Cooperation and Competition in Synchronous Open Quantum Systems

TL;DR

This paper explores how synchronization mechanisms in quantum systems can either cooperate or compete, depending on the system's mode and degeneracy, revealing complex dynamics in quantum thermal machines.

Contribution

It introduces the interplay of entrainment and mutual synchronization in quantum systems, highlighting their dependence on system mode and degeneracy.

Findings

Synchronization persists with increasing degeneracy levels.

Mutual synchronization dominates in the thermodynamic limit.

Mechanisms can either cooperate or compete based on the machine's mode.

Abstract

Synchronization between limit cycle oscillators can arise through entrainment to an external drive or through mutual coupling. The interplay between the two mechanisms has been studied in classical synchronizing systems, but not in quantum systems. Here, we point out that competition and cooperation between the two mechanisms can occur due to phase pulling and phase repulsion in quantum systems. We study their interplay in collectively driven degenerate quantum thermal machines and show that these mechanisms either cooperate or compete depending on the working mode of the machine (refrigerator or engine). The entrainment-mutual synchronization interplay persists with an increase in the number of degenerate levels, while in the thermodynamic limit of degeneracy, mutual synchronization dominates. Overall, our work investigates the effect of degeneracy and multilevel scaling of quantum synchronization and shows how different synchronizing mechanisms can cooperate and compete in quantum systems.