Fig. 5: Two-level time crystal with dynamic coupling at large NB.
a The time crystals are created at t = 0. Frequencies are plotted in the rotating frame Δω = ω − ω0. b Initially the ground level (black line) is located in the bulk and the excited level (solid green line) at the surface. At t ≈ 3.8 s (vertical dash lines), the ground level moves smoothly to the surface in an avoided crossing. Dotted green line shows a linear interpolation of the excited-state frequency at the crossing. c Most of the population follows the ground level (black line) movement from bulk to surface, identified by a sharp increase in the exponential relaxation rate τ (fitted dash lines and values marked in the figure). Total population is normalised to one at the crossing. d Population oscillations between the time crystals are seen as a side-band of the bulk crystal trace in panel a at frequency ωside band. The side band’s frequency separation from the bulk trace, ∣ωB − ωside band∣ (solid black line), is equal to the frequency separation of the main traces, ∣ωB − ωS∣ (magenta dash line). e The coupling Ω can be extracted from the side band and main trace amplitudes, in good agreement with that estimated by linear interpolation from the separation of the main traces in panel b (horizontal dash line). In this measurement, temperature was 150 μK and ω0/(2π) = 624 kHz.
