Synchronization and Asynchronization in Non-Hermitian Systems

Synchronization and asynchronization are ubiquitous occurrences in a wide range of natural and artificial systems. The underlying mechanisms responsible for these events are typically complex, presenting a considerable difficulty to grasp the crucial elements that cause synchronization or asynchronization. Moreover, real-world systems frequently encounter energy exchanges with their surrounding environment, synchronization and asynchronization in such non-Hermitian systems have not been fully understood. In this work, we study the synchronization and asynchronization phenomena in a simple non-Hermitian system that involves two coupled bosonic modes. We find that such an open system evolves towards a state of lower dissipation as it synchronizes, whereby the existence of particular symmetries, such as anti-parity-time (anti-𝒫𝒯) symmetry and 𝒫𝒯 symmetry, impact synchronization. Peculiarly, we show that when the anti-𝒫𝒯 symmetry is broken or the 𝒫𝒯 symmetry is unbroken, a state of asynchronization occurs as the result of the degeneracy of imaginary parts of the eigenvalues. We designate this occurrence as 'degeneracy-induced asynchronization'. Our findings shed light on generating and controlling synchronization and asynchronization in non-Hermitian systems.