Injection locking of Rydberg dissipative time crystals

Non-equilibrium Rydberg gases exhibit exotic many-body phases stabilized by the interplay of coherent interactions and dissipation. Strong Rydberg interactions drive sustained limit cycle oscillations, whose robustness, long-range temporal order, and spontaneous time-translation symmetry breaking establish a dissipative time crystal (DTC). Collective self-entrainment in driven ensembles leads to global synchronization and a dominant oscillation frequency. Here, injection locking of a Rydberg DTC is demonstrated using a radio-frequency (RF) electric field that gradually pulls the intrinsic oscillation toward the injected frequency. Above a critical threshold, full synchronization occurs, with the locking bandwidth scaling linearly with RF amplitude. This includes synchronization of higher-order harmonics, revealing entrainment of the system's nonlinear temporal dynamics. The phenomenon parallels injection locking in classical nonlinear systems, but emerges here in a strongly interacting quantum medium. This approach establishes a new method for stabilizing and controlling time-crystalline temporal order, with applications in precision sensing, quantum metrology, and timekeeping.