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Script to determine appropriate trap parameters to transfer BEC between static lattices.

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Karthik 2025-02-04 00:02:07 +01:00
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*.png
*.pyc
*.mat
*.gif
*.mp4
*.bat
.ipynb_checkpoints/
.vscode/

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Estimations/EstimatesForStaticLattice.m Normal file
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%% 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;
%% Example usage:
a_s = 100 * BohrRadius; % Scattering length in meters
N = 1e5; % Number of atoms
v_x = 10;
v_y = 10;
v_z = 1E3;
[R_x, R_y, R_z] = calculateThomasFermiRadiusFromTrapParameters(v_x, v_y, v_z, N, a_s, Dy164Mass);
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);
%%
% Define the parameters
Power_values = linspace(1, 10, 50); % Laser powers (W), from 1 W to 10 W
waist_values = linspace(10e-6, 100e-6, 50); % Beam waists (m), from 10 µm to 100 µm
% Constants
a_s = 100 * BohrRadius; % Scattering length in meters
N = 1e5; % Number of atoms
AngleBetweenBeams = 9.44;
Wavelength = 532e-9; % Laser wavelength in meters
alpha = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
R_z_matrix = zeros(length(waist_values), length(Power_values)); % Preallocate a matrix to store the R_z values
% Loop over all combinations of P and w0
for i = 1:length(waist_values)
for j = 1:length(Power_values)
% Calculate the Thomas-Fermi radii for each P and w0
[R_z, LatticeConstant, AxialTrapFrequency] = calculateThomasFermiRadiusFromLatticeParameters(Power_values(j), waist_values(i), AngleBetweenBeams, Wavelength, N, a_s, Dy164Mass, alpha);
% Store the result in the matrix
R_z_matrix(i, j) = R_z * 1e6; % Convert R_z to µm
end
end
% Plot the resulting matrix
figure(1)
clf
set(gcf,'Position',[50 50 950 750])
imagesc(Power_values, waist_values * 1e6, R_z_matrix); % Specify x and y data for axes
hold on
[contour_matrix, contour_handle] = contour(Power_values, waist_values * 1e6, R_z_matrix, 'LineColor', 'white', 'LineWidth', 1.5);
clabel(contour_matrix, contour_handle, 'FontSize', 12, 'Color', 'black', 'LabelSpacing', 600); % Adjust LabelSpacing for better placement
set(gca, 'YDir', 'normal'); % Correct the y-axis direction
cbar = colorbar; % Add a colorbar
xlabel('Laser Power (W)','FontSize',16);
ylabel('Beam Waist (\mum)', 'Interpreter', 'tex','FontSize',16);
ylabel(cbar,'R_z (\mum)', 'Interpreter', 'tex','FontSize',16,'Rotation',270)
title(['\bf d = ' num2str(LatticeConstant * 1E6) ' \mum ; \bf \nu_z = ' num2str(round((AxialTrapFrequency/ (2*pi)) * 1E-3),3) ' kHz'],'fontsize',16, 'Interpreter', 'tex');
%%
function [R_x, R_y, R_z] = calculateThomasFermiRadiusFromTrapParameters(v_x, v_y, v_z, N, a, m)
% Calculate the Thomas-Fermi radius of a BEC.
%
% Parameters:
% omega_x, omega_y, omega_z: Trap frequencies in x, y, z directions (Hz)
% N: Number of atoms
% a: s-wave scattering length (m)
% m: Mass of the atom (kg)
%
% Returns:
% R_x, R_y, R_z: Thomas-Fermi radii in meters
omega_x = 2*pi*v_x; % Trap frequency in x direction (Hz)
omega_y = 2*pi*v_y; % Trap frequency in y direction (Hz)
omega_z = 2*pi*v_z; % Trap frequency in z direction (Hz)
% Calculate the geometric mean of trap frequencies
omega_bar = (omega_x * omega_y * omega_z)^(1/3);
% Constants
PlanckConstantReduced = 6.62607015E-34/(2*pi); % Reduced Planck's constant (J⋅s)
% Calculate the mean harmonic oscillator length
a_ho = sqrt(PlanckConstantReduced / (m * omega_bar));
% Calculate the chemical potential
mu = 0.5 * PlanckConstantReduced * omega_bar * (15 * N * a / a_ho)^(2/5);
% Calculate Thomas-Fermi radii
R_x = sqrt(2 * mu / (m * omega_x^2));
R_y = sqrt(2 * mu / (m * omega_y^2));
R_z = sqrt(2 * mu / (m * omega_z^2));
end
function [R_TF, d_lat, omega_eff] = calculateThomasFermiRadiusFromLatticeParameters(P, w_z, theta, lambda, N, a, m, alpha)
% Calculate Thomas-Fermi radius of a BEC in a Gaussian potential
%
% Inputs:
% P - Laser power (W)
% w_z - Beam waist (m)
% theta - angle between beams
% N - Number of atoms
% a - s-wave scattering length (m)
% m - Atomic mass (kg)
%
% Output:
% R_TF - Thomas-Fermi radius (m)
% Constants
PlanckConstantReduced = 6.62607015E-34/(2*pi); % Reduced Planck's constant (J⋅s)
% Calculate trap depth
I = (2 * P) / (pi * w_z^2);
U_single = alpha * I;
V_o = 4 * U_single;
% Calculate lattice constant
d_lat = lambda / (2 * cos(deg2rad(theta)/2));
% Calculate effective trapping frequency
omega_eff = (pi / d_lat) * sqrt(2 * V_o / m);
% Calculate chemical potential
a_ho = sqrt(PlanckConstantReduced / m * omega_eff);
mu = 0.5 * PlanckConstantReduced * omega_eff * (15 * N * a / a_ho)^(2/5); % Shallow lattice
% Calculate Thomas-Fermi radius
R_TF = sqrt(2 * mu / (m * omega_eff^2));
end