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Corrected dipolar potential with angular dependence.

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Karthik 2024-11-01 14:36:04 +01:00
parent 212c9e1b56
commit e28988b0ef
1 changed files with 28 additions and 27 deletions
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55
Quasi2DBogoliubovSpectrum.m
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@ -28,48 +28,49 @@ Dy164Mass = 163.929174751*1.660539066E-27;
Dy164IsotopicAbundance = 0.2826; Dy164IsotopicAbundance = 0.2826;
DyMagneticMoment = 9.93*9.274009994E-24; DyMagneticMoment = 9.93*9.274009994E-24;
%% Dispersion relation of the quasiparticle excitations %% Bogoliubov excitation spectrum for quasi-2D dipolar gas with QF correction
AtomNumber = 1E5; AtomNumber = 1E5; % Total atom number in the system
wz = 2*pi*72.4; wz = 2*pi*72.4; % Trap frequency in the tight confinement direction
lz = sqrt(PlanckConstantReduced/(Dy164Mass*wz)); % Defining a harmonic oscillator length lz = sqrt(PlanckConstantReduced/(Dy164Mass*wz)); % Defining a harmonic oscillator length
as = 102.4*BohrRadius; % Scattering length as = 102.515*BohrRadius; % Scattering length
Trapsize = 7.6; Trapsize = 7.5815; % Trap is assumed to be a box of finite extent , given here in units of the harmonic oscillator length
alpha = 0; alpha = 0; % Polar angle of dipole moment
phi = 0; phi = 0; % Azimuthal angle of momentum vector
MeanWidth = 2.8215042184E3*lz; MeanWidth = 5.7304888515*lz; % Mean width of Gaussian ansatz
k = linspace(0, 1e7, 1000); k = linspace(0, 3e6, 1000); % Vector of magnitudes of k vector
AtomNumberDensity = AtomNumber / (Trapsize * lz)^2; % Areal density of atoms
AtomNumberDensity = AtomNumber / (Trapsize * lz)^2;
add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length
eps_dd = add/as; eps_dd = add/as; % Relative interaction strength
gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength
gdd = VacuumPermeability*DyMagneticMoment^2/3;
[fk,Fka,Ukk] = computePotentialInMomentumSpace(k, lz, alpha, phi, gs, eps_dd); [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, alpha, phi); % DDI potential in k-space
% == Quantum Fluctuations term == % % == Quantum Fluctuations term == %
gQF = ((256 * PlanckConstantReduced^2) / (15*Dy164Mass*MeanWidth^3)) * as^(5/2) * (1 + ((3/2) * eps_dd^2)); gammaQF = (32/3) * gs * (as^3/pi)^(1/2) * (1 + ((3/2) * eps_dd^2));
gamma5 = sqrt(2/5) / (sqrt(pi) * MeanWidth)^(3/2);
gQF = gamma5 * gammaQF;
% == Dispersion relation == %
DeltaK = ((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2)); DeltaK = ((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2));
EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK);
figure(1) figure(1)
set(gcf,'Position',[100 100 950 750]) set(gcf,'Position',[50 50 950 750])
% xvals = (k .* lz/sqrt(2));
xvals = (k .* add); xvals = (k .* add);
yvals = EpsilonK ./ (PlanckConstantReduced * wz); yvals = EpsilonK ./ PlanckConstant;
plot(xvals, yvals,LineWidth=2.0) plot(xvals, yvals,LineWidth=2.0)
% xlim([3.45, 3.65]) 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')
% ylim([0, 0.001]) xlabel('$k_{\rho}a_{dd}$','fontsize',16,'interpreter','latex')
title(horzcat(['$a_s = ',num2str(1/eps_dd),'a_{dd}, '], ['na_{dd}^2 = ',num2str(AtomNumberDensity * add^2),'$']),'fontsize',16,'interpreter','latex') ylabel('$\epsilon(k_{\rho})/h$ (Hz)','fontsize',16,'interpreter','latex')
xlabel('$ka_{dd}$','fontsize',16,'interpreter','latex')
ylabel('$\epsilon(k)/\hbar \omega_z$','fontsize',16,'interpreter','latex')
grid on grid on
%% %%
function [fk,Fka,Ukk] = computePotentialInMomentumSpace(k, lz, alpha, phi, gs, eps_dd)
fk = (3 * sqrt(pi)) * (k .* lz/sqrt(2)) .* exp((k .* lz/sqrt(2)).^2) .* erfc((k .* lz/sqrt(2))) ; function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, alpha, phi)
Fka = (fk .* sin(deg2rad(phi))^2 - 1) + (cos(deg2rad(alpha))^2 .* (3 - (fk .* (sin(deg2rad(phi))^2 + 1)))); Go = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2)));
Ukk = (gs/ (sqrt(2 * pi) * lz)) .* (1 + (eps_dd .* Fka)); gamma4 = 1/(sqrt(2*pi) * MeanWidth);
Fka = (3 * cos(deg2rad(alpha))^2 - 1) + ((3 * Go) .* ((sin(deg2rad(alpha))^2 .* sin(deg2rad(phi))^2) - cos(deg2rad(alpha))^2));
Ukk = (gs + (gdd * Fka)) * gamma4;
end end