76 lines
4.8 KiB
Matlab
76 lines
4.8 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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%% Bogoliubov excitation spectrum for quasi-2D dipolar gas with QF correction
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AtomNumber = 1E5; % Total atom number in the system
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wz = 2*pi*72.4; % Trap frequency in the tight confinement direction
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lz = sqrt(PlanckConstantReduced/(Dy164Mass*wz)); % Defining a harmonic oscillator length
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as = 102.515*BohrRadius; % Scattering length
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Trapsize = 7.5815; % Trap is assumed to be a box of finite extent , given here in units of the harmonic oscillator length
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alpha = 0; % Polar angle of dipole moment
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phi = 0; % Azimuthal angle of momentum vector
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MeanWidth = 5.7304888515*lz; % Mean width of Gaussian ansatz
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k = linspace(0, 3e6, 1000); % Vector of magnitudes of k vector
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AtomNumberDensity = AtomNumber / (Trapsize * lz)^2; % Areal density of atoms
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add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length
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eps_dd = add/as; % Relative interaction strength
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gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength
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gdd = VacuumPermeability*DyMagneticMoment^2/3;
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[Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, alpha, phi); % DDI potential in k-space
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% == Quantum Fluctuations term == %
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gammaQF = (32/3) * gs * (as^3/pi)^(1/2) * (1 + ((3/2) * eps_dd^2));
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gamma5 = sqrt(2/5) / (sqrt(pi) * MeanWidth)^(3/2);
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gQF = gamma5 * gammaQF;
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% == Dispersion relation == %
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DeltaK = ((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2));
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EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK);
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figure(1)
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set(gcf,'Position',[50 50 950 750])
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xvals = (k .* add);
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yvals = EpsilonK ./ PlanckConstant;
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plot(xvals, yvals,LineWidth=2.0)
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title(horzcat(['$a_s = ',num2str(round(1/eps_dd,3)),'a_{dd}, '], ['na_{dd}^2 = ',num2str(round(AtomNumberDensity * add^2,4)),'$']),'fontsize',16,'interpreter','latex')
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xlabel('$k_{\rho}a_{dd}$','fontsize',16,'interpreter','latex')
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ylabel('$\epsilon(k_{\rho})/h$ (Hz)','fontsize',16,'interpreter','latex')
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grid on
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%%
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function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, alpha, phi)
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Go = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2)));
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gamma4 = 1/(sqrt(2*pi) * MeanWidth);
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Fka = (3 * cos(deg2rad(alpha))^2 - 1) + ((3 * Go) .* ((sin(deg2rad(alpha))^2 .* sin(deg2rad(phi))^2) - cos(deg2rad(alpha))^2));
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Ukk = (gs + (gdd * Fka)) * gamma4;
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end |