量子渐近相位揭示了量子同步的特征
Quantum asymptotic phase reveals signatures of quantum synchronization
摘要：
近年来，量子非线性振子的同步问题引起了人们的广泛关注。为了表征量子振荡动力学，我们最近提出了一个完全量子力学定义的渐近相位，这是一个关键的数量在经典的非线性振荡器的同步分析（加藤和中尾2022混沌32 063133）。在本工作中，我们进一步扩展了这一理论，并引入了多个渐近相位使用的伴随Liouville超算子的量子非线性谐振子的本征算符与不同的基频。在强量子区分析了具有克尔效应的量子范德波尔振子，指出该系统具有几个不同的基频。通过引入序参量和功率谱的相关量子渐近相位，我们揭示了相位锁定的系统与谐波驱动在几个不同的频率，一个明确的量子签名观察到的强量子制度，可以被解释为一个环面上的同步，而不是一个简单的极限环。
英文摘要：
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.
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