Fig. 1: Conceptualization and experimental realization of a time rondeau crystal.
a, Tree diagram giving an overview of parametrically (meta)stable equilibrium and non-equilibrium quantum phases of matter; tree branches show different types of drive characterized by their spectral decomposition (square boxes) (Methods). The family of RMDs (see also Fig. 2) we implement interpolates between structured random and aperiodic drives (orange frame). A comparison of DTC (green rectangle) and time rondeau crystal (orange rectangle): although both temporal orders show period-doubling dynamics at stroboscopic times, t = MT, the micromotion dynamics of the time rondeau crystal is (tunably) disordered. b, System comprising randomly placed dipolar interacting 13C nuclear spins in a diamond. The dashed lines indicate relevant dipole–dipole interactions. c–e, Example dataset of the experimental observation of rondeau order. Data represent a single-shot measurement of the 13C nuclei polarization projected onto the x axis of its rotating frame. τ = 74.4 μs, N+ = 200, N− = 100, θx = π/2 at γy = 0.98π for a 1-RMD sequence. Figure 2 provides details of the experimental sequence. c, Full 16-s dataset comprising 720 pulses. The 1/e lifetime, Te, exceeds 170 periods, corresponding to 4 s or JTe ≈ 2.6 × 103. d, Zoomed-in view into a window comprising 20 full stroboscopic cycles. The signal flips sign after each full cycle; however, the point within one cycle in which the signal flips is random, clearly indicating the coexistence of long-range temporal order and short-range temporal disorder. e, DFT amplitude for disordered micromotion (brown) and ordered stroboscopic (blue) dynamics; in stark contrast to the δ peak in the stroboscopic dynamics (blue arrow), the micromotion (brown) is almost flat in the entire frequency window of 0 ≤ ν < π with a (linear) suppression for ν→π.
