Phase synchronization in coupled bistable oscillators

Jessop, M. R.; Li, W.; Armour, A. D.

Abstract

We introduce a simple model system to study synchronization theoretically in quantum oscillators that are not just in limit-cycle states, but rather display a more complex bistable dynamics. Our oscillator model is purely dissipative, with a two-photon gain balanced by single-and three-photon loss processes. When the gain rate is low, loss processes dominate and the oscillator has a very low photon occupation number. In contrast, for large gain rates, the oscillator is driven into a limit-cycle state where photon numbers can become large. The bistability emerges between these limiting cases with a region of coexistence of limit-cycle and low-occupation states. Although an individual oscillator has no preferred phase, when two of them are coupled together a relative phase preference is generated which can indicate synchronization of the dynamics. We find that the form and strength of the relative phase preference varies widely depending on the dynamical states of the oscillators. In the limit-cycle regime, the phase distribution is π-periodic with peaks at 0 and π, whilst in the low-occupation regime π-periodic phase distributions can be produced with peaks at π/2 and 3π/2. Tuning the coupled system between these two regimes reveals a region where the relative phase distribution has π/2-periodicity.

Citation

Jessop, M. R., Li, W., & Armour, A. D. (2020). Phase synchronization in coupled bistable oscillators. Physical Review Research, 2(1), Article 013233. https://doi.org/10.1103/physrevresearch.2.013233

• Journal Article Type: Article
• Acceptance Date: Jan 23, 2020
• Online Publication Date: Feb 28, 2020
• Publication Date: Feb 28, 2020
• Deposit Date: Jan 28, 2020
• Publicly Available Date: Feb 28, 2020
• Journal: Physical Review Research
• Electronic ISSN: 2643-1564
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 2
• Issue: 1
• Article Number: 013233
• DOI: https://doi.org/10.1103/physrevresearch.2.013233
• Public URL: https://nottingham-repository.worktribe.com/output/3821745
• Publisher URL: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.013233