论文标题
量子渐近阶段揭示了量子同步的特征
Quantum asymptotic phase reveals signatures of quantum synchronization
论文作者
论文摘要
量子非线性振荡器的同步最近引起了很多关注。为了表征量子振荡动力学，我们最近提出了对渐近阶段的完全量子力学定义，这是经典非线性振荡器的同步分析中的关键量（Kato和Nakao 2022 Chaos 32 Chaos 32 063133）。在这项工作中，我们进一步扩展了这一理论，并使用与不同基本频率相关的量子非线性振荡器的Liouville超级操作机的邻接eigototic阶段引入了多个渐近阶段。我们在强量量子状态下分析了具有KERR效应的量子范围振荡器，并表明该系统具有几种不同的基本频率。通过根据相关的量渐近阶段引入顺序参数和功率谱，我们揭示了系统在几个不同频率下使用谐波驱动器的相位锁定，仅在强量量子状态下观察到的显式量子签名，可以将其解释为在圆环上同步而不是简单的限制周期。
Synchronization of quantum nonlinear oscillators has attracted much attention recently. To characterize the quantum oscillatory dynamics, we recently proposed a fully quantum-mechanical definition of the asymptotic phase, which is a key quantity in the synchronization analysis of classical nonlinear oscillators (Kato and Nakao 2022 Chaos 32 063133). In this work, we further extend this theory and introduce multiple asymptotic phases using the eigenoperators of the adjoint Liouville superoperator of the quantum nonlinear oscillator associated with different fundamental frequencies. We analyze a quantum van der Pol oscillator with Kerr effect in the strong quantum regime and show that the system has several different fundamental frequencies. By introducing order parameters and power spectra in terms of the associated quantum asymptotic phases, we reveal that phase locking of the system with a harmonic drive at several different frequencies, an explicit quantum signature observed only in the strong quantum regime, can be interpreted as synchronization on a torus rather than a simple limit cycle.
