam = 10;
% Scan Sideband Detuning and Power Ratio
DetuningArray = linspace(-0.5,-10, NumberOfPointsForFirstParam) * Helper.PhysicsConstants.BlueLinewidth;
SidebandPowerArray = linspace(0.1,0.9, NumberOfPointsForSecondParam) * MOT2D.TotalPower;
BluePowerArray = MOT2D.TotalPower - SidebandPowerArray;
LoadingRateArray = zeros(NumberOfPointsForFirstParam, NumberOfPointsForSecondParam);
StandardErrorArray = zeros(NumberOfPointsForFirstParam, NumberOfPointsForSecondParam);
ConfidenceIntervalArray = zeros(NumberOfPointsForFirstParam, NumberOfPointsForSecondParam, 2);
tStart = tic;
for i = 1:NumberOfPointsForFirstParam
SidebandBeam.Detuning = DetuningArray(i);
for j = 1:NumberOfPointsForSecondParam
SidebandBeam.Power = SidebandPowerArray(j);
CoolingBeam.Power = BluePowerArray(j);
[LoadingRateArray(i,j), StandardErrorArray(i,j), ConfidenceIntervalArray(i,j,:)] = MOT2D.runSimulation(Oven);
end
end
tEnd = toc(tStart);
fprintf('Total Computational Time: %0.1f seconds. \n', tEnd);
clear OptionsStruct
% - Plot results
FirstParameterArray = DetuningArray;
SecondParameterArray = SidebandPowerArray;
QuantityOfInterestArray = LoadingRateArray;
OptionsStruct = struct;
OptionsStruct.RescalingFactorForFirstParameter = (Helper.PhysicsConstants.BlueLinewidth)^-1;
OptionsStruct.XLabelString = 'Sideband Detuning (\Delta/\Gamma)';
OptionsStruct.RescalingFactorForSecondParameter = 1000;
OptionsStruct.YLabelString = 'Sideband Power (mW)';
OptionsStruct.RescalingFactorForQuantityOfInterest = 1e-10;
OptionsStruct.ZLabelString = 'Loading rate (x 10^{10} atoms/s)';
OptionsStruct.TitleString = sprintf('Magnetic Gradient = %.0f (G/cm)', MOT2D.MagneticGradient * 100);
options = Helper.convertstruct2cell(OptionsStruct);
Plotter.plotResultForTwoParameterScan(FirstParameterArray, SecondParameterArray, QuantityOfInterestArray, options{:})
clear OptionsStruct