Bubble density measurements at J = 1 and different hz magnitudes, with hx = 0.002 and t = 2 s. The bubble sizes of n = 1, 2...6 are seen to be dominant around their respective resonances hz = –2 J / n , indicated by the vertical dotted lines. The data in a were intentionally sampled at a time after the hz ( t ) modulation stops, marking the onset of thermalization. The non-monotonic 1-bubble density curve is due to faster thermalization at the resonance compared with the surrounding hz values. The error bars across the entire figure come from counting errors on the annealer and are smaller than the size of the symbols.