431 lines
15 KiB
Matlab
431 lines
15 KiB
Matlab
FR_choice = 1;
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ABKG_choice = 1;
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% Get the full spectrum
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[B, a_s] = getFullFeschbachSpectrum(FR_choice, ABKG_choice);
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% Define the plotting range
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x_limits = [1.15, 2.7];
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y_limits = [0, 150];
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% Find indices within our x-range
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mask = (B >= x_limits(1)) & (B <= x_limits(2));
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B_plot = B(mask);
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a_s_plot = a_s(mask);
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% Identify resonances to mask (looking at the spectrum, we'll mask around 2.174G and 2.336G)
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resonances_to_mask = [2.174, 2.336];
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mask_width = 0.1; % Width to mask around each resonance (in G)
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% Create a mask for the regions to keep (1 = keep, 0 = mask)
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keep_mask = true(size(B_plot));
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for res = resonances_to_mask
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keep_mask = keep_mask & (B_plot < (res - mask_width) | B_plot > (res + mask_width));
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end
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% Create masked version
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B_masked = B_plot(keep_mask);
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a_s_masked = a_s_plot(keep_mask);
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% Interpolate over the masked regions
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a_s_interp = interp1(B_masked, a_s_masked, B_plot, 'pchip');
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% --- Find the remaining resonances (peaks) in the interpolated data ---
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% Use findpeaks to detect peaks (adjust MinPeakProminence as needed)
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[peaks, locs] = findpeaks(abs(a_s_interp), 'MinPeakProminence', 20); % Tune this!
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remaining_resonances = B_plot(locs); % Positions of remaining resonances
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% --- Select the two resonances of interest (1.3G and 2.59G) ---
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% If automatic detection fails, manually define them:
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target_resonances = [1.3, 2.59]; % Manually specified (adjust as needed)
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% OR use the closest detected resonances:
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% target_resonances = remaining_resonances(abs(remaining_resonances - 1.3) < 0.2 & abs(remaining_resonances - 2.59) < 0.2);
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% --- Extract the curve BETWEEN these two resonances ---
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res1 = min(target_resonances); % Lower resonance (1.3G)
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res2 = max(target_resonances); % Upper resonance (2.59G)
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between_mask = (B_plot > res1) & (B_plot < res2); % No masking here, since resonances are already removed
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B_between = B_plot(between_mask);
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a_s_between = a_s_interp(between_mask);
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% --- Plotting ---
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figure(1);
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set(gcf,'Position',[100 100 950 750])
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set(gca,'FontSize',16,'Box','On','Linewidth',2);
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hold on;
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% Plot the interpolated spectrum (without 2.174G and 2.336G)
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plot(B_plot, a_s_interp, 'k-', 'LineWidth', 1, 'DisplayName', 'Interpolated spectrum');
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% Highlight the region between 1.3G and 2.59G
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plot(B_between, a_s_between, 'm-', 'LineWidth', 2, 'DisplayName', 'Between 1.3G and 2.59G');
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% Formatting
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xlim(x_limits);
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ylim([0, 150]);
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xlabel('Magnetic Field (G)');
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ylabel('Scattering Length (a_0)');
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title('Interpolated Spectrum: Region Between 1.3G and 2.59G');
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legend('Location', 'southeast');
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grid on;
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hold off;
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%%
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% Load data
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FSData = load('20260605_ALSData.mat');
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x = FSData.data(:,1);
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y = FSData.data(:,2) * 166 * 1E-5;
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y_err = FSData.data(:,3) * 166 * 1E-5;
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% --- Plotting ---
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figure(2); clf;
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set(gcf,'Position',[100 100 950 750])
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set(gca,'FontSize',16,'Box','On','Linewidth',2);
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hold on;
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% Plot data with error bars, no connecting lines (only points)
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errorbar(x, y, y_err, 'ko', ...
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'MarkerFaceColor', 'r', ... % Filled black circles
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'MarkerSize', 6, ... % Size of data points
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'LineStyle', 'none', ... % No connecting line
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'LineWidth', 1.5, ... % Width of error bars
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'DisplayName', 'As measured with ALS on a cold thermal cloud');
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% Formatting
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xlabel('Magnetic Field (G)');
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ylabel('Atom Number');
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legend('Location', 'southeast');
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grid on;
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box on;
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hold off;
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%% Combined plot
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figure(3); clf;
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set(gcf, 'Position', [100, 100, 950, 750]);
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set(gca, 'FontSize', 16, 'Box', 'On', 'LineWidth', 2);
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hold on;
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% ========== Define Shaded Regions ==========
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% Format: [x_start, x_end, label]
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regions = [
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2.45, 2.52, "BEC";
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2.35, 2.45, "SSD/SS";
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2.1, 2.35, "ID/IS";
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1.4, 2.1, "TBD"
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];
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% Colors for each region (semi-transparent)
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region_colors = [
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0.85, 0.9, 1.0; % light blue
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0.9, 1.0, 0.85; % light green
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1.0, 0.9, 0.85; % light red
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0.95, 0.95, 0.95 % light gray
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];
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ylims = [0, 150]; % Adjust as needed
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for i = 1:size(regions,1)
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x1 = str2double(regions(i,1));
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x2 = str2double(regions(i,2));
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label = string(regions(i,3));
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fill([x1 x2 x2 x1], [ylims(1) ylims(1) ylims(2) ylims(2)], ...
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region_colors(i,:), ...
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'FaceAlpha', 0.9, 'EdgeColor', 'none', 'HandleVisibility', 'off');
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text((x1 + x2)/2, mean(ylims), label, ...
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'HorizontalAlignment', 'center', ...
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'VerticalAlignment', 'middle', ...
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'FontSize', 14, 'FontWeight', 'bold', ...
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'Rotation', 90); % Vertical orientation
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end
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% ========== LEFT Y-AXIS ==========
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yyaxis left
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plot(B_plot, a_s_interp, 'k-', 'LineWidth', 1.5, 'DisplayName', 'Interpolated Dy-164 Feshbach spectrum');
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plot(B_between, a_s_between, 'm-', 'LineWidth', 2.5, 'DisplayName', 'Region between 1.3G and 2.59G');
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ylabel('Scattering Length (a_0)');
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ylim(ylims);
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% ========== RIGHT Y-AXIS ==========
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yyaxis right
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ax = gca;
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ax.YColor = [0.75 0 0]; % Make right y-axis red to match data points
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FSData = load('20260605_ALSData.mat');
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x = FSData.data(:,1);
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y = FSData.data(:,2) * 166 * 1E-5;
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y_err = FSData.data(:,3) * 166 * 1E-5;
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errorbar(x, y, y_err, 'ko', ...
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'MarkerFaceColor', 'r', ...
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'MarkerSize', 6, ...
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'LineStyle', 'none', ...
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'LineWidth', 1.5, ...
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'DisplayName', 'As measured with ALS on a cold thermal cloud');
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ylabel('Atom Number');
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% ========== Shared Formatting ==========
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xlabel('Magnetic Field (G)');
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xlim([1.15, 2.7]);
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grid on;
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legend('Location', 'southeast');
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title('BEC-SSD/SS-ID/IS Regimes');
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hold off;
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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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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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% 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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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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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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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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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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% 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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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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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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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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function [B, a_s] = getFullFeschbachSpectrum(FR_choice, ABKG_choice)
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% plotScatteringLength(FR_choice, ABKG_choice)
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% Plots the Dy-164 scattering length vs B field based on PhysRevX.9.021012 Suppl. Fig. S5
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%
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% Inputs:
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% FR_choice: 1 = new resonance parameters, 2 = old
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% ABKG_choice: 1 = lower a_bkg, 2 = mid, 3 = upper
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%
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% Example:
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% plotScatteringLength(1, 1);
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if nargin < 1, FR_choice = 1; end
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if nargin < 2, ABKG_choice = 1; end
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% Choose background scattering length
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if FR_choice == 1 % New values
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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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end
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% Resonance positions (G) and widths (G)
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resonanceB = [1.295, 1.306, 2.174, 2.336, 2.591, 2.740, 2.803, 2.780, ...
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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, 0.0010, 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 % Old values
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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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end
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% Resonance positions (G) and widths (G)
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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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% Magnetic field range for plotting (G)
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B = linspace(0.5, 8, 2000);
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% Compute scattering length using product formula
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a_s = a_bkg * ones(size(B));
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for j = 1:length(resonanceB)
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a_s = a_s .* (1 - resonancewB(j) ./ (B - resonanceB(j)));
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end
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end
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function [t, B_ramp, a_check] = generateLinearBRamp(B_between, a_s_between, a_start, a_end, T, Nt)
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% Generates a B-field ramp (B_ramp) to produce a linear a_s ramp from a_start to a_end.
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% Uses precomputed LUT: B_between (magnetic field) and a_s_between (scattering length).
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%
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% Inputs:
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% B_between - Magnetic field values (G) between resonances [vector]
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% a_s_between - Corresponding scattering lengths (a_0) [vector]
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% a_start, a_end - Target scattering length range (a_0)
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% T - Total ramp time (s)
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% Nt - Number of time steps
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%
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% Outputs:
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% t - Time vector (s)
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% B_ramp - Generated B-field ramp (G)
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% a_check - Verified a_s(t) using interpolation (a_0)
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% --- 1. Time vector ---
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t = linspace(0, T, Nt);
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% --- 2. Ensure LUT is sorted and unique ---
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[a_s_sorted, sort_idx] = unique(a_s_between); % Remove duplicates and sort
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B_sorted = B_between(sort_idx);
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% --- 3. Generate target linear a_s ramp ---
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a_target = linspace(a_start, a_end, Nt);
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% --- 4. Interpolate B(t) from a_s -> B ---
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B_ramp = interp1(a_s_sorted, B_sorted, a_target, 'pchip', 'extrap');
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% --- 5. Verify a_s(t) by re-interpolating ---
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a_check = interp1(B_sorted, a_s_sorted, B_ramp, 'pchip');
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end
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