Fig. 3: Characteristics of rondeau order.

a, Amplitude of DFT of the polarization micromotion dynamics for Floquet DTC (pink) and 2-RMD (blue). In contrast to Floquet DTCs, which feature only a single δ peak, the micromotion of the time rondeau crystal has finite support on the entire frequency spectrum. b, Amplitude of DFT of the 2-RMD sequence (Methods) that generated the data in a. The Fourier amplitudes of the drive and micromotion are mirror images of one another with respect to the ν = π/2 axis (referred to as π shifted). c, Fourier amplitudes for RMD sequences n = 0, 1 and 2 on a log–log scale; the Floquet data point would appear at (π − ν) = 0 and is, thus, not shown. The dashed lines are linear fits to the data with slopes α₀ = (0 ± 0.1), α₁ = (1.0 ± 0.1) and α₂ = (1.9 ± 0.1) for n = 0, 1 and 2, respectively. The different multipole orders show distinctive high-frequency suppression, in good agreement with the theoretical predictions (α_n = n). The RMD data point represents the mean over 20 realizations of the random drive; error bars indicate the standard deviation; all datasets are normalized by the same normalization constant, here chosen as the maximum value of the n = 2 Fourier amplitude; we set ε = 0.03π; and the other parameters are the same as those in Fig. 1.