diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/AnalyzeResults.m b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/AnalyzeResults.m deleted file mode 100644 index 95703ba..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/AnalyzeResults.m +++ /dev/null @@ -1,364 +0,0 @@ -%% Across range of a_s, n - -% load('.\Results\ExtractingKRoton_Result_Below1000.mat') -% load('.\Results\ExtractingKRoton_Result_Above1000.mat') -load('.\Results\ExtractingKRoton_Result_Above10000.mat') - -PlanckConstantReduced = 6.62607015E-34/(2*pi); -AtomicMassUnit = 1.660539066E-27; -Dy164Mass = 163.929174751*AtomicMassUnit; -VacuumPermeability = 1.25663706212E-6; -BohrMagneton = 9.274009994E-24; -BohrRadius = 5.2917721067E-11; -DyMagneticMoment = 9.93*BohrMagneton; - -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length - -% Create a tiled layout with tighter spacing -figure(17) -clf -set(gcf,'Position',[50 50 1800 500]) -t = tiledlayout(1, 3, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid - -% First subplot -nexttile; % Equivalent to subplot(2, 2, 1) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - eps_dd_values = data_struct(idx).eps_dd_values; - plot(theta_values, eps_dd_values, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$\epsilon_{dd}$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Second subplot -nexttile; % Equivalent to subplot(2, 2, 2) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - n_values = data_struct(idx).n_values; - plot(theta_values, n_values * 1E-15, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$n (\times 10^{3} \mu m^{-2})$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Third subplot -nexttile; % Equivalent to subplot(2, 2, 3) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - k_roton_values = data_struct(idx).k_roton_values; - plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); -grid on -legend('location', 'northeast','fontsize', 10, 'Interpreter','latex') - -% Adjust layout to minimize space -t.TileSpacing = 'compact'; % Minimize space between tiles -t.Padding = 'compact'; % Minimize padding around the layout - -% Convert to units relevant to experiment - -% Create a tiled layout with tighter spacing -figure(18) -clf -set(gcf,'Position',[50 50 1800 500]) -t = tiledlayout(1, 3, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid - -% First subplot -nexttile; % Equivalent to subplot(2, 2, 1) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - eps_dd_values = data_struct(idx).eps_dd_values; - plot(theta_values, (1 ./ eps_dd_values) * (add / BohrRadius), '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$a_s (\times a_o)$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'southeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Second subplot -nexttile; % Equivalent to subplot(2, 2, 2) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - n_values = data_struct(idx).n_values; - Lx = 10e-6; - Ly = 10e-6; - AtomNumber = n_values .* Lx * Ly; - plot(theta_values, AtomNumber * 1e-5, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('Atom number in a trap of area 100 $\mu m^2 (\times 10^{5})$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Third subplot -nexttile; % Equivalent to subplot(2, 2, 3) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - lambda_roton_values = (2 * pi) ./ data_struct(idx).k_roton_values; - plot(theta_values, lambda_roton_values * 1E6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$\lambda_{roton} (\mu m)$','fontsize',16,'interpreter','latex'); -grid on -legend('location', 'northeast','fontsize', 10, 'Interpreter','latex') - -% Adjust layout to minimize space -t.TileSpacing = 'compact'; % Minimize space between tiles -t.Padding = 'compact'; % Minimize padding around the layout - -%% Fixed Density results - -load('.\Results\ExtractingKRoton_Result_FixedDensity_phi0.mat') - -PlanckConstantReduced = 6.62607015E-34/(2*pi); -AtomicMassUnit = 1.660539066E-27; -Dy164Mass = 163.929174751*AtomicMassUnit; -VacuumPermeability = 1.25663706212E-6; -BohrMagneton = 9.274009994E-24; -BohrRadius = 5.2917721067E-11; -DyMagneticMoment = 9.93*BohrMagneton; - -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length - -% Create a tiled layout with tighter spacing -figure(19) -clf -set(gcf,'Position',[50 50 1200 500]) -t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid - -% First subplot -nexttile; -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - eps_dd_values = data_struct(idx).eps_dd_values; - plot(theta_values, eps_dd_values, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$\epsilon_{dd}$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Second subplot -nexttile; -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - k_roton_values = data_struct(idx).k_roton_values; - plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); -grid on -legend('location', 'northeast','fontsize', 10, 'Interpreter','latex') - -% Adjust layout to minimize space -t.TileSpacing = 'compact'; % Minimize space between tiles -t.Padding = 'compact'; % Minimize padding around the layout - -% Create a tiled layout with tighter spacing -figure(20) -clf -set(gcf,'Position',[50 50 1200 500]) -t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid - -% First subplot -nexttile; -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - eps_dd_values = data_struct(idx).eps_dd_values; - plot(theta_values, (1 ./ eps_dd_values) * (add / BohrRadius), '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$a_s (\times a_o)$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'northwest', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Second subplot -nexttile; -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - lambda_roton_values = (2 * pi) ./ data_struct(idx).k_roton_values; - semilogy(theta_values, lambda_roton_values * 1E6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -% ylim([0 2]) -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$\lambda_{roton} (\mu m)$','fontsize',16,'interpreter','latex'); -grid on -legend('location', 'southeast','fontsize', 10, 'Interpreter','latex') - -% Adjust layout to minimize space -t.TileSpacing = 'compact'; % Minimize space between tiles -t.Padding = 'compact'; % Minimize padding around the layout - -%% Fixed Density results - compare two orthogonal directions - -data0 = load('.\Results\ExtractingKRoton_Result_FixedDensity_phi0.mat'); -data90 = load('.\Results\ExtractingKRoton_Result_FixedDensity_phi90.mat'); - -PlanckConstantReduced = 6.62607015E-34/(2*pi); -AtomicMassUnit = 1.660539066E-27; -Dy164Mass = 163.929174751*AtomicMassUnit; -VacuumPermeability = 1.25663706212E-6; -BohrMagneton = 9.274009994E-24; -BohrRadius = 5.2917721067E-11; -DyMagneticMoment = 9.93*BohrMagneton; - -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length - -% Create a tiled layout with tighter spacing -figure(21) -clf -set(gcf,'Position',[50 50 1200 500]) -t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid - -idx = 4; - -% First subplot -nexttile; -theta_values = data0.data_struct(idx).theta_values; -eps_dd_values = data0.data_struct(idx).eps_dd_values; -plot(theta_values, eps_dd_values, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data0.data_struct(idx).wz_value), ' Hz; $\phi = 0^\circ$']); -hold on -theta_values = data90.data_struct(idx).theta_values; -eps_dd_values = data90.data_struct(idx).eps_dd_values; -plot(theta_values, eps_dd_values, '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data90.data_struct(idx).wz_value), ' Hz; $\phi = 90^\circ$']); -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$\epsilon_{dd}$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'northeast', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Second subplot -nexttile; -theta_values = data0.data_struct(idx).theta_values; -k_roton_values = data0.data_struct(idx).k_roton_values; -plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data0.data_struct(idx).wz_value), ' Hz; $\phi = 0^\circ$']); -hold on -theta_values = data90.data_struct(idx).theta_values; -k_roton_values = data90.data_struct(idx).k_roton_values; -plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data90.data_struct(idx).wz_value), ' Hz; $\phi = 90^\circ$']); -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); -grid on -legend('location', 'northeast','fontsize', 10, 'Interpreter','latex') - -% Adjust layout to minimize space -t.TileSpacing = 'compact'; % Minimize space between tiles -t.Padding = 'compact'; % Minimize padding around the layout - - -% Create a tiled layout with tighter spacing -figure(22) -clf -set(gcf,'Position',[50 50 1200 500]) -t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x2 grid - -% First subplot -nexttile; -theta_values = data0.data_struct(idx).theta_values; -eps_dd_values = data0.data_struct(idx).eps_dd_values; -plot(theta_values, (1 ./ eps_dd_values) * (add / BohrRadius), '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data0.data_struct(idx).wz_value), ' Hz; $\phi = 0^\circ$']); -hold on -theta_values = data90.data_struct(idx).theta_values; -eps_dd_values = data90.data_struct(idx).eps_dd_values; -plot(theta_values, (1 ./ eps_dd_values) * (add / BohrRadius), '-o', 'LineWidth', 2.0, 'DisplayName', ['$w_z = 2 \pi \times $', num2str(data90.data_struct(idx).wz_value), ' Hz; $\phi = 90^\circ$']); -xlabel('$\theta$', 'fontsize', 16, 'interpreter', 'latex'); -ylabel('$a_s (\times a_o)$', 'fontsize', 16, 'interpreter', 'latex'); -grid on -legend('location', 'northwest', 'fontsize', 10, 'Interpreter', 'latex'); % Reduced font size - -% Second subplot -nexttile; -theta_values = data0.data_struct(idx).theta_values; -k_roton_values = data0.data_struct(idx).k_roton_values; -lambda_roton_values = (2 * pi) ./ k_roton_values; -semilogy(theta_values, lambda_roton_values * 1E6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data0.data_struct(idx).wz_value), ' Hz; $\phi = 0^\circ$']); -hold on -theta_values = data90.data_struct(idx).theta_values; -k_roton_values = data90.data_struct(idx).k_roton_values; -lambda_roton_values = (2 * pi) ./ k_roton_values; -semilogy(theta_values, lambda_roton_values * 1E6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data90.data_struct(idx).wz_value), ' Hz; $\phi = 90^\circ$']); -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$\lambda_{roton} (\mu m)$','fontsize',16,'interpreter','latex'); -grid on -legend('location', 'northwest','fontsize', 10, 'Interpreter','latex') - -% Adjust layout to minimize space -t.TileSpacing = 'compact'; % Minimize space between tiles -t.Padding = 'compact'; % Minimize padding around the layout - -%% -%{ -figure(13) -clf -set(gcf,'Position',[50 50 950 750]) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - eps_dd_values = data_struct(idx).eps_dd_values; - plot(theta_values, eps_dd_values, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$\epsilon_{dd}$','fontsize',16,'interpreter','latex'); -% title([''],'fontsize',16,'interpreter','latex') -grid on -legend('location', 'northeast','fontsize', 16, 'Interpreter','latex') - -figure(14) -clf -set(gcf,'Position',[50 50 950 750]) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - eps_dd_values = data_struct(idx).eps_dd_values; - plot(theta_values, (1./eps_dd_values) * (add/BohrRadius), '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$a_s (\times a_o)$','fontsize',16,'interpreter','latex'); -% title([''],'fontsize',16,'interpreter','latex') -grid on -legend('location', 'southeast','fontsize', 16, 'Interpreter','latex') - -figure(15) -clf -set(gcf,'Position',[50 50 950 750]) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - n_values = data_struct(idx).n_values; - plot(theta_values, n_values * 1E-15, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$n (\times 10^{3} \mu m^{-2})$','fontsize',16,'interpreter','latex'); -% title([''],'fontsize',16,'interpreter','latex') -grid on -legend('location', 'northeast','fontsize', 16, 'Interpreter','latex') - -figure(16) -clf -set(gcf,'Position',[50 50 950 750]) -for idx = 1:length(data_struct) - theta_values = data_struct(idx).theta_values; - k_roton_values = data_struct(idx).k_roton_values; - plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0, DisplayName=['$w_z = 2 \pi \times $', num2str(data_struct(idx).wz_value), ' Hz']); - hold on -end -xlabel('$\theta$','fontsize',16,'interpreter','latex'); -ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); -% title([''],'fontsize',16,'interpreter','latex') -grid on -legend('location', 'northeast','fontsize', 16, 'Interpreter','latex') -%} diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/DipolarDispersion2D.m b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/DipolarDispersion2D.m deleted file mode 100644 index b487963..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/DipolarDispersion2D.m +++ /dev/null @@ -1,251 +0,0 @@ -%% 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*AtomicMassUnit; -Dy164IsotopicAbundance = 0.2826; -DyMagneticMoment = 9.93*BohrMagneton; - -%% 2-D DDI Potential in k-space, with Gaussian ansatz width determined by constrained minimization -% With user-defined values of interaction, density and tilt - -% w0 = 2*pi*61.6316; % Angular frequency unit [s^-1] -% l0 = sqrt(PlanckConstantReduced/(Dy164Mass*w0)); -% % Defining a harmonic oscillator length - heredue to the choice of w0, l0 -% is 1 micrometer - -wz = 2 * pi * 300; % Trap frequency in the tight confinement direction -lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length - -% Number of grid points in each direction -Params.Nx = 128; -Params.Ny = 128; -Params.Lx = 150*1e-6; -Params.Ly = 150*1e-6; -[Transf] = setupSpace(Params); - -nadd2s = 0.110; % Number density * add^2 -as_to_add = 0.782; % 1/edd -Params.theta = 57; % Polar angle of dipole moment -Params.eta = 0; % Azimuthal angle of dipole moment - -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length -gdd = VacuumPermeability*DyMagneticMoment^2/3; - -x0 = 5; -Aineq = []; -Bineq = []; -Aeq = []; -Beq = []; -lb = [1]; -ub = [10]; -nonlcon = []; -fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); - -AtomNumberDensity = nadd2s / add^2; % Number density of atoms -as = as_to_add * add; % Scattering length -eps_dd = add/as; % Relative interaction strength -gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength -TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); -sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); - -MeanWidth = sigma * lz; - -% == 2-D DDI Potential in k-space == % -VDk = compute2DPotentialInMomentumSpace(Transf, Params, MeanWidth); -VDk_fftshifted = fftshift(VDk); - -figure(8) -clf -set(gcf,'Position',[50 50 950 750]) -imagesc(fftshift(Transf.kx)*1e-6, fftshift(Transf.ky)*1e-6, VDk_fftshifted); % Specify x and y data for axes -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -cbar1 = colorbar; -cbar1.Label.Interpreter = 'latex'; -xlabel('$k_x l_o$','fontsize',16,'interpreter','latex'); -ylabel('$k_y l_o$','fontsize',16,'interpreter','latex'); -title(['2-D DDI Potential: $\theta = ',num2str(Params.theta), '; \eta = ', num2str(Params.eta),'$'],'fontsize',16,'interpreter','latex') - -% == Quantum Fluctuations term == % -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; - -EpsilonK = zeros(length(Transf.ky), length(Transf.kx)); -gs_tilde = gs / (sqrt(2*pi) * MeanWidth); - -% == Dispersion relation == % -for idx = 1:length(Transf.kx) - for jdx = 1:length(Transf.ky) - DeltaK = ((PlanckConstantReduced^2 .* (Transf.kx(idx).^2 + Transf.ky(jdx).^2)) ./ (2 * Dy164Mass)) + (2 * AtomNumberDensity * gs_tilde) + ((2 * AtomNumberDensity) .* VDk_fftshifted(jdx, idx)) + (3 * gQF * AtomNumberDensity^(3/2)); - EpsilonK(jdx, idx) = sqrt(((PlanckConstantReduced^2 .* (Transf.kx(idx).^2 + Transf.ky(jdx).^2)) ./ (2 * Dy164Mass)) .* DeltaK); - end -end - -EpsilonK = double(imag(EpsilonK) ~= 0); % 'isreal' returns 0 for complex numbers and 1 for real numbers, so we negate it - -figure(9) -clf -set(gcf,'Position',[50 50 950 750]) -imagesc(fftshift(Transf.kx)*1e-6, fftshift(Transf.ky)*1e-6, EpsilonK); % Specify x and y data for axes -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -cbar1 = colorbar; -cbar1.Label.Interpreter = 'latex'; -xlabel('$k_x l_o$','fontsize',16,'interpreter','latex'); -ylabel('$k_y l_o$','fontsize',16,'interpreter','latex'); -title(['2-D Dispersion: $\theta = ',num2str(Params.theta), '; \eta = ', num2str(Params.eta),'$'],'fontsize',16,'interpreter','latex') - -%% Cycle through angles - -% Define values for theta and eta -theta_values = 0:10:90; % Range of theta values (you can modify this) -eta_values = 0:10:90; % Range of eta values (you can modify this) - -% Set up VideoWriter object to produce a movie -% v = VideoWriter('potential_movie', 'MPEG-4'); % Create a video object -% v.FrameRate = 5; % Frame rate of the video -% open(v); % Open the video file - -% Loop over theta and eta values -for theta = theta_values - for eta = eta_values - % Update Params with current theta and eta - Params.theta = theta; - Params.eta = eta; - - % Compute the potential for the current theta and eta - % == 2-D DDI Potential in k-space == % - VDk = compute2DPotentialInMomentumSpace(Transf, Params, MeanWidth); - VDk_fftshifted = fftshift(VDk); - - % == Quantum Fluctuations term == % - 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; - - EpsilonK = zeros(length(Transf.ky), length(Transf.kx)); - gs_tilde = gs / (sqrt(2*pi) * MeanWidth); - - % == Dispersion relation == % - for idx = 1:length(Transf.kx) - for jdx = 1:length(Transf.ky) - DeltaK = ((PlanckConstantReduced^2 .* (Transf.kx(idx).^2 + Transf.ky(jdx).^2)) ./ (2 * Dy164Mass)) + (2 * AtomNumberDensity * gs_tilde) + ((2 * AtomNumberDensity) .* VDk_fftshifted(jdx, idx)) + (3 * gQF * AtomNumberDensity^(3/2)); - EpsilonK(jdx, idx) = sqrt(((PlanckConstantReduced^2 .* (Transf.kx(idx).^2 + Transf.ky(jdx).^2)) ./ (2 * Dy164Mass)) .* DeltaK); - end - end - - EpsilonK = double(imag(EpsilonK) ~= 0); % 'isreal' returns 0 for complex numbers and 1 for real numbers, so we negate it - - % Plot the result - figure(10) - clf - set(gcf,'Position',[50 50 950 750]) - imagesc(fftshift(Transf.kx)*1e-6, fftshift(Transf.ky)*1e-6, EpsilonK); % Specify x and y data for axes - set(gca, 'YDir', 'normal'); % Correct the y-axis direction - cbar1 = colorbar; - cbar1.Label.Interpreter = 'latex'; - xlabel('$k_x l_o$','fontsize',16,'interpreter','latex'); - ylabel('$k_y l_o$','fontsize',16,'interpreter','latex'); - title(['2-D Dispersion: $\theta = ',num2str(Params.theta), '; \eta = ', num2str(Params.eta),'$'],'fontsize',16,'interpreter','latex') - - % Capture the frame and write to video - % frame = getframe(gcf); % Capture the current figure - % writeVideo(v, frame); % Write the frame to the video - end -end - -% Close the video file -% close(v); - -%% -function [Transf] = setupSpace(Params) - - Transf.Xmax = 0.5*Params.Lx; - Transf.Ymax = 0.5*Params.Ly; - - Nx = Params.Nx; - Ny = Params.Ny; - - % Fourier grids - x = linspace(-0.5*Params.Lx,0.5*Params.Lx-Params.Lx/Params.Nx,Params.Nx); - Kmax = pi*Params.Nx/Params.Lx; - kx = linspace(-Kmax,Kmax,Nx+1); - kx = kx(1:end-1); - dkx = kx(2)-kx(1); - kx = fftshift(kx); - - y = linspace(-0.5*Params.Ly,0.5*Params.Ly-Params.Ly/Params.Ny,Params.Ny); - Kmax = pi*Params.Ny/Params.Ly; - ky = linspace(-Kmax,Kmax,Ny+1); - ky = ky(1:end-1); - dky = ky(2)-ky(1); - ky = fftshift(ky); - - [Transf.X,Transf.Y] = ndgrid(x,y); - [Transf.KX,Transf.KY] = ndgrid(kx,ky); - Transf.x = x; - Transf.y = y; - Transf.kx = kx; - Transf.ky = ky; - Transf.dx = x(2)-x(1); - Transf.dy = y(2)-y(1); - Transf.dkx = dkx; - Transf.dky = dky; -end - -function VDk = compute2DPotentialInMomentumSpace(Transf, Params, MeanWidth) -% == Calculating the DDI potential in Fourier space with appropriate cutoff == % - % Angles of the dipole moment are defined in and away from the X-Z plane - % Interaction in K space - QX = Transf.KX*MeanWidth/sqrt(2); - QY = Transf.KY*MeanWidth/sqrt(2); - - Qsq = QX.^2 + QY.^2; - absQ = sqrt(Qsq); - QDsq = QX.^2*cos(Params.eta)^2 + QY.^2*sin(Params.eta)^2; % eta here is the azimuthal angle of the dipole moment (angle from the x-axis) - - % Bare interaction - Fpar = -1 + 3*sqrt(pi)*QDsq.*erfcx(absQ)./absQ; % Scaled complementary error function erfcx(x) = e^(x^2) * erfc(x) - Fperp = 2 - 3*sqrt(pi).*absQ.*erfcx(absQ); - Fpar(absQ == 0) = -1; - - % Full DDI - VDk = (Fpar*sin(Params.theta)^2 + Fperp*cos(Params.theta)^2); % theta here is the polar angle of the dipole moment (angle from the z-axis) -end - -function ret = computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced) - eps_dd = add/as; % Relative interaction strength - MeanWidth = x * lz; - gammaQF = (32/3) * gs * (as^3/pi)^(1/2) * (1 + ((3/2) * eps_dd^2)); % Quantum Fluctuations term - gamma4 = 1/(sqrt(2*pi) * MeanWidth); - gamma5 = sqrt(2/5) / (sqrt(pi) * MeanWidth)^(3/2); - gQF = gamma5 * gammaQF; - Energy_AxialComponent = (PlanckConstantReduced * wz) * ((lz^2/(4 * MeanWidth^2)) + (MeanWidth^2/(4 * lz^2))); - Energy_TransverseComponent = (0.5 * (gs + (2*gdd)) * gamma4 * AtomNumberDensity) + ((2/5) * gQF * AtomNumberDensity^(3/2)); - ret = (Energy_AxialComponent + Energy_TransverseComponent) / (PlanckConstantReduced * wz); -end - - - diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ExtractingKRoton.m b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ExtractingKRoton.m deleted file mode 100644 index bb7ce0f..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ExtractingKRoton.m +++ /dev/null @@ -1,503 +0,0 @@ -%% 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*AtomicMassUnit; -Dy164IsotopicAbundance = 0.2826; -DyMagneticMoment = 9.93*BohrMagneton; - -%% Extracting values from the roton instability boundary for tilted dipoles - -%-------TEST-------% -% nadd2s = 0.05:0.005:0.25; -% as_to_add = 0.76:0.001:0.81; - -%-------DEPLOY-------% -nadd2s = 0.005:0.005:0.5; -as_to_add = 0.250:0.001:1.15; - -data_struct = struct; - -% wz_values = [150, 300, 500, 750]; -% kvec = linspace(0, 5e6, 1000); % Vector of magnitudes of k vector - -wz_values = [1000, 3000, 5000, 7000]; -kvec = linspace(0, 15e6, 1000); % Vector of magnitudes of k vector - -% wz_values = [10000, 13000, 15000]; -% kvec = linspace(0, 25e6, 1000); % Vector of magnitudes of k vector - -theta_values = 0:5:45; % Range of theta values -phi = 0; % Azimuthal angle of momentum vector - -for mainloop_idx = 1:length(wz_values) - format long - - PlanckConstantReduced = 6.62607015E-34/(2*pi); - AtomicMassUnit = 1.660539066E-27; - Dy164Mass = 163.929174751*AtomicMassUnit; - VacuumPermeability = 1.25663706212E-6; - BohrMagneton = 9.274009994E-24; - DyMagneticMoment = 9.93*BohrMagneton; - - wz = 2 * pi * wz_values(mainloop_idx); % Trap frequency in the tight confinement direction - lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length - add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length - gdd = VacuumPermeability*DyMagneticMoment^2/3; - var_widths = zeros(length(as_to_add), length(nadd2s)); - - x0 = 5; - Aineq = []; - Bineq = []; - Aeq = []; - Beq = []; - lb = [1]; - ub = [10]; - nonlcon = []; - fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); - - for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - as = (as_to_add(jdx) * add); % Scattering length - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); - sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); - var_widths(jdx, idx) = sigma; - end - end - - eps_dd_values = zeros(length(theta_values), 1); - n_values = zeros(length(theta_values), 1); - k_roton_values = zeros(length(theta_values), 1); - - for idx = 1:length(theta_values) - theta = theta_values(idx); - [eps_dd_values(idx), n_values(idx), k_roton_values(idx)] = extractFromBoundaryCurve(theta, phi, nadd2s, as_to_add, var_widths, wz, lz, kvec); - end - - data_struct(mainloop_idx).wz_value = wz / (2 * pi); - data_struct(mainloop_idx).theta_values = theta_values; - data_struct(mainloop_idx).eps_dd_values = eps_dd_values; - data_struct(mainloop_idx).n_values = n_values; - data_struct(mainloop_idx).k_roton_values = k_roton_values; - - %{ - figure(13) - clf - set(gcf,'Position',[50 50 950 750]) - plot(theta_values, eps_dd_values, '-o', LineWidth=2.0) - xlabel('$\theta$','fontsize',16,'interpreter','latex'); - ylabel('$\epsilon_{dd}$','fontsize',16,'interpreter','latex'); - % title([''],'fontsize',16,'interpreter','latex') - grid on - - figure(14) - clf - set(gcf,'Position',[50 50 950 750]) - plot(theta_values, (1./eps_dd_values) * (add/BohrRadius), '-o', LineWidth=2.0) - xlabel('$\theta$','fontsize',16,'interpreter','latex'); - ylabel('$a_s (\times a_o)$','fontsize',16,'interpreter','latex'); - % title([''],'fontsize',16,'interpreter','latex') - grid on - - figure(15) - clf - set(gcf,'Position',[50 50 950 750]) - plot(theta_values, n_values * 1E-15, '-o', LineWidth=2.0) - xlabel('$\theta$','fontsize',16,'interpreter','latex'); - ylabel('$n (\times 10^{3} \mu m^{-2})$','fontsize',16,'interpreter','latex'); - % title([''],'fontsize',16,'interpreter','latex') - grid on - - figure(16) - clf - set(gcf,'Position',[50 50 950 750]) - plot(theta_values, k_roton_values * 1E-6, '-o', LineWidth=2.0) - xlabel('$\theta$','fontsize',16,'interpreter','latex'); - ylabel('$k_{roton} (\mu m^{-1})$','fontsize',16,'interpreter','latex'); - % title([''],'fontsize',16,'interpreter','latex') - grid on - %} -end - -save('.\Results\ExtractingKRoton_Result.mat', 'data_struct'); - -%% Extracting values from the roton instability boundary for tilted dipoles - fixed atom number, trap frequency - -%-------DEPLOY-------% - -N = 1E5; -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length -area = 100; % in square micrometers -ppmum = N / area; -nadd2s = ppmum*1E12*add^2; -as_to_add = 0.150:0.001:1.15; - -data_struct = struct; - -wz_values = [500, 750, 1000, 2000]; -kvec = linspace(0, 15e6, 1000); % Vector of magnitudes of k vector - -theta_values = 0:5:90; % Range of theta values -phi = 90; % Azimuthal angle of momentum vector - -for mainloop_idx = 1:length(wz_values) - format long - - PlanckConstantReduced = 6.62607015E-34/(2*pi); - AtomicMassUnit = 1.660539066E-27; - Dy164Mass = 163.929174751*AtomicMassUnit; - VacuumPermeability = 1.25663706212E-6; - BohrMagneton = 9.274009994E-24; - DyMagneticMoment = 9.93*BohrMagneton; - - wz = 2 * pi * wz_values(mainloop_idx); % Trap frequency in the tight confinement direction - lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length - add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length - gdd = VacuumPermeability*DyMagneticMoment^2/3; - var_widths = zeros(length(as_to_add), length(nadd2s)); - - x0 = 5; - Aineq = []; - Bineq = []; - Aeq = []; - Beq = []; - lb = [1]; - ub = [10]; - nonlcon = []; - fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); - - for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - as = (as_to_add(jdx) * add); % Scattering length - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); - sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); - var_widths(jdx, idx) = sigma; - end - end - - eps_dd_values = zeros(length(theta_values), 1); - k_roton_values = zeros(length(theta_values), 1); - - for idx = 1:length(theta_values) - theta = theta_values(idx); - [eps_dd_values(idx), k_roton_values(idx)] = extractFromBoundaryPoint(theta, phi, nadd2s, as_to_add, var_widths, wz, lz, kvec); - end - - data_struct(mainloop_idx).wz_value = wz / (2 * pi); - data_struct(mainloop_idx).theta_values = theta_values; - data_struct(mainloop_idx).eps_dd_values = eps_dd_values; - data_struct(mainloop_idx).k_roton_values = k_roton_values; - -end - -save('.\Results\ExtractingKRoton_Result_FixedDensity_phi90.mat', 'data_struct'); -%% -function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi) - Go = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2))); - gamma4 = 1/(sqrt(2*pi) * MeanWidth); - Fka = (3 * cos(deg2rad(theta))^2 - 1) + ((3 * Go) .* ((sin(deg2rad(theta))^2 .* sin(deg2rad(phi))^2) - cos(deg2rad(theta))^2)); - Ukk = (gs + (gdd * Fka)) * gamma4; -end - -function ret = computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced) - eps_dd = add/as; % Relative interaction strength - MeanWidth = x * lz; - gammaQF = (32/3) * gs * (as^3/pi)^(1/2) * (1 + ((3/2) * eps_dd^2)); % Quantum Fluctuations term - gamma4 = 1/(sqrt(2*pi) * MeanWidth); - gamma5 = sqrt(2/5) / (sqrt(pi) * MeanWidth)^(3/2); - gQF = gamma5 * gammaQF; - Energy_AxialComponent = (PlanckConstantReduced * wz) * ((lz^2/(4 * MeanWidth^2)) + (MeanWidth^2/(4 * lz^2))); - Energy_TransverseComponent = (0.5 * (gs + (2*gdd)) * gamma4 * AtomNumberDensity) + ((2/5) * gQF * AtomNumberDensity^(3/2)); - ret = (Energy_AxialComponent + Energy_TransverseComponent) / (PlanckConstantReduced * wz); -end - -function [eps_dd, AtomNumberDensity, k_roton] = extractFromBoundaryCurve(theta, phi, nadd2s, as_to_add, var_widths, wz, lz, kvec) - - format long - - PlanckConstantReduced = 6.62607015E-34/(2*pi); - AtomicMassUnit = 1.660539066E-27; - Dy164Mass = 163.929174751*AtomicMassUnit; - VacuumPermeability = 1.25663706212E-6; - BohrMagneton = 9.274009994E-24; - DyMagneticMoment = 9.93*BohrMagneton; - add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length - gdd = VacuumPermeability*DyMagneticMoment^2/3; - phase_diagram = zeros(length(as_to_add), length(nadd2s)); - w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction - l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length - - for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - as = (as_to_add(jdx) * add); % Scattering length - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - MeanWidth = var_widths(jdx, idx) * lz; % Mean width of Gaussian ansatz - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(kvec, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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 .* kvec.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) .* DeltaK); - phase_diagram(jdx, idx) = ~isreal(EpsilonK); - end - end - %{ - figure(11) - clf - set(gcf,'Position',[50 50 950 750]) - imagesc(nadd2s, as_to_add, phase_diagram); % Specify x and y data for axes - set(gca, 'YDir', 'normal'); % Correct the y-axis direction - colorbar; % Add a colorbar - xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex'); - ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex'); - title(['$\theta = ',num2str(theta), '; \phi = 0','$', '(Along Y)'],'fontsize',16,'interpreter','latex') - %} - %-------------% - - matrix = phase_diagram; - - % Initialize arrays to store row and column indices of transitions - row_indices = []; - col_indices = []; - - % Loop through the matrix to find transitions from 0 to 1 - [rows, cols] = size(matrix); - for j = 1:cols - for i = 2:rows - if matrix(i-1, j) == 1 && matrix(i, j) == 0 - row_indices = [row_indices; i-1]; - col_indices = [col_indices; j]; - break; % Stop after the first transition in the column - end - end - end - - % Now extract the values from the corresponding vectors - xvals = zeros(length(col_indices), 1); - yvals = zeros(length(row_indices), 1); - for k = 1:length(row_indices) - row = row_indices(k); - col = col_indices(k); - xvals(k) = nadd2s(col); - yvals(k) = as_to_add(row); - end - - instability_boundary = [xvals, yvals]; - - %-------------% - - % Degree of the polynomial to fit - n = 5; % For a quadratic fit - - % Fit the polynomial - p = polyfit(xvals, yvals, n); - - % Display the polynomial coefficients - % disp('Polynomial coefficients:'); - % disp(p); - - % Evaluate the polynomial at points in x - y_fit = polyval(p, xvals); - - %{ - % Plot the original data and the fitted polynomial curve - figure(12); - clf - set(gcf,'Position',[50 50 950 750]) - plot(xvals, yvals, 'o', 'LineWidth', 2.0, 'DisplayName', 'Extracted boundary points'); % Original data - hold on; - plot(xvals, y_fit, '-r','LineWidth', 2.0, 'DisplayName', ['Polynomial Fit (degree ' num2str(n) ')']); % Fitted curve - ylim([min(as_to_add) max(as_to_add)]) - xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex'); - ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex') - title(['$\theta = ',num2str(theta), '; \phi = 0','$', '(Along Y)'],'fontsize',16,'interpreter','latex') - legend('show'); - grid on; - %} - [val, idx] = max(y_fit); - - % Round down to 4 decimal places - rounded_val = floor(val * 10^4) / 10^4; - % Find nearest from original vector of boundary points - [~, nearest_idx] = min(abs(instability_boundary(:, 2) - rounded_val)); - nearest_val = instability_boundary(nearest_idx, 2); - % Choose the scalar value between the two - if ~isscalar(nearest_val) - val = rounded_val; - else - val = nearest_val; - idx = nearest_idx; - end - - AtomNumberDensity = xvals(idx) / add^2; % Areal density of atoms - as = val * add; % Scattering length - eps_dd = 1/val; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - x0 = 5; - Aineq = []; - Bineq = []; - Aeq = []; - Beq = []; - lb = [1]; - ub = [10]; - nonlcon = []; - fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); - TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); - sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); - MeanWidth = sigma * lz; % Mean width of Gaussian ansatz - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(kvec, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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; - DeltaK = ((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) .* DeltaK); - k_roton_indices = find(imag(EpsilonK) ~= 0); - if ~isempty(k_roton_indices) - k_roton = median(kvec(k_roton_indices)); - else - k_roton = NaN; - end -end - -function [eps_dd, k_roton] = extractFromBoundaryPoint(theta, phi, nadd2s, as_to_add, var_widths, wz, lz, kvec) - - format long - - PlanckConstantReduced = 6.62607015E-34/(2*pi); - AtomicMassUnit = 1.660539066E-27; - Dy164Mass = 163.929174751*AtomicMassUnit; - VacuumPermeability = 1.25663706212E-6; - BohrMagneton = 9.274009994E-24; - DyMagneticMoment = 9.93*BohrMagneton; - add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length - gdd = VacuumPermeability*DyMagneticMoment^2/3; - phase_diagram = zeros(length(as_to_add), length(nadd2s)); - w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction - l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length - - for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - as = (as_to_add(jdx) * add); % Scattering length - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - MeanWidth = var_widths(jdx, idx) * lz; % Mean width of Gaussian ansatz - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(kvec, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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 .* kvec.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) .* DeltaK); - phase_diagram(jdx, idx) = ~isreal(EpsilonK); - end - end - - matrix = phase_diagram; - - % Initialize arrays to store row and column indices of transitions - row_indices = []; - col_indices = []; - - % Loop through the matrix to find transitions from 0 to 1 - [rows, cols] = size(matrix); - for j = 1:cols - for i = 2:rows - if matrix(i-1, j) == 1 && matrix(i, j) == 0 - row_indices = [row_indices; i-1]; - col_indices = [col_indices; j]; - break; % Stop after the first transition in the column - end - end - end - - % Now extract the values from the corresponding vectors - xvals = zeros(length(col_indices), 1); - yvals = zeros(length(row_indices), 1); - for k = 1:length(row_indices) - row = row_indices(k); - col = col_indices(k); - xvals(k) = nadd2s(col); - yvals(k) = as_to_add(row); - end - - instability_boundary = [xvals, yvals]; - - if ~isempty(instability_boundary) - val = instability_boundary(2); - AtomNumberDensity = instability_boundary(1) / add^2; % Areal density of atoms - as = val * add; % Scattering length - eps_dd = 1/val; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - x0 = 5; - Aineq = []; - Bineq = []; - Aeq = []; - Beq = []; - lb = [1]; - ub = [10]; - nonlcon = []; - fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); - TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); - sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); - MeanWidth = sigma * lz; % Mean width of Gaussian ansatz - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(kvec, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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; - DeltaK = ((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) + ((2 * AtomNumberDensity) .* Ukk) + (3 * gQF * AtomNumberDensity^(3/2)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* kvec.^2) ./ (2 * Dy164Mass)) .* DeltaK); - k_roton_indices = find(imag(EpsilonK) ~= 0); - if ~isempty(k_roton_indices) - k_roton = median(kvec(k_roton_indices)); - else - k_roton = NaN; - end - else - eps_dd = NaN; - k_roton = NaN; - end -end \ No newline at end of file diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/FeshbachResonances.nb b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/FeshbachResonances.nb deleted file mode 100644 index e43f15e..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/FeshbachResonances.nb +++ /dev/null @@ -1,1526 +0,0 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - -(*** Wolfram Notebook File ***) -(* http://www.wolfram.com/nb *) - -(* CreatedBy='Mathematica 12.2' *) - -(*CacheID: 234*) -(* Internal cache information: -NotebookFileLineBreakTest -NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 77877, 1518] -NotebookOptionsPosition[ 76510, 1486] -NotebookOutlinePosition[ 77008, 1504] 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a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/RIBForTiltedDipoles.m b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/RIBForTiltedDipoles.m deleted file mode 100644 index d5e398a..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/RIBForTiltedDipoles.m +++ /dev/null @@ -1,146 +0,0 @@ -%% 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*AtomicMassUnit; -Dy164IsotopicAbundance = 0.2826; -DyMagneticMoment = 9.93*BohrMagneton; - -%% Roton instability boundary for tilted dipoles - -wz = 2 * pi * 72.4; % Trap frequency in the tight confinement direction -lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length -gdd = VacuumPermeability*DyMagneticMoment^2/3; - -nadd2s = 0.05:0.001:0.25; -as_to_add = 0.76:0.001:0.81; -var_widths = zeros(length(as_to_add), length(nadd2s)); - -x0 = 5; -Aineq = []; -Bineq = []; -Aeq = []; -Beq = []; -lb = [1]; -ub = [10]; -nonlcon = []; -fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); - -for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - as = (as_to_add(jdx) * add); % Scattering length - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); - sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); - var_widths(jdx, idx) = sigma; - end -end - -% ====================================================================================================================================================== % - -theta = 0; % Polar angle of dipole moment -phi = 0; % Azimuthal angle of momentum vector -k = linspace(0, 2.25e6, 1000); % Vector of magnitudes of k vector -instability_boundary = zeros(length(as_to_add), length(nadd2s)); -ScatteringLengths = zeros(length(as_to_add), 1); -AtomNumber = zeros(length(nadd2s), 1); -w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction -l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length -tsize = 10 * l0; - -for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - AtomNumber(idx) = AtomNumberDensity*tsize^2; - as = (as_to_add(jdx) * add); % Scattering length - ScatteringLengths(jdx) = as/BohrRadius; - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - MeanWidth = var_widths(jdx, idx) * lz; % Mean width of Gaussian ansatz - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); - instability_boundary(jdx, idx) = ~isreal(EpsilonK); - end -end - -nadd2s_from_figure = [0.04974, 0.05383, 0.05655, 0.06609, 0.06916, 0.07291, 0.07836, 0.08517, 0.09063, 0.0978, 0.10459, 0.11345, 0.11822, 0.12231, 0.12674, 0.13117, 0.13560, 0.14003, 0.14548, 0.15127, 0.15775, 0.16660, 0.17546, 0.18364, 0.19557, 0.20579, 0.21839, 0.23850, 0.25144]; -as_to_add_from_figure = [0.76383, 0.76766, 0.76974, 0.77543, 0.77675, 0.77828, 0.78003, 0.78178, 0.78288, 0.7840, 0.78474, 0.78540, 0.78562, 0.78572, 0.78583, 0.78583, 0.78583, 0.78583, 0.78567, 0.78551, 0.78529, 0.78485, 0.78441, 0.78386, 0.78310, 0.78233, 0.78135, 0.77970, 0.77861]; - -figure(6) -clf -set(gcf,'Position',[50 50 950 750]) -% - -imagesc(nadd2s, as_to_add, instability_boundary); % Specify x and y data for axes -hold on -plot(nadd2s_from_figure, as_to_add_from_figure, 'r*-', 'LineWidth', 2); % Plot the curve (red line) -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -colorbar; % Add a colorbar -xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex'); -ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex'); - -%{ -imagesc(AtomNumber*1E-5, ScatteringLengths, instability_boundary); % Specify x and y data for axes -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -cbar1 = colorbar; -cbar1.Label.Interpreter = 'latex'; -ylabel(cbar1,'$(\times 10^{-31})$','FontSize',16,'Rotation',270) -xlabel(' Atom number for a trap area of 100$\mu m^2 ~ (\times 10^5)$','fontsize',16,'interpreter','latex'); -ylabel('Scattering length ($\times a_0$)','fontsize',16,'interpreter','latex'); -%} - -title('Roton instability boundary','fontsize',16,'interpreter','latex') - -%% -function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi) - Go = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2))); - gamma4 = 1/(sqrt(2*pi) * MeanWidth); - Fka = (3 * cos(deg2rad(theta))^2 - 1) + ((3 * Go) .* ((sin(deg2rad(theta))^2 .* sin(deg2rad(phi))^2) - cos(deg2rad(theta))^2)); - Ukk = (gs + (gdd * Fka)) * gamma4; -end - -function ret = computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced) - eps_dd = add/as; % Relative interaction strength - MeanWidth = x * lz; - gammaQF = (32/3) * gs * (as^3/pi)^(1/2) * (1 + ((3/2) * eps_dd^2)); % Quantum Fluctuations term - gamma4 = 1/(sqrt(2*pi) * MeanWidth); - gamma5 = sqrt(2/5) / (sqrt(pi) * MeanWidth)^(3/2); - gQF = gamma5 * gammaQF; - Energy_AxialComponent = (PlanckConstantReduced * wz) * ((lz^2/(4 * MeanWidth^2)) + (MeanWidth^2/(4 * lz^2))); - Energy_TransverseComponent = (0.5 * (gs + (2*gdd)) * gamma4 * AtomNumberDensity) + ((2/5) * gQF * AtomNumberDensity^(3/2)); - ret = (Energy_AxialComponent + Energy_TransverseComponent) / (PlanckConstantReduced * wz); -end \ No newline at end of file diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/RIBForTiltedDipoles_TwoDirections.m b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/RIBForTiltedDipoles_TwoDirections.m deleted file mode 100644 index 03dfe28..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/RIBForTiltedDipoles_TwoDirections.m +++ /dev/null @@ -1,318 +0,0 @@ -%% 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*AtomicMassUnit; -Dy164IsotopicAbundance = 0.2826; -DyMagneticMoment = 9.93*BohrMagneton; - -%% Roton instability boundary for tilted dipoles - -wz = 2 * pi * 72.4; % Trap frequency in the tight confinement direction -lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length -gdd = VacuumPermeability*DyMagneticMoment^2/3; - -nadd2s = 0.005:0.0025:0.5; -as_to_add = 0.3:0.025:0.95; -var_widths = zeros(length(as_to_add), length(nadd2s)); - -x0 = 5; -Aineq = []; -Bineq = []; -Aeq = []; -Beq = []; -lb = [1]; -ub = [10]; -nonlcon = []; -fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); - -for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - as = (as_to_add(jdx) * add); % Scattering length - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); - sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); - var_widths(jdx, idx) = sigma; - end -end - -%% ====================================================================================================================================================== % - -figure(7) -clf -set(gcf,'Position',[50 50 1850 750]) - -theta = 66; % Polar angle of dipole moment -phi = 0; % Azimuthal angle of momentum vector -k = linspace(0, 2.25e6, 1000); % Vector of magnitudes of k vector -instability_boundary = zeros(length(as_to_add), length(nadd2s)); -ScatteringLengths = zeros(length(as_to_add), 1); -AtomNumber = zeros(length(nadd2s), 1); -w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction -l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length -tsize = 10 * l0; - -for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - AtomNumber(idx) = AtomNumberDensity*tsize^2; - as = (as_to_add(jdx) * add); % Scattering length - ScatteringLengths(jdx) = as/BohrRadius; - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - MeanWidth = var_widths(jdx, idx) * lz; % Mean width of Gaussian ansatz - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); - instability_boundary(jdx, idx) = ~isreal(EpsilonK); - end -end - -subplot(1, 2, 1); % 1 row, 2 columns, first subplot -imagesc(nadd2s, as_to_add, instability_boundary); % Specify x and y data for axes -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -colorbar; % Add a colorbar -caxis([0 1]) -xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex'); -ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex'); - -title(['Along Y: $\theta = ',num2str(theta), '; \phi = ', num2str(phi),'$'],'fontsize',16,'interpreter','latex') - -theta = 66; % Polar angle of dipole moment -phi = 90; % Azimuthal angle of momentum vector -k = linspace(0, 2.25e6, 1000); % Vector of magnitudes of k vector -instability_boundary = zeros(length(as_to_add), length(nadd2s)); -ScatteringLengths = zeros(length(as_to_add), 1); -AtomNumber = zeros(length(nadd2s), 1); -w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction -l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length -tsize = 10 * l0; - -for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - AtomNumber(idx) = AtomNumberDensity*tsize^2; - as = (as_to_add(jdx) * add); % Scattering length - ScatteringLengths(jdx) = as/BohrRadius; - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - MeanWidth = var_widths(jdx, idx) * lz; % Mean width of Gaussian ansatz - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); - instability_boundary(jdx, idx) = ~isreal(EpsilonK); - end -end - -% set(gcf,'Position',[50 50 950 750]) -subplot(1, 2, 2); % 1 row, 2 columns, first subplot -imagesc(nadd2s, as_to_add, instability_boundary); % Specify x and y data for axes -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -colorbar; % Add a colorbar -caxis([0 1]) -xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex'); -ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex'); - -title(['Along X: $\theta = ',num2str(theta), '; \phi = ', num2str(phi),'$'],'fontsize',16,'interpreter','latex') - -%{ -imagesc(AtomNumber*1E-5, ScatteringLengths, instability_boundary); % Specify x and y data for axes -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -cbar1 = colorbar; -cbar1.Label.Interpreter = 'latex'; -caxis([0 1]) -% ylabel(cbar1,'$(\times 10^{-31})$','FontSize',16,'Rotation',270) -xlabel(' Atom number for a trap area of 100$\mu m^2 ~ (\times 10^5)$','fontsize',16,'interpreter','latex'); -ylabel('Scattering length ($\times a_0$)','fontsize',16,'interpreter','latex'); -%} - -sgtitle('Mean-field instability boundary','fontsize',16,'interpreter','latex') - -%% Cycle through angles - -% Define values for theta and phi -theta_values = 0:2:90; % Range of theta values (you can modify this) - -% Set up VideoWriter object to produce a movie -v = VideoWriter('rib_movie', 'MPEG-4'); % Create a video object -v.FrameRate = 5; % Frame rate of the video -open(v); % Open the video file - -for theta = theta_values - figure(7) - clf - set(gcf,'Position',[50 50 1850 750]) - phi = 0; % Azimuthal angle of momentum vector - k = linspace(0, 2.25e6, 1000); % Vector of magnitudes of k vector - instability_boundary = zeros(length(as_to_add), length(nadd2s)); - ScatteringLengths = zeros(length(as_to_add), 1); - AtomNumber = zeros(length(nadd2s), 1); - w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction - l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length - tsize = 10 * l0; - - for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - AtomNumber(idx) = AtomNumberDensity*tsize^2; - as = (as_to_add(jdx) * add); % Scattering length - ScatteringLengths(jdx) = as/BohrRadius; - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - MeanWidth = var_widths(jdx, idx) * lz; % Mean width of Gaussian ansatz - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); - instability_boundary(jdx, idx) = ~isreal(EpsilonK); - end - end - - subplot(1, 2, 1); % 1 row, 2 columns, first subplot - imagesc(nadd2s, as_to_add, instability_boundary); % Specify x and y data for axes - set(gca, 'YDir', 'normal'); % Correct the y-axis direction - colorbar; % Add a colorbar - caxis([0 1]) - xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex'); - ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex'); - - title(['Along Y: $\theta = ',num2str(theta), '; \phi = ', num2str(phi),'$'],'fontsize',16,'interpreter','latex') - - phi = 90; % Azimuthal angle of momentum vector - k = linspace(0, 2.25e6, 1000); % Vector of magnitudes of k vector - instability_boundary = zeros(length(as_to_add), length(nadd2s)); - ScatteringLengths = zeros(length(as_to_add), 1); - AtomNumber = zeros(length(nadd2s), 1); - w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction - l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length - tsize = 10 * l0; - - for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - AtomNumber(idx) = AtomNumberDensity*tsize^2; - as = (as_to_add(jdx) * add); % Scattering length - ScatteringLengths(jdx) = as/BohrRadius; - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - MeanWidth = var_widths(jdx, idx) * lz; % Mean width of Gaussian ansatz - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); - instability_boundary(jdx, idx) = ~isreal(EpsilonK); - end - end - - % set(gcf,'Position',[50 50 950 750]) - subplot(1, 2, 2); % 1 row, 2 columns, first subplot - imagesc(nadd2s, as_to_add, instability_boundary); % Specify x and y data for axes - set(gca, 'YDir', 'normal'); % Correct the y-axis direction - colorbar; % Add a colorbar - caxis([0 1]) - xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex'); - ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex'); - - title(['Along X: $\theta = ',num2str(theta), '; \phi = ', num2str(phi),'$'],'fontsize',16,'interpreter','latex') - - %{ - imagesc(AtomNumber*1E-5, ScatteringLengths, instability_boundary); % Specify x and y data for axes - set(gca, 'YDir', 'normal'); % Correct the y-axis direction - cbar1 = colorbar; - cbar1.Label.Interpreter = 'latex'; - caxis([0 1]) - % ylabel(cbar1,'$(\times 10^{-31})$','FontSize',16,'Rotation',270) - xlabel(' Atom number for a trap area of 100$\mu m^2 ~ (\times 10^5)$','fontsize',16,'interpreter','latex'); - ylabel('Scattering length ($\times a_0$)','fontsize',16,'interpreter','latex'); - %} - - % Capture the frame and write to video - frame = getframe(gcf); % Capture the current figure - writeVideo(v, frame); % Write the frame to the video - - % sgtitle('Mean-field instability boundary','fontsize',16,'interpreter','latex') -end - -% Close the video file -close(v); - -%% -function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi) - Go = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2))); - gamma4 = 1/(sqrt(2*pi) * MeanWidth); - Fka = (3 * cos(deg2rad(theta))^2 - 1) + ((3 * Go) .* ((sin(deg2rad(theta))^2 .* sin(deg2rad(phi))^2) - cos(deg2rad(theta))^2)); - Ukk = (gs + (gdd * Fka)) * gamma4; -end - -function ret = computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced) - eps_dd = add/as; % Relative interaction strength - MeanWidth = x * lz; - gammaQF = (32/3) * gs * (as^3/pi)^(1/2) * (1 + ((3/2) * eps_dd^2)); % Quantum Fluctuations term - gamma4 = 1/(sqrt(2*pi) * MeanWidth); - gamma5 = sqrt(2/5) / (sqrt(pi) * MeanWidth)^(3/2); - gQF = gamma5 * gammaQF; - Energy_AxialComponent = (PlanckConstantReduced * wz) * ((lz^2/(4 * MeanWidth^2)) + (MeanWidth^2/(4 * lz^2))); - Energy_TransverseComponent = (0.5 * (gs + (2*gdd)) * gamma4 * AtomNumberDensity) + ((2/5) * gQF * AtomNumberDensity^(3/2)); - ret = (Energy_AxialComponent + Energy_TransverseComponent) / (PlanckConstantReduced * wz); -end - - - diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ReproduceBlairBlakieResults.m b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ReproduceBlairBlakieResults.m deleted file mode 100644 index f718de5..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ReproduceBlairBlakieResults.m +++ /dev/null @@ -1,335 +0,0 @@ -%% 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*AtomicMassUnit; -Dy164IsotopicAbundance = 0.2826; -DyMagneticMoment = 9.93*BohrMagneton; - -%% Bogoliubov excitation spectrum for quasi-2D dipolar gas with QF correction -AtomNumber = 1E5; % Total atom number in the system -wz = 2 * pi * 72.4; % Trap frequency in the tight confinement direction -lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length -as = 102.515 * BohrRadius; % Scattering length -Trapsize = 7.5815 * lz; % Trap is assumed to be a box of finite extent , given here in units of the harmonic oscillator length -theta = 0; % Polar angle of dipole moment -phi = 0; % Azimuthal angle of momentum vector -MeanWidth = 5.7304888515 * lz; % Mean width of Gaussian ansatz -k = linspace(0, 2e6, 1000); % Vector of magnitudes of k vector - -% no = 2.0429e+15, eps_dd = 1.2755, as = 5.4249e-09 - -AtomNumberDensity = AtomNumber / Trapsize^2; % Areal density of atoms -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length -eps_dd = add/as; % Relative interaction strength -gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength -gdd = VacuumPermeability*DyMagneticMoment^2/3; - -[Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - -% == Quantum Fluctuations term == % -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)); -EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); - -figure(1) -set(gcf,'Position',[50 50 950 750]) -xvals = (k .* add); -yvals = EpsilonK ./ PlanckConstant; -plot(xvals, yvals,LineWidth=2.0) -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') -xlabel('$k_{\rho}a_{dd}$','fontsize',16,'interpreter','latex') -ylabel('$\epsilon(k_{\rho})/h$ (Hz)','fontsize',16,'interpreter','latex') -grid on - -%% For different interaction strengths - -AtomNumber = 1E5; % Total atom number in the system -wz = 2 * pi * 72.4; % Trap frequency in the tight confinement direction -lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length -Trapsize = 7.5815 * lz; % Trap is assumed to be a box of finite extent , given here in units of the harmonic oscillator length -theta = 0; % Polar angle of dipole moment -phi = 0; % Azimuthal angle of momentum vector -MeanWidth = 5.7304888515 * lz; % Mean width of Gaussian ansatz -k = linspace(0, 2e6, 1000); % Vector of magnitudes of k vector - -AtomNumberDensity = AtomNumber / Trapsize^2; % Areal density of atoms -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length - -ScatteringLengths = [108.5, 105.9, 103.3, 102.5150]; -eps_dds = zeros(1, length(ScatteringLengths)); -EpsilonKs = zeros(length(k), length(ScatteringLengths)); -for idx = 1:length(ScatteringLengths) - - as = ScatteringLengths(idx) * BohrRadius; % Scattering length - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); - - eps_dds(idx) = eps_dd; - EpsilonKs(:,idx) = EpsilonK; -end - -figure(2) -clf -set(gcf,'Position',[50 50 950 750]) -xvals = (k .* add); -yvals = EpsilonKs(:, 1) ./ PlanckConstant; -plot(xvals, yvals,LineWidth=2.0, DisplayName=['$a_s = ',num2str(round(1/eps_dds(1),3)),'a_{dd}$']) -hold on -for idx = 2:length(ScatteringLengths) - yvals = EpsilonKs(:, idx) ./ PlanckConstant; - plot(xvals, yvals,LineWidth=2.0, DisplayName=['$a_s = ',num2str(round(1/eps_dds(idx),3)),'a_{dd}$']) -end -title(['$na_{dd}^2 = ',num2str(round(AtomNumberDensity * add^2,4)),'$'],'fontsize',16,'interpreter','latex') -xlabel('$k_{\rho}a_{dd}$','fontsize',16,'interpreter','latex') -ylabel('$\epsilon(k_{\rho})/h$ (Hz)','fontsize',16,'interpreter','latex') -grid on -legend('location', 'northwest','fontsize',16, 'Interpreter','latex') - -%% For 3 points on the roton instability boundary - -wz = 2 * pi * 72.4; % Trap frequency in the tight confinement direction -lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length -theta = 0; % Polar angle of dipole moment -phi = 0; % Azimuthal angle of momentum vector -k = linspace(0, 2.25e6, 1000); % Vector of magnitudes of k vector - -nadd2s = [0.0844, 0.0978, 0.123]; -as_to_add = [0.7730, 0.7840, 0.7819]; -var_widths = [4.97165, 5.7296048721, 5.93178]; - -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length -EpsilonKs = zeros(length(k), length(nadd2s)); -ScatteringLengths = zeros(length(as_to_add), 1); -AtomNumber = zeros(length(nadd2s), 1); -w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction -l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length -tsize = 10 * l0; - -for idx = 1:length(nadd2s) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - AtomNumber(idx) = AtomNumberDensity*tsize^2; - as = (as_to_add(idx) * add); % Scattering length - ScatteringLengths(idx) = as/BohrRadius; - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - MeanWidth = var_widths(idx) * lz; % Mean width of Gaussian ansatz - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); - EpsilonKs(:,idx) = EpsilonK; -end - -figure(3) -clf -set(gcf,'Position',[50 50 950 750]) -xvals = (k .* add); -yvals = EpsilonKs(:, 1) ./ PlanckConstant; -plot(xvals, yvals,LineWidth=2.0, DisplayName=['$a_s = ',num2str(round(as_to_add(1),4)),'a_{dd}, na_{dd}^2 = ',num2str(round(nadd2s(1),4)),'$']) -hold on -for idx = 2:length(nadd2s) - yvals = EpsilonKs(:, idx) ./ PlanckConstant; - plot(xvals, yvals,LineWidth=2.0, DisplayName=['$a_s = ',num2str(round(as_to_add(idx),4)),'a_{dd}, na_{dd}^2 = ',num2str(round(nadd2s(idx),4)),'$']) -end -xlabel('$k_{\rho}a_{dd}$','fontsize',16,'interpreter','latex') -ylabel('$\epsilon(k_{\rho})/h$ (Hz)','fontsize',16,'interpreter','latex') -grid on -legend('location', 'northwest','fontsize',16, 'Interpreter','latex') - -%% Mean widths of the variational Gaussian ansatz - extremize the total mean field energy per particle wrt to the variational parameter - -wz = 2 * pi * 72.4; % Trap frequency in the tight confinement direction -lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length -gdd = VacuumPermeability*DyMagneticMoment^2/3; -AtomNumberDensity = 0.0978 / add^2; -as = 0.784 * add; % Scattering length -gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength -TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); - -x0 = 5; -Aineq = []; -Bineq = []; -Aeq = []; -Beq = []; -lb = [1]; -ub = [7]; -nonlcon = []; -fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); -sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); -fprintf(['Variational width of Gaussian ansatz = ' num2str(sigma) ' * lz \n']) - -%% Mean widths of the variational Gaussian ansatz - extremize the total mean field energy per particle wrt to the variational parameter - -wz = 2 * pi * 72.4; % Trap frequency in the tight confinement direction -lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length -gdd = VacuumPermeability*DyMagneticMoment^2/3; - -nadd2s = 0.05:0.001:0.25; -as_to_add = 0.74:0.001:0.79; -var_widths = zeros(length(as_to_add), length(nadd2s)); - -x0 = 5; -Aineq = []; -Bineq = []; -Aeq = []; -Beq = []; -lb = [1]; -ub = [10]; -nonlcon = []; -fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); - -for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - as = (as_to_add(jdx) * add); % Scattering length - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); - sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); - var_widths(jdx, idx) = sigma; - end -end - -figure(4) -clf -set(gcf,'Position',[50 50 950 750]) -imagesc(nadd2s, as_to_add, var_widths); % Specify x and y data for axes -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -colorbar; % Add a colorbar -xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex'); -ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex'); - -% ====================================================================================================================================================== % - -theta = 0; % Polar angle of dipole moment -phi = 0; % Azimuthal angle of momentum vector -k = linspace(0, 2.25e6, 1000); % Vector of magnitudes of k vector -instability_boundary = zeros(length(as_to_add), length(nadd2s)); -ScatteringLengths = zeros(length(as_to_add), 1); -AtomNumber = zeros(length(nadd2s), 1); -w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction -l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length -tsize = 10 * l0; - -for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - AtomNumber(idx) = AtomNumberDensity*tsize^2; - as = (as_to_add(jdx) * add); % Scattering length - ScatteringLengths(jdx) = as/BohrRadius; - eps_dd = add/as; % Relative interaction strength - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - gdd = VacuumPermeability*DyMagneticMoment^2/3; - MeanWidth = var_widths(jdx, idx) * lz; % Mean width of Gaussian ansatz - - [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi); % DDI potential in k-space - - % == Quantum Fluctuations term == % - 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)); - EpsilonK = sqrt(((PlanckConstantReduced^2 .* k.^2) ./ (2 * Dy164Mass)) .* DeltaK); - instability_boundary(jdx, idx) = ~isreal(EpsilonK); - end -end - -nadd2s_from_figure = [0.04974, 0.05383, 0.05655, 0.06609, 0.06916, 0.07291, 0.07836, 0.08517, 0.09063, 0.0978, 0.10459, 0.11345, 0.11822, 0.12231, 0.12674, 0.13117, 0.13560, 0.14003, 0.14548, 0.15127, 0.15775, 0.16660, 0.17546, 0.18364, 0.19557, 0.20579, 0.21839, 0.23850, 0.25144]; -as_to_add_from_figure = [0.76383, 0.76766, 0.76974, 0.77543, 0.77675, 0.77828, 0.78003, 0.78178, 0.78288, 0.7840, 0.78474, 0.78540, 0.78562, 0.78572, 0.78583, 0.78583, 0.78583, 0.78583, 0.78567, 0.78551, 0.78529, 0.78485, 0.78441, 0.78386, 0.78310, 0.78233, 0.78135, 0.77970, 0.77861]; - -figure(5) -clf -set(gcf,'Position',[50 50 950 750]) - - -imagesc(nadd2s, as_to_add, instability_boundary); % Specify x and y data for axes -hold on -plot(nadd2s_from_figure, as_to_add_from_figure, 'r*-', 'LineWidth', 2); % Plot the curve (red line) -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -colorbar; % Add a colorbar -xlabel('$na_{dd}^2$','fontsize',16,'interpreter','latex'); -ylabel('$a_s/a_{dd}$','fontsize',16,'interpreter','latex'); - -%{ -imagesc(AtomNumber*1E-5, ScatteringLengths, instability_boundary); % Specify x and y data for axes -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -cbar1 = colorbar; -cbar1.Label.Interpreter = 'latex'; -ylabel(cbar1,'$(\times 10^{-31})$','FontSize',16,'Rotation',270) -xlabel(' Atom number for a trap area of 100$\mu m^2 ~ (\times 10^5)$','fontsize',16,'interpreter','latex'); -ylabel('Scattering length ($\times a_0$)','fontsize',16,'interpreter','latex'); -title('Roton instability boundary','fontsize',16,'interpreter','latex') -%} - -%% -function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi) - Go = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2))); - gamma4 = 1/(sqrt(2*pi) * MeanWidth); - Fka = (3 * cos(deg2rad(theta))^2 - 1) + ((3 * Go) .* ((sin(deg2rad(theta))^2 .* sin(deg2rad(phi))^2) - cos(deg2rad(theta))^2)); - Ukk = (gs + (gdd * Fka)) * gamma4; -end - -function ret = computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced) - eps_dd = add/as; % Relative interaction strength - MeanWidth = x * lz; - gammaQF = (32/3) * gs * (as^3/pi)^(1/2) * (1 + ((3/2) * eps_dd^2)); % Quantum Fluctuations term - gamma4 = 1/(sqrt(2*pi) * MeanWidth); - gamma5 = sqrt(2/5) / (sqrt(pi) * MeanWidth)^(3/2); - gQF = gamma5 * gammaQF; - Energy_AxialComponent = (PlanckConstantReduced * wz) * ((lz^2/(4 * MeanWidth^2)) + (MeanWidth^2/(4 * lz^2))); - Energy_TransverseComponent = (0.5 * (gs + (2*gdd)) * gamma4 * AtomNumberDensity) + ((2/5) * gQF * AtomNumberDensity^(3/2)); - ret = (Energy_AxialComponent + Energy_TransverseComponent) / (PlanckConstantReduced * wz); -end - - - diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ScalingOfTheQFTerm.m b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ScalingOfTheQFTerm.m deleted file mode 100644 index 4c5ee06..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/ScalingOfTheQFTerm.m +++ /dev/null @@ -1,89 +0,0 @@ -%% 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*AtomicMassUnit; -Dy164IsotopicAbundance = 0.2826; -DyMagneticMoment = 9.93*BohrMagneton; - -%% Scaling of the QF term - -wz = 2 * pi * 72.4; % Trap frequency in the tight confinement direction -lz = sqrt(PlanckConstantReduced/(Dy164Mass * wz)); % Defining a harmonic oscillator length -gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength -add = VacuumPermeability*DyMagneticMoment^2*Dy164Mass/(12*pi*PlanckConstantReduced^2); % Dipole length -gdd = VacuumPermeability*DyMagneticMoment^2/3; - -nadd2s = 0.05:0.01:0.25; -as_to_add = 0.76:0.01:0.81; - -QF = zeros(length(as_to_add), length(nadd2s)); -ScatteringLengths = zeros(length(as_to_add), 1); -AtomNumber = zeros(length(nadd2s), 1); -w0 = 2 * pi * 61.6316; % Trap frequency in the tight confinement direction -l0 = sqrt(PlanckConstantReduced/(Dy164Mass * w0)); % Defining a harmonic oscillator length -tsize = 10 * l0; - -x0 = 5; -Aineq = []; -Bineq = []; -Aeq = []; -Beq = []; -lb = [1]; -ub = [10]; -nonlcon = []; -fminconopts = optimoptions(@fmincon,'Display','off', 'StepTolerance', 1.0000e-11, 'MaxIterations',1500); - -for idx = 1:length(nadd2s) - for jdx = 1:length(as_to_add) - AtomNumberDensity = nadd2s(idx) / add^2; % Areal density of atoms - AtomNumber(idx) = AtomNumberDensity*tsize^2; - as = (as_to_add(jdx) * add); % Scattering length - gs = 4 * pi * PlanckConstantReduced^2/Dy164Mass * as; % Contact interaction strength - ScatteringLengths(jdx) = as/BohrRadius; - TotalEnergyPerParticle = @(x) computeTotalEnergyPerParticle(x, as, AtomNumberDensity, wz, lz, gs, add, gdd, PlanckConstantReduced); - sigma = fmincon(TotalEnergyPerParticle, x0, Aineq, Bineq, Aeq, Beq, lb, ub, nonlcon, fminconopts); - eps_dd = add/as; % Relative interaction strength - - % == Quantum Fluctuations term == % - MeanWidth = sigma * lz; - 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; - QF(jdx, idx) = 3 * gQF * AtomNumberDensity^(3/2); - end -end - -figure -clf -set(gcf,'Position',[50 50 950 750]) -imagesc(AtomNumber*1E-5, ScatteringLengths, QF * 1E31); % Specify x and y data for axes -set(gca, 'YDir', 'normal'); % Correct the y-axis direction -cbar1 = colorbar; -cbar1.Label.Interpreter = 'latex'; -ylabel(cbar1,'$(\times 10^{-31})$','FontSize',16,'Rotation',270) -xlabel(' Atom number for a trap area of 100$\mu m^2 ~ (\times 10^5)$','fontsize',16,'interpreter','latex'); -ylabel('Scattering length ($\times a_0$)','fontsize',16,'interpreter','latex'); -title('Scaling of the quantum fluctuations term','fontsize',16,'interpreter','latex') \ No newline at end of file diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/bwhpc_matlab_gpe_sim_cpu.slurm b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/bwhpc_matlab_gpe_sim_cpu.slurm deleted file mode 100644 index ad3e154..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/bwhpc_matlab_gpe_sim_cpu.slurm +++ /dev/null @@ -1,38 +0,0 @@ -#!/bin/bash -########### Begin SLURM header ########### -#Partition -#SBATCH --partition=cpu-single -# Request number of nodes and CPU cores per node for job -#SBATCH --nodes=1 -#SBATCH --ntasks-per-node=1 -#SBATCH --cpus-per-task=10 -#SBATCH --mem=2G -# Estimated wallclock time for job -#SBATCH --time=00:30:00 -#SBATCH --job-name=simulation -#SBATCH --error=simulation.err -#SBATCH --output=simulation.out - -########### End SLURM header ########## - -echo "Working Directory: $PWD" -echo "Running on host $HOSTNAME" -echo "Job id: $SLURM_JOB_ID" -echo "Job name: $SLURM_JOB_NAME" -echo "Number of nodes allocated to job: $SLURM_JOB_NUM_NODES" -echo "Number of cores allocated to job: $SLURM_JOB_CPUS_PER_NODE" - - -# Load module -module load math/matlab/R2023a - -echo Directory is `pwd` -echo "Initiating Job..." - -# Start a Matlab program -matlab -nodisplay -nosplash -r "ExtractingKRoton" - -# notice for tests -echo "Job terminated successfully" - -exit diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/roton_instability_project.json b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/roton_instability_project.json deleted file mode 100644 index 5036949..0000000 --- a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/roton_instability_project.json +++ /dev/null @@ -1 +0,0 @@ -{"version":[4,2],"axesColl":[{"name":"XY","type":"XYAxes","isLogX":false,"isLogY":false,"noRotation":true,"calibrationPoints":[{"px":304.86283783783784,"py":633.6364864864864,"dx":"0.1","dy":"0.745","dz":null},{"px":694.7418918918919,"py":633.6364864864864,"dx":"0.2","dy":"0.745","dz":null},{"px":107.59864864864865,"py":573.8594594594595,"dx":"0.1","dy":"0.745","dz":null},{"px":107.59864864864865,"py":27.895945945945947,"dx":"0.2","dy":"0.79","dz":null}]}],"datasetColl":[{"name":"Default 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\ No newline at end of file diff --git a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/roton_instability_project.tar b/Estimations/DipolarDispersionAndRotonInstabilityBoundary/roton_instability_project.tar deleted file mode 100644 index 9be76ad..0000000 Binary files a/Estimations/DipolarDispersionAndRotonInstabilityBoundary/roton_instability_project.tar and /dev/null differ diff --git a/Estimations/RotonInstability/AnalyzeResults.m b/Estimations/RotonInstability/AnalyzeResults.m index 95703ba..3520c0a 100644 --- a/Estimations/RotonInstability/AnalyzeResults.m +++ b/Estimations/RotonInstability/AnalyzeResults.m @@ -1,8 +1,8 @@ %% Across range of a_s, n -% load('.\Results\ExtractingKRoton_Result_Below1000.mat') -% load('.\Results\ExtractingKRoton_Result_Above1000.mat') -load('.\Results\ExtractingKRoton_Result_Above10000.mat') +% load('.\Results\ExtractingParameters_Result_Below1000.mat') +% load('.\Results\ExtractingParameters_Result_Above1000.mat') +load('.\Results\ExtractingParameters_Result_Above10000.mat') PlanckConstantReduced = 6.62607015E-34/(2*pi); AtomicMassUnit = 1.660539066E-27; @@ -119,7 +119,7 @@ t.Padding = 'compact'; % Minimize padding around the layout %% Fixed Density results -load('.\Results\ExtractingKRoton_Result_FixedDensity_phi0.mat') +load('.\Results\ExtractingParameters_Result_FixedDensity_phi0.mat') PlanckConstantReduced = 6.62607015E-34/(2*pi); AtomicMassUnit = 1.660539066E-27; @@ -206,8 +206,8 @@ t.Padding = 'compact'; % Minimize padding around the layout %% Fixed Density results - compare two orthogonal directions -data0 = load('.\Results\ExtractingKRoton_Result_FixedDensity_phi0.mat'); -data90 = load('.\Results\ExtractingKRoton_Result_FixedDensity_phi90.mat'); +data0 = load('.\Results\ExtractingParameters_Result_FixedDensity_phi0.mat'); +data90 = load('.\Results\ExtractingParameters_Result_FixedDensity_phi90.mat'); PlanckConstantReduced = 6.62607015E-34/(2*pi); AtomicMassUnit = 1.660539066E-27; diff --git a/Estimations/RotonInstability/ExtractingKRoton.m b/Estimations/RotonInstability/ExtractingParameters.m similarity index 99% rename from Estimations/RotonInstability/ExtractingKRoton.m rename to Estimations/RotonInstability/ExtractingParameters.m index bb7ce0f..111df4c 100644 --- a/Estimations/RotonInstability/ExtractingKRoton.m +++ b/Estimations/RotonInstability/ExtractingParameters.m @@ -143,7 +143,7 @@ for mainloop_idx = 1:length(wz_values) %} end -save('.\Results\ExtractingKRoton_Result.mat', 'data_struct'); +save('.\Results\ExtractingParameters_Result.mat', 'data_struct'); %% Extracting values from the roton instability boundary for tilted dipoles - fixed atom number, trap frequency @@ -216,7 +216,7 @@ for mainloop_idx = 1:length(wz_values) end -save('.\Results\ExtractingKRoton_Result_FixedDensity_phi90.mat', 'data_struct'); +save('.\Results\ExtractingParameters_Result_FixedDensity_phi90.mat', 'data_struct'); %% function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, theta, phi) Go = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2)));