Quantum manifestations of converse symmetry breaking

Abstract

Quantum synchronization holds promise in advancing quantum technologies such as sensing, communication, and computation. A key challenge in this rapidly developing field is to identify mechanisms that can promote the emergence of synchronous dynamics. Here, we show that quantum synchronization can be enhanced by introducing controlled heterogeneity in the form of coupling mismatches. Using spin van der Pol oscillators as a model system, we show that this mechanism constitutes a quantum analog of the phenomenon of converse symmetry breaking previously identified in classical oscillator networks, where a synchronous state is stabilized by explicit symmetry breaking. We quantify how quantum effects modify this behavior by tuning the degree of quantumness through variations of the spin quantum number. These findings suggest that quantum synchronization can be enhanced in experiments by harnessing rather than suppressing heterogeneity.

The paper asks whether converse symmetry breaking—stabilization of classical synchronous dynamics by explicitly breaking network symmetry—has a counterpart in quantum synchronization. It studies identical spin van der Pol oscillators with heterogeneous couplings, using the spin quantum number $S\geq1$ to connect quantum and classical regimes. A Lindblad network model combines coherent and dissipative couplings specified by a complex matrix. Its classical limit is derived as coupled Landau–Lifshitz-type equations. For a three-spin network, coupling mismatches $\Delta_n$, constrained by $\sum_n\Delta_n=0$, break cyclic node-permutation symmetry while preserving a classical synchronous solution. Jacobian eigenvalues show that this solution is unstable for homogeneous coupling but becomes stable for suitable mismatches. Quantum calculations evaluate steady-state synchronization through a normalized spin-variance observable, whose unnormalized eigenvalue bounds are $S(N-1)/N$ and $S(S+1)$ for integer $NS$. Exact master-equation simulations, including spins up to $S=8$, find reduced variance under suitable coupling heterogeneity, with the contrast increasing with $S$. Pairwise relative-phase distributions provide a second diagnostic. Unlike the classical network, the quantum examples predominantly exhibit enhanced synchronization between individual pairs rather than simultaneous strong synchronization of all three spins. Larger-spin behavior is explored through approximate Langevin dynamics. This treatment drops higher-order phase-space derivatives, selected diffusion terms, and coupling-dependent noise, and introduces an artificial regularization preventing escape toward a stable polar fixed point. Finite regularization remains in the numerical classical comparison. The study is restricted to small networks; a trapped-ion implementation is outlined rather than demonstrated experimentally.