Fig. 2: Observation of quantized bubbles.
From: Stirring the false vacuum via interacting quantized bubbles on a 5,564-qubit quantum annealer
a–d, Bubble density measurements at J = 1 and different hz magnitudes, with hx = 0.002 and t = 2 μs (a and b), hx = 0.05 and t = 1 μs (c) and hx = 0.1 and t = 1 μs (d). The bubble sizes of n = 1, 2…6 are seen to be dominant around their respective resonances hz = –2J/n, indicated by the vertical dotted lines. The times shown in b–d were chosen to allow the number of bubbles to grow and limit the impact of thermal effects, whereas 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 chosen values of hx represent the cases in which we observed the most prominent resonant peaks and showcase the point that an increase of two orders of magnitude in hx is required to observe higher-n resonances. In b and c, we probably see more than one resonance at a time due to hz(t) going through multiple n-bubble resonances (hz = –2J/n) as it goes from a positive value to a specific resonance. This means that if we are probing the 3-bubble resonance, for example, we are also crossing the 4-, 5- and 6-bubble resonances beforehand. If we take into account additional thermalization and bubble interaction effects, there is a high likelihood of observing a few higher resonances (n = 4, 5 and 6), alongside n = 3 (for example, in c). The error bars across the entire figure come from counting errors on the annealer and are smaller than the size of the symbols.
