Microwave-controlled switching of continuous time-crystalline behavior in driven-dissipative Rydberg ensembles

We propose a microwave-controlled interaction switch for driven-dissipative Rydberg ensembles. Through microwave dressing, the effective interaction is continuously reshaped from a short-range form dominated by van der Waals coupling to a longer-range form with an enhanced dipole-exchange contribution. This switch drives stationary-to-oscillatory transitions in both macroscopic thermal gases and two-dimensional (2D) lattices. In the mean-field description of thermal gases, microwave-controlled interaction tuning induces a supercritical Hopf bifurcation from a steady state to a stable limit cycle, giving rise to dissipative continuous time-crystalline behavior. In 2D lattices, where spatial correlations become important, cumulant-expansion calculations show that the same switching mechanism remains effective beyond mean-field theory. Although correlations reduce the classical oscillatory region, they sustain a correlation-modified oscillatory regime and additionally generate an oscillatory regime absent in mean-field theory. These results show that the proposed switch provides a unified route to controlling dissipative oscillatory behavior from thermal Rydberg gases to 2D lattices.