近日，新加坡南洋理工大学的Yuan Shen与新加坡国立大学的Wai-Keong Mok以及韩国庆北大学的Changsuk Noh等人合作并取得一项新进展。经过不懈努力，他们发现了强非线性诱导的量子同步效应。相关研究成果已于2023年5月23日在国际知名学术期刊《物理评论A》上发表。

据悉，在量子同步中，一个典型的范例是Stuart-Landau振荡器的量子类比，它在非线性很弱（即趋近于零）的情况下对应于van der Pol振荡器。然而，由于这种限制，量子Stuart-Landau振荡器无法捕捉到由非线性引起的有趣现象，例如弛豫振荡。

为了克服这个缺陷，研究人员提出了一种替代模型，将Duffing–van der Pol振荡器近似为具有有限大非线性的形式，同时保持数值计算的可处理性。这使他们能够揭示在深度量子强非线性区域中没有经典类比的一些有趣现象，例如振幅死亡在共振情况下的持续存在。他们还观察到了反应耦合的量子振荡器中非线性诱导的位置相关性。随着非线性的增加，这种耦合振荡呈现出越来越强的相关性，直到达到某个最大值。这种行为在经典情况下是不存在的。此外，他们展示了强非线性如何扩大单个和耦合振荡器之间的同步带宽。这一效应可以用来诱导两个初始处于振幅死亡状态的振荡器之间的互同步现象。

附：英文原文

Title: Quantum synchronization effects induced by strong nonlinearities

Author: Yuan Shen, Wai-Keong Mok, Changsuk Noh, Ai Qun Liu, Leong-Chuan Kwek, Weijun Fan, Andy Chia

Issue&Volume: 2023/05/23

Abstract: A paradigm for quantum synchronization is the quantum analog of the Stuart-Landau oscillator, which corresponds to a van der Pol oscillator in the limit of weak (i.e., vanishingly small) nonlinearity. Due to this limitation, the quantum Stuart-Landau oscillator fails to capture interesting nonlinearity-induced phenomena such as relaxation oscillations. To overcome this deficiency, we propose an alternative model that approximates the Duffing–van der Pol oscillator to finitely large nonlinearities while remaining numerically tractable. This allows us to uncover interesting phenomena in the deep-quantum strongly nonlinear regime with no classical analog, such as the persistence of amplitude death on resonance. We also report nonlinearity-induced position correlations in reactively coupled quantum oscillators. Such coupled oscillations become more and more correlated with increasing nonlinearity before reaching some maximum. Again, this behavior is absent classically. We also show how strong nonlinearity can enlarge the synchronization bandwidth in both single and coupled oscillators. This effect can be harnessed to induce mutual synchronization between two oscillators initially in amplitude death.

DOI: 10.1103/PhysRevA.107.053713

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.053713