Latest script to choose resonance range, ignore resonances between two chosen ones and generate a B Field ramp that results in a linear ramp in scattering length.
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% --- User setup ---
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resIndex = 1; % resonance index (1-based)
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duration = 0.5; % total ramp time [s]
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N_points = 300; % number of time points
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FR_choice = 1; % resonance data choice (1=new, 0=old)
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ABKG_choice = 1; % background scattering length choice (1,2,3)
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side = 'right'; % 'left' or 'right' side of resonance
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a_range = [111, 100]; % desired ramp of scattering length (a0), can be descending
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doPlot = true; % show resonance and ramp region
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% --- Main script ---
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FR_choice = 1;
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ABKG_choice = 1;
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% --- Generate ramp ---
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[t, B_t, a_t] = makeLinearScatteringRamp(resIndex, duration, N_points, ...
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FR_choice, ABKG_choice, side, a_range, doPlot);
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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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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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% --- Plot results ---
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figure;
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% Options for ramp generation
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options = struct(...
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'smoothingMethod', 'sgolay', ...
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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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);
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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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subplot(2,1,1);
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plot(t, B_t, 'b-', 'LineWidth', 1.5);
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ylabel('B (G)', 'Interpreter', 'tex');
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title('Magnetic field B(t)', 'Interpreter', 'tex');
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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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subplot(2,1,2);
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plot(t, a_t, 'r-', 'LineWidth', 1.5);
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ylabel('Scattering length a ($a_0$)', 'Interpreter', 'latex');
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xlabel('Time (s)', 'Interpreter', 'tex');
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title('Linear ramp of a(t)', 'Interpreter', 'tex');
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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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% 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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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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plot(B_ramp([1 end]), a_check([1 end]), 'ro', 'MarkerSize', 8); % endpoints
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xline(min(B_ramp), '--b', 'B_{min}');
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xline(max(B_ramp), '--b', 'B_{max}');
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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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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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grid on;
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%% Function: makeLinearScatteringRamp
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function [timeGrid, B_ramp, a_ramp] = makeLinearScatteringRamp(resIndex, duration, N_points, ...
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FR_choice, ABKG_choice, side, a_range, doPlot)
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% Generates B(t) that linearly ramps scattering length a(t) over time avoiding divergence.
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% Works with increasing or decreasing a_range.
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%% --- generateSmoothBRamp ---
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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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% --- Resonance parameters ---
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if FR_choice == 1
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switch ABKG_choice
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case 1, a_bkg = 85.5;
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case 2, a_bkg = 93.5;
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case 3, a_bkg = 77.5;
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otherwise, error('Invalid ABKG_choice');
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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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end
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a_target = a_start + (a_end - a_start) * base;
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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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valid_idx = a_between > 0 & a_between < 150;
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[a_sorted, sort_idx] = sort(a_between(valid_idx));
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B_sorted = B_between(valid_idx);
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B_sorted = B_sorted(sort_idx);
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B_of_a = @(a) interp1(a_sorted, B_sorted, a, 'linear', 'extrap');
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B_raw = B_of_a(a_target);
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% --- Smoothing ---
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switch opts.smoothingMethod
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case 'sgolay'
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B_smooth = sgolayfilt(B_raw, opts.sgolayOrder, opts.sgolayFrameLength);
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case 'lowpass'
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dt = T / (Nt - 1); Fs = 1 / dt;
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B_smooth = lowpass(B_raw, Fs / 20, Fs);
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case 'none'
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B_smooth = B_raw;
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otherwise
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error('Unknown smoothing method');
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end
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% --- Bound the ramp ---
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B_smooth = min(max(B_smooth, opts.Bmin), opts.Bmax);
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% --- Enforce max dB/dt ---
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dt = T / (Nt - 1);
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for i = 2:Nt
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delta = B_smooth(i) - B_smooth(i-1);
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if abs(delta/dt) > opts.maxRampRate
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delta = sign(delta) * opts.maxRampRate * dt;
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B_smooth(i) = B_smooth(i-1) + delta;
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end
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end
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B_ramp = B_smooth;
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% --- Verify a_s(t) from B_ramp ---
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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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%% --- extractBetweenResonances ---
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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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B1 = resonanceB(idx(1)); B2 = resonanceB(idx(2));
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w1 = resonancewB(idx(1)); w2 = resonancewB(idx(2));
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Bvis = linspace(min(B1, B2) - 20*min(w1,w2), max(B1, B2) + 20*min(w1,w2), 2000);
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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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avis = a_of_B(Bvis);
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between_idx = Bvis >= min(B1,B2) & Bvis <= max(B1,B2);
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B_between = Bvis(between_idx);
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a_between = avis(between_idx);
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end
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function [B_range, a_values] = fullResonanceCurve(FR_choice, ABKG_choice, selectedRange)
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[a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_choice, selectedRange);
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B_range = linspace(min(resonanceB)-0.2, max(resonanceB)+0.2, 3000);
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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_values = a_of_B(B_range);
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end
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function [a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_choice, selectedRange)
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if FR_choice == 1
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a_bkg_list = [85.5, 93.5, 77.5];
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resonanceB = [1.295, 1.306, 2.174, 2.336, 2.591, 2.740, 2.803, ...
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2.780, 3.357, 4.949, 5.083, 7.172, 7.204, 7.134, 76.9];
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resonancewB = [0.009, 0.010, 0.0005, 0.0005, 0.001, 0.0005, 0.021, ...
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0.015, 0.043, 0.0005, 0.130, 0.024, 0.0005, 0.036, 3.1];
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else
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switch ABKG_choice
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case 1, a_bkg = 87.2;
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case 2, a_bkg = 95.2;
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case 3, a_bkg = 79.2;
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otherwise, error('Invalid ABKG_choice');
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end
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a_bkg_list = [87.2, 95.2, 79.2];
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resonanceB = [1.298, 2.802, 3.370, 5.092, 7.154, 2.592, 2.338, 2.177];
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resonancewB = [0.018, 0.047, 0.048, 0.145, 0.020, 0.008, 0.001, 0.001];
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end
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a_bkg = a_bkg_list(ABKG_choice);
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% --- Filter resonanceB and resonancewB if selectedRange is provided ---
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if nargin >= 3 && ~isempty(selectedRange)
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minB = min(selectedRange); maxB = max(selectedRange);
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keep_idx = (resonanceB >= minB) & (resonanceB <= maxB);
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% --- Scattering length formula ---
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a_of_B = @(B) arrayfun(@(b) ...
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a_bkg * prod(1 - resonancewB ./ (b - resonanceB)), ...
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B);
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% Keep only the lowest and highest resonance in the selected range
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if sum(keep_idx) >= 2
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B_sub = resonanceB(keep_idx);
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w_sub = resonancewB(keep_idx);
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[~, idx_lo] = min(B_sub);
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[~, idx_hi] = max(B_sub);
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% --- Select resonance ---
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B0 = resonanceB(resIndex);
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wB = resonancewB(resIndex);
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% --- Define B scan range ---
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Bpad = 15 * wB;
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switch lower(side)
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case 'left'
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Bscan = linspace(B0 - Bpad, B0 - wB, 2000)';
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case 'right'
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Bscan = linspace(B0 + wB, B0 + Bpad, 2000)';
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otherwise
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error('side must be ''left'' or ''right''');
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end
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% --- Evaluate scattering length over Bscan ---
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aScan = a_of_B(Bscan);
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% --- Filter out any NaNs or extreme values ---
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valid = isfinite(aScan) & abs(aScan) < 1e4;
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Bscan = Bscan(valid);
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aScan = aScan(valid);
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% --- Sort aScan and Bscan by ascending aScan ---
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[aSorted, idx] = sort(aScan);
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BSorted = Bscan(idx);
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% --- Remove duplicates in aSorted for interp1 ---
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[uniqueA, iau] = unique(aSorted);
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uniqueB = BSorted(iau);
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% --- Clip requested a_range to LUT limits ---
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requestedMin = min(a_range);
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requestedMax = max(a_range);
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lutMin = uniqueA(1);
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lutMax = uniqueA(end);
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if requestedMin < lutMin
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warning('Requested a_range min clipped to LUT minimum.');
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requestedMin = lutMin;
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end
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if requestedMax > lutMax
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warning('Requested a_range max clipped to LUT maximum.');
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requestedMax = lutMax;
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end
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% --- Construct linear ramp in a ---
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% Use original order of a_range endpoints to respect increasing or decreasing ramp
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if a_range(1) < a_range(2)
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% ascending ramp
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a_lin = linspace(requestedMin, requestedMax, N_points);
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resonanceB = [B_sub(idx_lo), B_sub(idx_hi)];
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resonancewB = [w_sub(idx_lo), w_sub(idx_hi)];
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else
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% descending ramp
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a_lin = linspace(requestedMax, requestedMin, N_points);
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error('Selected resonance range does not include at least two resonances.');
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end
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end
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end
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% --- Interpolate B from LUT ---
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B_lin = interp1(uniqueA, uniqueB, a_lin, 'pchip');
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% --- Output time and ramp ---
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timeGrid = linspace(0, duration, N_points)';
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B_ramp = B_lin(:);
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a_ramp = a_lin(:);
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% --- Optional plot ---
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if nargin >= 8 && doPlot
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Bvis = linspace(B0 - 20*wB, B0 + 20*wB, 2000);
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avis = a_of_B(Bvis);
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figure;
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plot(Bvis, avis, 'k-', 'DisplayName', 'Full a(B)');
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hold on;
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plot(B_ramp, a_ramp, 'r-', 'LineWidth', 2, 'DisplayName', 'Ramp a(t)');
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xlabel('B (G)');
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ylabel('a ($a_0$)', 'Interpreter', 'latex');
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title(sprintf('Feshbach Resonance #%d at B0=%.3f G (%s side)', resIndex, B0, side), 'Interpreter', 'tex');
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legend('Location','best');
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grid on;
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end
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end
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