Discrete time crystal in a finite chain of Rydberg atoms without disorder

We study the collective dynamics of a clean Floquet system of cold atoms, numerically simulating two realistic set-ups based on a regular chain of interacting Rydberg atoms driven by laser fields. In both cases, the population evolution and its Fourier spectrum display clear signatures of a discrete time crystal (DTC), exhibiting the appearance of a robust subharmonic oscillation which persists on a time scale increasing with the chain size, within a certain range of control parameters. We also characterize how the DTC stability is affected by dissipative processes, typically present in this atomic system even though the Rydberg state is very long lived.