115 lines
4.9 KiB
Matlab
115 lines
4.9 KiB
Matlab
%% Physical constants
|
|
PlanckConstant = 6.62607015E-34;
|
|
PlanckConstantReduced = 6.62607015E-34/(2*pi);
|
|
FineStructureConstant = 7.2973525698E-3;
|
|
ElectronMass = 9.10938291E-31;
|
|
GravitationalConstant = 6.67384E-11;
|
|
ProtonMass = 1.672621777E-27;
|
|
AtomicMassUnit = 1.660539066E-27;
|
|
BohrRadius = 5.2917721067E-11;
|
|
BohrMagneton = 9.274009994E-24;
|
|
BoltzmannConstant = 1.38064852E-23;
|
|
StandardGravityAcceleration = 9.80665;
|
|
SpeedOfLight = 299792458;
|
|
StefanBoltzmannConstant = 5.670373E-8;
|
|
ElectronCharge = 1.602176634E-19;
|
|
VacuumPermeability = 1.25663706212E-6;
|
|
DielectricConstant = 8.8541878128E-12;
|
|
ElectronGyromagneticFactor = -2.00231930436153;
|
|
AvogadroConstant = 6.02214076E23;
|
|
ZeroKelvin = 273.15;
|
|
GravitationalAcceleration = 9.80553;
|
|
VacuumPermittivity = 1 / (SpeedOfLight^2 * VacuumPermeability);
|
|
HartreeEnergy = ElectronCharge^2 / (4 * pi * VacuumPermittivity * BohrRadius);
|
|
AtomicUnitOfPolarizability = (ElectronCharge^2 * BohrRadius^2) / HartreeEnergy; % Or simply 4*pi*VacuumPermittivity*BohrRadius^3
|
|
|
|
% Dy specific constants
|
|
Dy164Mass = 163.929174751*1.660539066E-27;
|
|
Dy164IsotopicAbundance = 0.2826;
|
|
DyMagneticMoment = 9.93*9.274009994E-24;
|
|
|
|
%% Lattice spacing
|
|
|
|
Wavelength = 532e-9;
|
|
theta = linspace(1.5, 18.0, 100);
|
|
LatticeSpacing = Wavelength ./ (2.*sin((theta*pi/180)/2));
|
|
|
|
figure(1);
|
|
set(gcf,'Position',[100 100 950 750])
|
|
plot(theta, LatticeSpacing * 1E6, LineWidth=2.0)
|
|
xlim([0 19]);
|
|
ylim([0.5 21]);
|
|
xlabel('Angle (deg)', FontSize=16)
|
|
ylabel('Lattice spacing (µm)', FontSize=16)
|
|
title(['\bf Upper bound = ' num2str(round(max(LatticeSpacing * 1E6),1)) ' µm ; \bf Lower bound = ' num2str(round(min(LatticeSpacing * 1E6),1)) ' µm'], FontSize=16)
|
|
grid on
|
|
%% Scaling of vertical trap frequency with lattice spacing
|
|
Wavelength = 532e-9;
|
|
a = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
|
|
Power = 5;
|
|
waist_y = 250E-6;
|
|
waist_z = 50E-6;
|
|
TrapDepth = ((8 * a * Power) / (pi * waist_y * waist_z)) / (BoltzmannConstant * 1E-6); % in µK
|
|
thetas = linspace(1.5, 18.0, 100);
|
|
LatticeSpacings = zeros(1, length(thetas));
|
|
Omega_z = zeros(1, length(thetas));
|
|
|
|
for idx = 1:length(thetas)
|
|
theta = 0.5 * thetas(idx) .* pi/180;
|
|
LatticeSpacings(idx) = Wavelength ./ (2.*sin(theta));
|
|
Omega_z(idx) = sqrt(((16 * a * Power) / (pi * Dy164Mass * waist_y * waist_z)) * ...
|
|
((2 * (cos(theta)/waist_z)^2) + ((Wavelength * sin(theta)/pi)^2 * ...
|
|
((1/waist_y^4) + (1/waist_z^4))) + (pi / LatticeSpacings(idx))^2));
|
|
|
|
end
|
|
|
|
nu_z = Omega_z ./ (2*pi);
|
|
|
|
figure(2);
|
|
set(gcf,'Position',[100 100 950 750])
|
|
plot(LatticeSpacings * 1E6, nu_z * 1E-3, LineWidth=2.0)
|
|
xlim([0.5 21]);
|
|
xlabel('Lattice spacing (µm)', FontSize=16)
|
|
ylabel('Trap frequency (kHz)', FontSize=16)
|
|
title(['\bf Upper bound = ' num2str(round(max(nu_z * 1E-3),2)) ' kHz ; \bf Lower bound = ' num2str(round(min(nu_z * 1E-3),2)) ' kHz'], FontSize=16)
|
|
grid on
|
|
|
|
%% Scaling of Recoil Energy - All energy scales in an optical lattice are naturally parametrized by the lattice recoil energy
|
|
|
|
LatticeSpacing = linspace(2E-6, 20E-6, 100);
|
|
RecoilEnergy = PlanckConstant^2 ./ (8 .* Dy164Mass .* LatticeSpacing.^2);
|
|
|
|
figure(3);
|
|
set(gcf,'Position',[100 100 950 750])
|
|
semilogy(LatticeSpacing * 1E6, RecoilEnergy/PlanckConstant, LineWidth=2.0, DisplayName=['\bf Max = ' num2str(round(max(RecoilEnergy / PlanckConstant),1)) ' Hz; Min = ' num2str(round(min(RecoilEnergy / PlanckConstant),1)) ' Hz'])
|
|
xlim([0.5 21]);
|
|
xlabel('Lattice spacing (µm)', FontSize=16)
|
|
ylabel('Recoil Energy (Hz)', FontSize=16)
|
|
title('\bf Scaling of Recoil Energy - All energy scales in an optical lattice are naturally parametrized by the lattice recoil energy', FontSize=12)
|
|
grid on
|
|
legend(FontSize=12)
|
|
|
|
%% Interference pattern spacing in ToF - de Broglie wavelength associated with the relative motion of atoms
|
|
|
|
ExpansionTime = linspace(1E-3, 20.0E-3, 100);
|
|
|
|
figure(4);
|
|
set(gcf,'Position',[100 100 950 750])
|
|
labels = [];
|
|
|
|
for ls = [2E-6:2E-6:5E-6 6E-6:6E-6:20E-6]
|
|
InteferencePatternSpacing = (PlanckConstant .* ExpansionTime) ./ (Dy164Mass * ls);
|
|
plot(ExpansionTime*1E3, InteferencePatternSpacing* 1E6, LineWidth=2.0, DisplayName=['\bf Lattice spacing = ' num2str(round(max(ls * 1E6),1)) ' µm'])
|
|
hold on
|
|
end
|
|
xlim([0 22]);
|
|
xlabel('Free expansion time (milliseconds)', FontSize=16)
|
|
ylabel('Interference pattern period (µm)', FontSize=16)
|
|
title('\bf Interference of condensates - Fringe period is the de Broglie wavelength associated with the relative motion of atoms', FontSize=12)
|
|
legend(labels, 'Location','NorthWest', FontSize=12);
|
|
grid on
|
|
legend show
|
|
|
|
|
|
|