Emergent synchronization mode in coupled Rydberg atomic chains

We report an oscillatory form in the two coupled dissipative Rydberg atomic chains by modulating its spacing. Such oscillation has $\ensuremath{\pi}$-phase difference between two neighboring sites, which distinguishes it from antiferromagnetic-type synchronization in the previous studies. Theoretically, we find a phase with two coexisting types of continuous time crystals and recognize that the transition belongs to Hopf and pitchfork bifurcation. Furthermore, we generalize the conclusion to multiple chains and verify the uniqueness of the synchronization mode. We also discuss its experimental feasibility.