Quantum synchronization at the critical point of Floquet driven Rydberg atoms

The criticality enhanced correlations and susceptibility allow weak periodic driving to induce collective synchronization due to critical slowing down, providing a unique platform to study non-equilibrium order emergence. This establishes a powerful paradigm for investigating non-equilibrium order formation, yet the fundamental mechanisms of critical-point synchronization remain poorly understood. Here, we utilize a microwave pulse as a seed to induce quantum synchronization at the critical point of Floquet driven Rydberg atoms. In the experiment, the microwave periodic driving on Rydberg states acts as a seeded temporal order in subspace, which triggers synchronization across the entire ensemble. The behavior of the emergent synchronized oscillation is elaborately linked to alterations in the seed, such as the relative phase shift and the frequency difference, which result in phase-dependent seeding and embryonic synchronization. This result opens up new possibilities for studying and harnessing time-dependent quantum many-body phenomena, offering insight into the behavior of complex many-body systems under seeding.