Modification to achieve true linear ramp in scattering length
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@ -1,45 +1,50 @@
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% --- Main script ---
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FR_choice = 1;
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ABKG_choice = 1;
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% Ramp parameters
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a_start = 91; % initial scattering length (a_0)
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a_end = 89; % final scattering length (a_0)
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T = 0.030; % ramp duration (s)
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a_start = 86; % initial scattering length (a_0)
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a_end = 85; % final scattering length (a_0)
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T = 0.030; % ramp duration (s)
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Nt = 1000; % number of time points
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ResonanceRange = [2.3, 3.0];
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% options.rampShape = @(t) a_start + (a_end - a_start) * sin(pi*t/T/2).^2;
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ResonanceRange = [1.2, 2.6];
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% Options for ramp generation
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options = struct(...
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'smoothingMethod', 'sgolay', ...
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options = struct( ...
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'smoothingMethod', 'sgolay', ... % 'sgolay', 'lowpass', or 'none'
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'sgolayOrder', 3, ...
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'sgolayFrameLength', 51, ...
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'maxRampRate', 5, ...
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'Bmin', 0.5, ...
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'Bmax', 3.5, ...
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'rampShape', 'linear' ... % 'linear', 'exponential', 'sigmoid', or function handle
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'rampShape', 'linear' ... % Choose: 'linear', 'exponential', 'sigmoid'
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);
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[t, B_ramp, a_check] = generateSmoothBRamp(FR_choice, ABKG_choice, a_start, a_end, ResonanceRange, T, Nt, options);
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% Plot
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figure(1);
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% ----- Plot results -----
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figure(1); clf
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subplot(2,1,1);
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plot(t, B_ramp, 'b-', 'LineWidth', 2);
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xlabel('Time (s)'); ylabel('B(t) (G)');
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title('Generated magnetic field ramp'); grid on;
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xlabel('Time (s)');
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ylabel('Magnetic field B(t) (G)');
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title('Generated magnetic field ramp B(t)');
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grid on;
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set(gca, 'FontSize', 14);
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subplot(2,1,2);
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plot(t, a_check, 'r--', 'LineWidth', 2);
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xlabel('Time (s)'); ylabel('a_s(B(t)) (a_0)');
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title('Resulting ramp in scattering length a_s(t)'); grid on;
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plot(t, a_check, 'r-', 'LineWidth', 2);
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xlabel('Time (s)');
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ylabel('Scattering length a_s(t) (a_0)');
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legend('Resulting a_s(t)');
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title('Scattering length ramp');
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grid on;
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set(gca, 'FontSize', 14);
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% Visualize full resonance curve and selected window
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[B_full, a_full] = extractBetweenResonances(FR_choice, ABKG_choice, ResonanceRange);
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[B_curve, a_curve] = fullResonanceCurve(FR_choice, ABKG_choice, ResonanceRange);
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figure(2);
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clf
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plot(B_curve, a_curve, 'k-', 'LineWidth', 1); hold on;
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plot(B_full, a_full, 'b-', 'LineWidth', 2); % zoomed-in region
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plot(B_ramp, a_check, 'r-', 'LineWidth', 2); % actual ramp
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@ -50,41 +55,25 @@ yline(min(a_check), '--r', 'a_{min}');
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yline(max(a_check), '--r', 'a_{max}');
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xlabel('B field (G)');
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ylabel('Scattering length a_s (a_0)');
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title('Resonance curve with selected B and a_s range', 'Interpreter','tex');
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title('Feshbach spectrum with selected B and a_s range', 'Interpreter','tex');
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legend('Full a(B)', 'Zoomed Region', 'Ramp a_s(t)', 'Ramp Endpoints', 'Location', 'NorthWest');
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ylim([0 150])
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set(gca, 'FontSize', 14)
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grid on;
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%% --- generateSmoothBRamp ---
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%% Helper functions
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function [t, B_ramp, a_check] = generateSmoothBRamp(FR_choice, ABKG_choice, a_start, a_end, selectedResRange, T, Nt, opts)
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% Time array
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t = linspace(0, T, Nt);
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% --- Generate base ramp shape ---
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ascending = (a_end > a_start);
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switch lower(class(opts.rampShape))
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case 'char'
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switch lower(opts.rampShape)
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case 'linear'
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base = t / T;
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case 'exponential'
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tau = T / 3;
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base = (1 - exp(-t / tau)) / (1 - exp(-T / tau));
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case 'sigmoid'
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s = 10 / T; center = T / 2;
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sigmoid = @(x) 1 ./ (1 + exp(-s * (x - center)));
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base = (sigmoid(t) - sigmoid(t(1))) / (sigmoid(t(end)) - sigmoid(t(1)));
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otherwise
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error('Unknown ramp shape string: %s', opts.rampShape);
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end
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case 'function_handle'
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base = opts.rampShape(t);
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otherwise
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error('Invalid type for rampShape. Use string or function handle.');
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if strcmp(opts.rampShape, 'linear')
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% Directly call helper for linear LUT ramp generation
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[t, B_ramp, a_check] = generateLinearBRampUsingLUT(FR_choice, ABKG_choice, a_start, a_end, selectedResRange, T, Nt);
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return
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end
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a_target = a_start + (a_end - a_start) * base;
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% Get target a_s(t) based on rampShape choice
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a_target = getTargetScatteringLength(t, T, a_start, a_end, opts.rampShape);
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% --- a(B) interpolation ---
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[B_between, a_between] = extractBetweenResonances(FR_choice, ABKG_choice, selectedResRange);
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@ -129,7 +118,30 @@ function [t, B_ramp, a_check] = generateSmoothBRamp(FR_choice, ABKG_choice, a_st
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a_check = a_of_B(B_ramp);
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end
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%% --- extractBetweenResonances ---
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function a_target = getTargetScatteringLength(t, T, a_start, a_end, rampShape)
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% If rampShape is a function handle, use it directly (for flexibility)
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if isa(rampShape, 'function_handle')
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a_target = rampShape(t);
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return
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end
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switch lower(rampShape)
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case 'exponential'
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tau = T / 3;
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base = (1 - exp(-t / tau)) / (1 - exp(-T / tau));
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a_target = a_start + (a_end - a_start) * base;
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case 'sigmoid'
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s = 10 / T; center = T / 2;
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sigmoid = @(x) 1 ./ (1 + exp(-s * (x - center)));
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base = (sigmoid(t) - sigmoid(t(1))) / (sigmoid(t(end)) - sigmoid(t(1)));
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a_target = a_start + (a_end - a_start) * base;
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otherwise
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error('Unknown ramp shape: %s', rampShape);
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end
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end
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function [B_between, a_between] = extractBetweenResonances(FR_choice, ABKG_choice, selectedRange)
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[a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_choice, selectedRange);
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[~, idx] = sort(resonancewB, 'descend');
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@ -186,3 +198,33 @@ function [a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_c
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end
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end
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function [t, B_ramp, a_check] = generateLinearBRampUsingLUT(FR_choice, ABKG_choice, a_start, a_end, selectedResRange, T, Nt)
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% Time vector
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t = linspace(0, T, Nt);
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% 1) Generate LUT of B and a_s(B)
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[B_between, a_between] = extractBetweenResonances(FR_choice, ABKG_choice, selectedResRange);
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% Restrict to physically meaningful range (optional)
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valid_idx = a_between > 0 & a_between < 150;
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B_lut = B_between(valid_idx);
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a_lut = a_between(valid_idx);
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% 2) Generate linear a_s ramp in time
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a_target = linspace(a_start, a_end, Nt);
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% 3) Interpolate B(t) from LUT a_s -> B
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% Make sure a_lut is sorted ascending
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[a_lut_sorted, idx_sort] = sort(a_lut);
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B_lut_sorted = B_lut(idx_sort);
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B_ramp = interp1(a_lut_sorted, B_lut_sorted, a_target, 'linear', 'extrap');
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% 4) Compute resulting a_s(t) for verification
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[a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_choice, selectedResRange);
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a_of_B = @(B) arrayfun(@(b) ...
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a_bkg * prod(1 - resonancewB ./ (b - resonanceB)), B);
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a_check = a_of_B(B_ramp);
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end
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