Spontaneous Macroscopic Quantum Synchronization in an Ensemble of Two-level Systems
arXiv:2511.10920
Abstract
Spontaneous macroscopic quantum synchronization is an emergent phenomenon where an ensemble of quantum oscillators achieves global phase coherence through the interplay of interaction and dissipation. To illuminate this phenomenon, we study an ensemble of two-level systems (TLS) and establish its associated nonlinear quantum master equation, for which self-consistent analytical solutions of quantum synchronization can be obtained. The trajectories on the Bloch sphere vividly illustrate how dissipation and interaction drive the system toward a synchronized state. We present a phase diagram for macroscopic synchronization as a function of interaction strength and the gain-to-damping ratio. Furthermore, we demonstrate full synchronization and partial synchronization between two groups of TLS with different natural frequencies. This work establishes ensemble of TLS as a remarkable system for understanding spontaneous quantum synchronization.
The interaction in Eq. (7) lacks permutation symmetry, as it explicitly depends on particle indices. Thus, Eq. (9) does not correspond to this model. Although the analysis is mathematically self-consistent, it mismatches the physical dynamics. To avoid confusion regarding the model's physical interpretation, we are withdrawing the manuscript