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arXiv:2610.01094

Quantum synchronization in atom-cavity coupled systems

Katha Haldar, Anushree Dey, Saikat Ghosh, Bimalendu Deb

quant-phSubmitted Oct 1, 2026• Announced Oct 2, 2026• 0 citations
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Abstract

We consider a cavity quantum electrodynamics (CQED) setup where an ensemble of spin-1 atoms driven by a classical field interacts with two driven cavity field modes. We show that the two sub-systems - the atoms and the two-mode cavity field, exhibit limit-cycle or quantum synchronization depending on the cavity drive strengths and other system parameters. In order to visualize the limit cycle and synchronization in the field, we introduce generalized two-mode field Husimi-Q function using SU(2) coherent states. For atomic spin states, we make use of spin-1 Husimi-Q function to visualize the same. We further corroborate the occurrence of field synchronization and limit cycle by analyzing $U(1)$ symmetry breaking, Wigner quasi-probability distribution, coherence properties of reduced field density matrix. Our results reveal intriguing interplay between the limit-cycle and quantum synchronization behavior, highlighting emergent quantum phenomena in driven dissipative interacting quantum systems. Additionally, we calculate Wehrl mutual information between the two modes and find that the field synchronization and Wehrl mutual information are mutually exclusive. Our study would be important to extract quantum advantages in quantum metrology using coupled atom-cavity systems.

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41 pages 9 figures

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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.