Fig. 3: Two-level time crystal dynamics at small NB.
a The signal from the pick-up coils, analysed with windowed Fourier transformation (FT), shows the bulk time crystal as a moving sharp peak. Frequency is plotted in the rotating frame Δω = ω − ω0. The excitation pulse at t = 0 is framed out for clarity. Initially ωB < ωS, but as the population in the bulk trap decays, at t = 3.3 s, the global ground state moves to the surface in an avoided crossing. The excited state, now located in the bulk, is simultaneously populated. Rabi (Josephson) population oscillations are seen as a side band. Coupling extracted from the side band extrapolates to Ω/(2π) = 1.7 ± 0.4 Hz at the crossing, in good agreement with the fitted simulation value Ω/(2π) ≈ 1.4 Hz. b The numerical simulation recreates the population transfer and the side band, confirming that the population transfer is due to Landau-Zener transition (analysis in Fig. 4). In the absence of measurement noise also the side band of the surface time trace is weakly visible. c Subtracting the simulation from the experiment shows that the point-wise residuals remain smaller than 5%. The relative difference is normalised by the total signal at the crossing. In this measurement temperature was 180 μK and ω0/(2π) = 833 kHz.
