Phase synchronization in coupled bistable oscillators
Phase synchronization in coupled bistable oscillators
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DOI：
10.1103/physrevresearch.2.013233
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发表时间：
2019-06
影响因子：
4.2
通讯作者：
M. R. Jessop;Weibin Li;A. Armour
中科院分区：
文献类型：
--
作者：
M. R. Jessop;Weibin Li;A. Armour
我们引入一个简单的模型系统来研究量子振荡器的同步理论，这些振荡器不仅处于极限环状态，而且显示出更复杂的量子动力学。我们的振荡器模型是纯粹的耗散，与单光子和三光子损失过程平衡的双光子增益。当增益率较低时，损耗过程占主导地位，并且振荡器具有非常低的光子占用数。相反，对于大的增益率，振荡器被驱动到光子数可以变得很大的极限环状态。双稳态出现在这些极限情况之间的极限环和低占领状态共存的区域。虽然单个振荡器没有优选的相位，但是当它们中的两个耦合在一起时，产生相对相位偏好，这可以指示动态的同步。我们发现，相对相位偏好的形式和强度变化很大，这取决于振子的动力学状态。在极限环制度，相位分布是$\pi$-周期性的峰值在$0$和$\pi$，而在低占用制度$\pi$-周期性相位分布可以产生峰值在$\pi/2$和$3\pi/2$。调谐这两个制度之间的耦合系统揭示了一个区域的相对相位分布有$\pi/2$-周期性。
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 $\pi$-periodic with peaks at $0$ and $\pi$, whilst in the low-occupation regime $\pi$-periodic phase distributions can be produced with peaks at $\pi/2$ and $3\pi/2$. Tuning the coupled system between these two regimes reveals a region where the relative phase distribution has $\pi/2$-periodicity.