Script to determine appropriate trap parameters to transfer BEC between static lattices.
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@ -6,5 +6,8 @@ Time-Series-Analyzer/Time-Series-Data
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*.png
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*.png
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*.pyc
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*.pyc
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*.mat
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*.mat
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*.gif
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*.mp4
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*.bat
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.ipynb_checkpoints/
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.ipynb_checkpoints/
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.vscode/
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.vscode/
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151
Estimations/EstimatesForStaticLattice.m
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151
Estimations/EstimatesForStaticLattice.m
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@ -0,0 +1,151 @@
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%% Physical constants
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PlanckConstant = 6.62607015E-34;
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PlanckConstantReduced = 6.62607015E-34/(2*pi);
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FineStructureConstant = 7.2973525698E-3;
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ElectronMass = 9.10938291E-31;
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GravitationalConstant = 6.67384E-11;
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ProtonMass = 1.672621777E-27;
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AtomicMassUnit = 1.660539066E-27;
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BohrRadius = 5.2917721067E-11;
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BohrMagneton = 9.274009994E-24;
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BoltzmannConstant = 1.38064852E-23;
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StandardGravityAcceleration = 9.80665;
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SpeedOfLight = 299792458;
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StefanBoltzmannConstant = 5.670373E-8;
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ElectronCharge = 1.602176634E-19;
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VacuumPermeability = 1.25663706212E-6;
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DielectricConstant = 8.8541878128E-12;
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ElectronGyromagneticFactor = -2.00231930436153;
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AvogadroConstant = 6.02214076E23;
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ZeroKelvin = 273.15;
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GravitationalAcceleration = 9.80553;
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VacuumPermittivity = 1 / (SpeedOfLight^2 * VacuumPermeability);
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HartreeEnergy = ElectronCharge^2 / (4 * pi * VacuumPermittivity * BohrRadius);
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AtomicUnitOfPolarizability = (ElectronCharge^2 * BohrRadius^2) / HartreeEnergy; % Or simply 4*pi*VacuumPermittivity*BohrRadius^3
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% Dy specific constants
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Dy164Mass = 163.929174751*AtomicMassUnit;
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Dy164IsotopicAbundance = 0.2826;
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DyMagneticMoment = 9.93*BohrMagneton;
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%% Example usage:
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a_s = 100 * BohrRadius; % Scattering length in meters
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N = 1e5; % Number of atoms
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v_x = 10;
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v_y = 10;
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v_z = 1E3;
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[R_x, R_y, R_z] = calculateThomasFermiRadiusFromTrapParameters(v_x, v_y, v_z, N, a_s, Dy164Mass);
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fprintf('Thomas-Fermi radii: R_x = %.2f µm, R_y = %.2f µm, R_z = %.2f µm\n', R_x*1e6, R_y*1e6, R_z*1e6);
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%%
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% Define the parameters
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Power_values = linspace(1, 10, 50); % Laser powers (W), from 1 W to 10 W
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waist_values = linspace(10e-6, 100e-6, 50); % Beam waists (m), from 10 µm to 100 µm
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% Constants
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a_s = 100 * BohrRadius; % Scattering length in meters
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N = 1e5; % Number of atoms
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AngleBetweenBeams = 9.44;
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Wavelength = 532e-9; % Laser wavelength in meters
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alpha = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
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R_z_matrix = zeros(length(waist_values), length(Power_values)); % Preallocate a matrix to store the R_z values
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% Loop over all combinations of P and w0
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for i = 1:length(waist_values)
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for j = 1:length(Power_values)
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% Calculate the Thomas-Fermi radii for each P and w0
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[R_z, LatticeConstant, AxialTrapFrequency] = calculateThomasFermiRadiusFromLatticeParameters(Power_values(j), waist_values(i), AngleBetweenBeams, Wavelength, N, a_s, Dy164Mass, alpha);
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% Store the result in the matrix
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R_z_matrix(i, j) = R_z * 1e6; % Convert R_z to µm
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end
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end
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% Plot the resulting matrix
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figure(1)
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clf
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set(gcf,'Position',[50 50 950 750])
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imagesc(Power_values, waist_values * 1e6, R_z_matrix); % Specify x and y data for axes
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hold on
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[contour_matrix, contour_handle] = contour(Power_values, waist_values * 1e6, R_z_matrix, 'LineColor', 'white', 'LineWidth', 1.5);
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clabel(contour_matrix, contour_handle, 'FontSize', 12, 'Color', 'black', 'LabelSpacing', 600); % Adjust LabelSpacing for better placement
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set(gca, 'YDir', 'normal'); % Correct the y-axis direction
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cbar = colorbar; % Add a colorbar
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xlabel('Laser Power (W)','FontSize',16);
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ylabel('Beam Waist (\mum)', 'Interpreter', 'tex','FontSize',16);
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ylabel(cbar,'R_z (\mum)', 'Interpreter', 'tex','FontSize',16,'Rotation',270)
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title(['\bf d = ' num2str(LatticeConstant * 1E6) ' \mum ; \bf \nu_z = ' num2str(round((AxialTrapFrequency/ (2*pi)) * 1E-3),3) ' kHz'],'fontsize',16, 'Interpreter', 'tex');
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%%
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function [R_x, R_y, R_z] = calculateThomasFermiRadiusFromTrapParameters(v_x, v_y, v_z, N, a, m)
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% Calculate the Thomas-Fermi radius of a BEC.
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%
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% Parameters:
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% omega_x, omega_y, omega_z: Trap frequencies in x, y, z directions (Hz)
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% N: Number of atoms
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% a: s-wave scattering length (m)
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% m: Mass of the atom (kg)
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%
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% Returns:
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% R_x, R_y, R_z: Thomas-Fermi radii in meters
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omega_x = 2*pi*v_x; % Trap frequency in x direction (Hz)
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omega_y = 2*pi*v_y; % Trap frequency in y direction (Hz)
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omega_z = 2*pi*v_z; % Trap frequency in z direction (Hz)
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% Calculate the geometric mean of trap frequencies
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omega_bar = (omega_x * omega_y * omega_z)^(1/3);
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% Constants
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PlanckConstantReduced = 6.62607015E-34/(2*pi); % Reduced Planck's constant (J⋅s)
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% Calculate the mean harmonic oscillator length
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a_ho = sqrt(PlanckConstantReduced / (m * omega_bar));
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% Calculate the chemical potential
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mu = 0.5 * PlanckConstantReduced * omega_bar * (15 * N * a / a_ho)^(2/5);
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% Calculate Thomas-Fermi radii
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R_x = sqrt(2 * mu / (m * omega_x^2));
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R_y = sqrt(2 * mu / (m * omega_y^2));
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R_z = sqrt(2 * mu / (m * omega_z^2));
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end
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function [R_TF, d_lat, omega_eff] = calculateThomasFermiRadiusFromLatticeParameters(P, w_z, theta, lambda, N, a, m, alpha)
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% Calculate Thomas-Fermi radius of a BEC in a Gaussian potential
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%
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% Inputs:
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% P - Laser power (W)
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% w_z - Beam waist (m)
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% theta - angle between beams
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% N - Number of atoms
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% a - s-wave scattering length (m)
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% m - Atomic mass (kg)
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%
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% Output:
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% R_TF - Thomas-Fermi radius (m)
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% Constants
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PlanckConstantReduced = 6.62607015E-34/(2*pi); % Reduced Planck's constant (J⋅s)
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% Calculate trap depth
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I = (2 * P) / (pi * w_z^2);
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U_single = alpha * I;
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V_o = 4 * U_single;
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% Calculate lattice constant
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d_lat = lambda / (2 * cos(deg2rad(theta)/2));
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% Calculate effective trapping frequency
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omega_eff = (pi / d_lat) * sqrt(2 * V_o / m);
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% Calculate chemical potential
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a_ho = sqrt(PlanckConstantReduced / m * omega_eff);
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mu = 0.5 * PlanckConstantReduced * omega_eff * (15 * N * a / a_ho)^(2/5); % Shallow lattice
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% Calculate Thomas-Fermi radius
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R_TF = sqrt(2 * mu / (m * omega_eff^2));
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end
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