Multipartite quantum synchronization in driven-dissipative spin networks

Abstract

Traditional studies of quantum synchronization in finite-dimensional spin systems usually focus on entrainment of a single spin to an external drive, leaving mutual synchronization among multiple spins poorly understood. We investigate mutual quantum synchronization across bipartite and tripartite spin architectures in a driven-dissipative cavity-coupled quantum Rabi network in the dispersive adiabatic regime. Inspired by the Kuramoto model of classical phase synchronization, we introduce a phase-space measure of quantum synchronization using the first angular moments of Husimi-Q phase distributions. To compare the collective phase localization with reduced-subsystem contributions and local individual phase locking, we construct a bipartite and tripartite synchronization gap. For two spins, the steady-state synchronization gap is negative. This reflects that the relative phase is localized more strongly than the individual spin phases can account for, signaling mutual synchronization beyond independent entrainment by the drive. For three spins in a triangular network, the synchronization gap is positive in the parameter regime studied, i.e., the collective three-body localization is bounded by the pairwise measures. Our results underscore that quantum phase synchronization strongly depends upon network topology and establish the phase-sensitive synchronization gaps as an effective diagnostic for multipartite phase correlations in open quantum systems.