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

Added the scaling of the Rabi oscillation frequency expected in K-D scattering.

Browse Source
This commit is contained in:
Karthik 2024-09-18 10:48:50 +02:00
parent e95284d24f
commit 85f4af3e60
1 changed files with 45 additions and 10 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

55
EstimatesForAccordionLattice.m
View File

@ -43,6 +43,7 @@ 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));
@ -74,22 +75,36 @@ title(['\bf Upper bound = ' num2str(round(max(nu_z * 1E-3),2)) ' kHz ; \bf Lower
grid on
%% Scaling of trap depth with power
a = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
waist_y = 250E-6;
waist_z = 50E-6;
Powers = linspace(0.1, 5, 100);
TrapDepth = ((8 * a .* Powers) ./ (pi * waist_y * waist_z)) / (BoltzmannConstant * 1E-6); % in µK
a = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
waist_y = 250E-6;
waist_z = 50E-6;
Powers = linspace(0.1, 5, 100);
TrapDepths = ((8 * a .* Powers) ./ (pi * waist_y * waist_z));
TrapDepthsInHz = TrapDepths ./ PlanckConstant; % in Hz
TrapDepthsInmicroK = TrapDepths ./ BoltzmannConstant; % in µK
TwoPhotonRecoilEnergy = (2*PlanckConstantReduced*2*pi/Wavelength)^2 / (2 * Dy164Mass);
TrapDepthsInUnitsOfRecoilEnergy = TrapDepths ./ TwoPhotonRecoilEnergy;
% TrapDepthsToPlot = TrapDepthsInHz * 1E-3;
% units = ' kHz';
% TrapDepthsToPlot = TrapDepthsInmicroK * 1E6;
% units = ' µK';
TrapDepthsToPlot = TrapDepthsInUnitsOfRecoilEnergy;
units = ' E_r';
figure(3);
set(gcf,'Position',[100 100 950 750])
plot(Powers, TrapDepth, LineWidth=2.0)
xlim([0.0 5.5]);
plot(Powers, TrapDepthsToPlot, LineWidth=2.0)
xlim([0.0 5.25]);
xlabel('Powers (W)', FontSize=16)
ylabel('Trap depth (µK)', FontSize=16)
title(['\bf Upper bound = ' num2str(round(max(TrapDepth),2)) ' µK ; \bf Lower bound = ' num2str(round(min(TrapDepth),2)) ' µK'], FontSize=16)
ylabel(['Trap depth (' units ' )'], FontSize=16)
title(['\bf Upper bound = ' num2str(round(max(TrapDepthsToPlot),2)) units '; \bf Lower bound = ' num2str(round(min(TrapDepthsToPlot),2)) units], FontSize=16)
grid on
%% Scaling of Recoil Energy - All energy scales in an optical lattice are naturally parametrized by the lattice recoil energy
%% Scaling of the lattice 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);
@ -124,5 +139,25 @@ legend(labels, 'Location','NorthWest', FontSize=12);
grid on
legend show
%% Scaling of frequency of oscillation in the first order in Kapitza-Dirac scattering
a = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
waist_y = 250E-6;
waist_z = 50E-6;
Powers = linspace(0.001, 0.4, 100);
TrapDepths = ((8 * a .* Powers) ./ (pi * waist_y * waist_z));
TwoPhotonRecoilEnergy = (2*PlanckConstantReduced*2*pi/Wavelength)^2 / (2 * Dy164Mass);
RabiOscillationFrequency = (1/PlanckConstantReduced) .* (sqrt(TrapDepths.^2/2 + TwoPhotonRecoilEnergy^2));
TrapDepthsInHz = TrapDepths./ PlanckConstant;
TwoPhotonRecoilEnergyInHz = TwoPhotonRecoilEnergy / PlanckConstant;
TrapDepthsInUnitsOfRecoilEnergy = TrapDepthsInHz ./ TwoPhotonRecoilEnergyInHz;
figure(6);
set(gcf,'Position',[100 100 950 750])
plot(TrapDepthsInUnitsOfRecoilEnergy, RabiOscillationFrequency .* 1E-3, LineWidth=2.0)
xlim([0 4]);
xlabel('Trap depths (E_r)', FontSize=16)
ylabel('Rabi oscillation frequency (kHz)', FontSize=16)
title(['\bf Upper bound = ' num2str(round(max(RabiOscillationFrequency .* 1E-3),1)) ' kHz; Lower bound = ' num2str(round(min(RabiOscillationFrequency .* 1E-3),1)) ' kHz'], FontSize=16)
grid on