FR_choice = 1; ABKG_choice = 1; a_start = 86; % initial scattering length (a_0) a_end = 85; % final scattering length (a_0) T = 0.030; % ramp duration (s) Nt = 1000; % number of time points ResonanceRange = [1.2, 2.6]; % Options for ramp generation options = struct( ... 'smoothingMethod', 'sgolay', ... % 'sgolay', 'lowpass', or 'none' 'sgolayOrder', 3, ... 'sgolayFrameLength', 51, ... 'maxRampRate', 5, ... 'Bmin', 0.5, ... 'Bmax', 3.5, ... 'rampShape', 'linear' ... % Choose: 'linear', 'exponential', 'sigmoid' ); [t, B_ramp, a_check] = generateSmoothBRamp(FR_choice, ABKG_choice, a_start, a_end, ResonanceRange, T, Nt, options); % ----- Plot results ----- figure(1); clf subplot(2,1,1); plot(t, B_ramp, 'b-', 'LineWidth', 2); xlabel('Time (s)'); ylabel('Magnetic field B(t) (G)'); title('Generated magnetic field ramp B(t)'); grid on; set(gca, 'FontSize', 14); subplot(2,1,2); plot(t, a_check, 'r-', 'LineWidth', 2); xlabel('Time (s)'); ylabel('Scattering length a_s(t) (a_0)'); legend('Resulting a_s(t)'); title('Scattering length ramp'); grid on; set(gca, 'FontSize', 14); % Visualize full resonance curve and selected window [B_full, a_full] = extractBetweenResonances(FR_choice, ABKG_choice, ResonanceRange); [B_curve, a_curve] = fullResonanceCurve(FR_choice, ABKG_choice, ResonanceRange); figure(2); clf plot(B_curve, a_curve, 'k-', 'LineWidth', 1); hold on; plot(B_full, a_full, 'b-', 'LineWidth', 2); % zoomed-in region plot(B_ramp, a_check, 'r-', 'LineWidth', 2); % actual ramp plot(B_ramp([1 end]), a_check([1 end]), 'ro', 'MarkerSize', 8); % endpoints xline(min(B_ramp), '--b', 'B_{min}'); xline(max(B_ramp), '--b', 'B_{max}'); yline(min(a_check), '--r', 'a_{min}'); yline(max(a_check), '--r', 'a_{max}'); xlabel('B field (G)'); ylabel('Scattering length a_s (a_0)'); title('Feshbach spectrum with selected B and a_s range', 'Interpreter','tex'); legend('Full a(B)', 'Zoomed Region', 'Ramp a_s(t)', 'Ramp Endpoints', 'Location', 'NorthWest'); ylim([0 150]) set(gca, 'FontSize', 14) grid on; %% Helper functions function [t, B_ramp, a_check] = generateSmoothBRamp(FR_choice, ABKG_choice, a_start, a_end, selectedResRange, T, Nt, opts) % Time array t = linspace(0, T, Nt); if strcmp(opts.rampShape, 'linear') % Directly call helper for linear LUT ramp generation [t, B_ramp, a_check] = generateLinearBRampUsingLUT(FR_choice, ABKG_choice, a_start, a_end, selectedResRange, T, Nt); return end % Get target a_s(t) based on rampShape choice a_target = getTargetScatteringLength(t, T, a_start, a_end, opts.rampShape); % --- a(B) interpolation --- [B_between, a_between] = extractBetweenResonances(FR_choice, ABKG_choice, selectedResRange); valid_idx = a_between > 0 & a_between < 150; [a_sorted, sort_idx] = sort(a_between(valid_idx)); B_sorted = B_between(valid_idx); B_sorted = B_sorted(sort_idx); B_of_a = @(a) interp1(a_sorted, B_sorted, a, 'linear', 'extrap'); B_raw = B_of_a(a_target); % --- Smoothing --- switch opts.smoothingMethod case 'sgolay' B_smooth = sgolayfilt(B_raw, opts.sgolayOrder, opts.sgolayFrameLength); case 'lowpass' dt = T / (Nt - 1); Fs = 1 / dt; B_smooth = lowpass(B_raw, Fs / 20, Fs); case 'none' B_smooth = B_raw; otherwise error('Unknown smoothing method'); end % --- Bound the ramp --- B_smooth = min(max(B_smooth, opts.Bmin), opts.Bmax); % --- Enforce max dB/dt --- dt = T / (Nt - 1); for i = 2:Nt delta = B_smooth(i) - B_smooth(i-1); if abs(delta/dt) > opts.maxRampRate delta = sign(delta) * opts.maxRampRate * dt; B_smooth(i) = B_smooth(i-1) + delta; end end B_ramp = B_smooth; % --- Verify a_s(t) from B_ramp --- [a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_choice, selectedResRange); a_of_B = @(B) arrayfun(@(b) ... a_bkg * prod(1 - resonancewB ./ (b - resonanceB)), B); a_check = a_of_B(B_ramp); end function a_target = getTargetScatteringLength(t, T, a_start, a_end, rampShape) % If rampShape is a function handle, use it directly (for flexibility) if isa(rampShape, 'function_handle') a_target = rampShape(t); return end switch lower(rampShape) case 'exponential' tau = T / 3; base = (1 - exp(-t / tau)) / (1 - exp(-T / tau)); a_target = a_start + (a_end - a_start) * base; case 'sigmoid' s = 10 / T; center = T / 2; sigmoid = @(x) 1 ./ (1 + exp(-s * (x - center))); base = (sigmoid(t) - sigmoid(t(1))) / (sigmoid(t(end)) - sigmoid(t(1))); a_target = a_start + (a_end - a_start) * base; otherwise error('Unknown ramp shape: %s', rampShape); end end function [B_between, a_between] = extractBetweenResonances(FR_choice, ABKG_choice, selectedRange) [a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_choice, selectedRange); [~, idx] = sort(resonancewB, 'descend'); B1 = resonanceB(idx(1)); B2 = resonanceB(idx(2)); w1 = resonancewB(idx(1)); w2 = resonancewB(idx(2)); Bvis = linspace(min(B1, B2) - 20*min(w1,w2), max(B1, B2) + 20*min(w1,w2), 2000); a_of_B = @(B) arrayfun(@(b) ... a_bkg * prod(1 - resonancewB ./ (b - resonanceB)), B); avis = a_of_B(Bvis); between_idx = Bvis >= min(B1,B2) & Bvis <= max(B1,B2); B_between = Bvis(between_idx); a_between = avis(between_idx); end function [B_range, a_values] = fullResonanceCurve(FR_choice, ABKG_choice, selectedRange) [a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_choice, selectedRange); B_range = linspace(min(resonanceB)-0.2, max(resonanceB)+0.2, 3000); a_of_B = @(B) arrayfun(@(b) ... a_bkg * prod(1 - resonancewB ./ (b - resonanceB)), B); a_values = a_of_B(B_range); end function [a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_choice, selectedRange) if FR_choice == 1 a_bkg_list = [85.5, 93.5, 77.5]; resonanceB = [1.295, 1.306, 2.174, 2.336, 2.591, 2.740, 2.803, ... 2.780, 3.357, 4.949, 5.083, 7.172, 7.204, 7.134, 76.9]; resonancewB = [0.009, 0.010, 0.0005, 0.0005, 0.001, 0.0005, 0.021, ... 0.015, 0.043, 0.0005, 0.130, 0.024, 0.0005, 0.036, 3.1]; else a_bkg_list = [87.2, 95.2, 79.2]; resonanceB = [1.298, 2.802, 3.370, 5.092, 7.154, 2.592, 2.338, 2.177]; resonancewB = [0.018, 0.047, 0.048, 0.145, 0.020, 0.008, 0.001, 0.001]; end a_bkg = a_bkg_list(ABKG_choice); % --- Filter resonanceB and resonancewB if selectedRange is provided --- if nargin >= 3 && ~isempty(selectedRange) minB = min(selectedRange); maxB = max(selectedRange); keep_idx = (resonanceB >= minB) & (resonanceB <= maxB); % Keep only the lowest and highest resonance in the selected range if sum(keep_idx) >= 2 B_sub = resonanceB(keep_idx); w_sub = resonancewB(keep_idx); [~, idx_lo] = min(B_sub); [~, idx_hi] = max(B_sub); resonanceB = [B_sub(idx_lo), B_sub(idx_hi)]; resonancewB = [w_sub(idx_lo), w_sub(idx_hi)]; else error('Selected resonance range does not include at least two resonances.'); end end end function [t, B_ramp, a_check] = generateLinearBRampUsingLUT(FR_choice, ABKG_choice, a_start, a_end, selectedResRange, T, Nt) % Time vector t = linspace(0, T, Nt); % 1) Generate LUT of B and a_s(B) [B_between, a_between] = extractBetweenResonances(FR_choice, ABKG_choice, selectedResRange); % Restrict to physically meaningful range (optional) valid_idx = a_between > 0 & a_between < 150; B_lut = B_between(valid_idx); a_lut = a_between(valid_idx); % 2) Generate linear a_s ramp in time a_target = linspace(a_start, a_end, Nt); % 3) Interpolate B(t) from LUT a_s -> B % Make sure a_lut is sorted ascending [a_lut_sorted, idx_sort] = sort(a_lut); B_lut_sorted = B_lut(idx_sort); B_ramp = interp1(a_lut_sorted, B_lut_sorted, a_target, 'linear', 'extrap'); % 4) Compute resulting a_s(t) for verification [a_bkg, resonanceB, resonancewB] = getResonanceParams(FR_choice, ABKG_choice, selectedResRange); a_of_B = @(B) arrayfun(@(b) ... a_bkg * prod(1 - resonancewB ./ (b - resonanceB)), B); a_check = a_of_B(B_ramp); end