163 lines
7.1 KiB
Matlab
163 lines
7.1 KiB
Matlab
%% Physical constants
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PlanckConstant = 6.62607015E-34;
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PlanckConstantReduced = 6.62607015E-34/(2*pi);
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FineStructureConstant = 7.2973525698E-3;
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ElectronMass = 9.10938291E-31;
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GravitationalConstant = 6.67384E-11;
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ProtonMass = 1.672621777E-27;
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AtomicMassUnit = 1.660539066E-27;
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BohrRadius = 5.2917721067E-11;
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BohrMagneton = 9.274009994E-24;
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BoltzmannConstant = 1.38064852E-23;
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StandardGravityAcceleration = 9.80665;
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SpeedOfLight = 299792458;
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StefanBoltzmannConstant = 5.670373E-8;
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ElectronCharge = 1.602176634E-19;
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VacuumPermeability = 1.25663706212E-6;
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DielectricConstant = 8.8541878128E-12;
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ElectronGyromagneticFactor = -2.00231930436153;
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AvogadroConstant = 6.02214076E23;
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ZeroKelvin = 273.15;
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GravitationalAcceleration = 9.80553;
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VacuumPermittivity = 1 / (SpeedOfLight^2 * VacuumPermeability);
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HartreeEnergy = ElectronCharge^2 / (4 * pi * VacuumPermittivity * BohrRadius);
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AtomicUnitOfPolarizability = (ElectronCharge^2 * BohrRadius^2) / HartreeEnergy; % Or simply 4*pi*VacuumPermittivity*BohrRadius^3
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% Dy specific constants
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Dy164Mass = 163.929174751*1.660539066E-27;
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Dy164IsotopicAbundance = 0.2826;
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DyMagneticMoment = 9.93*9.274009994E-24;
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%% Lattice spacing
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Wavelength = 532e-9;
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theta = linspace(1.5, 18.0, 100);
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LatticeSpacing = Wavelength ./ (2.*sin((theta*pi/180)/2));
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figure(1);
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set(gcf,'Position',[100 100 950 750])
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plot(theta, LatticeSpacing * 1E6, LineWidth=2.0)
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xlim([0 19]);
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ylim([0.5 21]);
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xlabel('Angle (deg)', FontSize=16)
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ylabel('Lattice spacing (µm)', FontSize=16)
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title(['\bf Upper bound = ' num2str(round(max(LatticeSpacing * 1E6),1)) ' µm ; \bf Lower bound = ' num2str(round(min(LatticeSpacing * 1E6),1)) ' µm'], FontSize=16)
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grid on
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%% Scaling of vertical trap frequency with lattice spacing
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Wavelength = 532e-9;
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a = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
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Power = 5;
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waist_y = 250E-6;
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waist_z = 50E-6;
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thetas = linspace(1.5, 18.0, 100);
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LatticeSpacings = zeros(1, length(thetas));
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Omega_z = zeros(1, length(thetas));
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for idx = 1:length(thetas)
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theta = 0.5 * thetas(idx) .* pi/180;
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LatticeSpacings(idx) = Wavelength ./ (2.*sin(theta));
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Omega_z(idx) = sqrt(((16 * a * Power) / (pi * Dy164Mass * waist_y * waist_z)) * ...
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((2 * (cos(theta)/waist_z)^2) + ((Wavelength * sin(theta)/pi)^2 * ...
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((1/waist_y^4) + (1/waist_z^4))) + (pi / LatticeSpacings(idx))^2));
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end
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nu_z = Omega_z ./ (2*pi);
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figure(2);
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set(gcf,'Position',[100 100 950 750])
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plot(LatticeSpacings * 1E6, nu_z * 1E-3, LineWidth=2.0)
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xlim([0.5 21]);
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xlabel('Lattice spacing (µm)', FontSize=16)
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ylabel('Trap frequency (kHz)', FontSize=16)
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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)
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grid on
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%% Scaling of trap depth with power
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a = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
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waist_y = 250E-6;
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waist_z = 50E-6;
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Powers = linspace(0.1, 5, 100);
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TrapDepths = ((8 * a .* Powers) ./ (pi * waist_y * waist_z));
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TrapDepthsInHz = TrapDepths ./ PlanckConstant; % in Hz
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TrapDepthsInmicroK = TrapDepths ./ BoltzmannConstant; % in µK
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TwoPhotonRecoilEnergy = (2*PlanckConstantReduced*2*pi/Wavelength)^2 / (2 * Dy164Mass);
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TrapDepthsInUnitsOfRecoilEnergy = TrapDepths ./ TwoPhotonRecoilEnergy;
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% TrapDepthsToPlot = TrapDepthsInHz * 1E-3;
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% units = ' kHz';
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% TrapDepthsToPlot = TrapDepthsInmicroK * 1E6;
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% units = ' µK';
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TrapDepthsToPlot = TrapDepthsInUnitsOfRecoilEnergy;
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units = ' E_r';
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figure(3);
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set(gcf,'Position',[100 100 950 750])
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plot(Powers, TrapDepthsToPlot, LineWidth=2.0)
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xlim([0.0 5.25]);
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xlabel('Powers (W)', FontSize=16)
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ylabel(['Trap depth (' units ' )'], FontSize=16)
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title(['\bf Upper bound = ' num2str(round(max(TrapDepthsToPlot),2)) units '; \bf Lower bound = ' num2str(round(min(TrapDepthsToPlot),2)) units], FontSize=16)
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grid on
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%% Scaling of the lattice recoil Energy - All energy scales in an optical lattice are naturally parametrized by the lattice recoil energy
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LatticeSpacing = linspace(2E-6, 20E-6, 100);
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RecoilEnergy = PlanckConstant^2 ./ (8 .* Dy164Mass .* LatticeSpacing.^2);
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figure(4);
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set(gcf,'Position',[100 100 950 750])
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semilogy(LatticeSpacing * 1E6, RecoilEnergy/PlanckConstant, LineWidth=2.0)
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xlim([0.5 21]);
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xlabel('Lattice spacing (µm)', FontSize=16)
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ylabel('Recoil Energy (Hz)', FontSize=16)
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title(['\bf Upper bound = ' num2str(round(max(RecoilEnergy / PlanckConstant),1)) ' Hz; Lower bound = ' num2str(round(min(RecoilEnergy / PlanckConstant),1)) ' Hz'], FontSize=16)
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grid on
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%% Interference pattern spacing in ToF - de Broglie wavelength associated with the relative motion of atoms
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ExpansionTime = linspace(1E-3, 20.0E-3, 100);
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figure(5);
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set(gcf,'Position',[100 100 950 750])
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labels = [];
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for ls = [2E-6:2E-6:5E-6 6E-6:6E-6:20E-6]
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InteferencePatternSpacing = (PlanckConstant .* ExpansionTime) ./ (Dy164Mass * ls);
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plot(ExpansionTime*1E3, InteferencePatternSpacing* 1E6, LineWidth=2.0, DisplayName=['\bf Lattice spacing = ' num2str(round(max(ls * 1E6),1)) ' µm'])
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hold on
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end
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xlim([0 22]);
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xlabel('Free expansion time (milliseconds)', FontSize=16)
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ylabel('Interference pattern period (µm)', FontSize=16)
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title('\bf Interference of condensates - Fringe period is the de Broglie wavelength associated with the relative motion of atoms', FontSize=12)
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legend(labels, 'Location','NorthWest', FontSize=12);
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grid on
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legend show
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%% Scaling of frequency of oscillation in the first order in Kapitza-Dirac scattering
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a = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
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waist_y = 250E-6;
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waist_z = 50E-6;
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Powers = linspace(0.001, 0.4, 100);
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TrapDepths = ((8 * a .* Powers) ./ (pi * waist_y * waist_z));
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TwoPhotonRecoilEnergy = (2*PlanckConstantReduced*2*pi/Wavelength)^2 / (2 * Dy164Mass);
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RabiOscillationFrequency = (1/PlanckConstantReduced) .* (sqrt(TrapDepths.^2/2 + TwoPhotonRecoilEnergy^2));
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TrapDepthsInHz = TrapDepths./ PlanckConstant;
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TwoPhotonRecoilEnergyInHz = TwoPhotonRecoilEnergy / PlanckConstant;
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TrapDepthsInUnitsOfRecoilEnergy = TrapDepthsInHz ./ TwoPhotonRecoilEnergyInHz;
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figure(6);
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set(gcf,'Position',[100 100 950 750])
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plot(TrapDepthsInUnitsOfRecoilEnergy, RabiOscillationFrequency .* 1E-3, LineWidth=2.0)
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xlim([0 4]);
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xlabel('Trap depths (E_r)', FontSize=16)
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ylabel('Rabi oscillation frequency (kHz)', FontSize=16)
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title(['\bf Upper bound = ' num2str(round(max(RabiOscillationFrequency .* 1E-3),1)) ' kHz; Lower bound = ' num2str(round(min(RabiOscillationFrequency .* 1E-3),1)) ' kHz'], FontSize=16)
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grid on |