二次耦合驱动量子范德波尔振荡器中的二次谐波相位锁定与同步阻断
Second harmonic phase locking and synchronization blockade in quadratically coupled driven quantum van der Pol oscillators
- Bharathidasan University（巴拉提达桑大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究二次耦合驱动量子范德波尔振荡器的动力学，发现2:1高阶同步、第一个振荡器的同步阻断、第二个振荡器的1:1相位锁定，以及双振荡器满足共振时的相互同步，揭示二次耦合对非经典同步的关键作用。
AI中文摘要：
我们研究了二次耦合系统在施加于第二个振荡器的外部驱动影响下的动力学，其中耦合促成了振荡器间2:1形式的高阶同步与相位锁定。我们的分析揭示了第一个振荡器中存在同步阻断，其特征是常规1:1相位锁定被完全抑制。相比之下，我们观察到直接受驱动的第二个振荡器与驱动实现同步，表现出1:1相位锁定，但显著处于二次谐波频率。对相应运动方程的经典平均场分析重现了这种不对称相位锁定几何，表明相位锁定结构本身可从非线性经典动力学角度理解。然而，量子分析揭示了同步阻断的微观起源。此外，我们证明当两个振荡器均满足共振条件时，系统呈现相互同步，借助非线性二次耦合实现相干能量交换。这种相互同步表现出同步区域，且在共振附近因能量态的谱分裂而出现同步区域的微妙抑制。我们在低激发子空间内对主方程进行微扰分析，结合布居统计与谱响应，分析稳态相位分布与同步度量。我们还提出了在囚禁离子与光机械装置中的可能实验实现方案。这些发现凸显了二次耦合在实现非经典同步现象中的关键作用，为量子控制策略及量子信息平台的开发提供了更深入的见解。
英文摘要：
We investigate the dynamics of a quadratically coupled system under the influence of an external drive applied to the second oscillator, where the coupling facilitates a high-order synchronization with phase-locking emerging in the form of 2:1 between the oscillators. Our analysis reveals a synchronization blockade in the first oscillator, characterized by the complete suppression of conventional 1:1 phase-locking with the drive. In contrast, we observe that the directly driven second oscillator synchronizes with the drive, showing 1:1 phase-locking but notably at second harmonic frequency. A classical mean-field analysis of the corresponding equations of motion reproduces this asymmetric phase-locking geometry which demonstrates that the phase-locking structure itself can be understood from the nonlinear classical dynamics. The quantum analysis, however, reveals the microscopic origin of the synchronization blockade. Furthermore, we show that the system exhibits mutual synchronization when both the oscillators satisfies the resonance condition, enabling coherent energy exchange facilitated by nonlinear quadratic coupling. The mutual synchronization shows synchronized regimes and also subtle suppression of synchronized regimes near resonance occurring due to spectral splitting of the energy states. Using perturbation analysis of the master equation within the low excitation subspace, we analyze steady-state phase distribution and synchronization measures, supported by population statistics and spectral responses. We also propose possible experimental realizations in trapped-ions and optomechanical setups. These findings highlight the crucial role of quadratic coupling in enabling nonclassical synchronization phenomena, offering deeper insights for quantum control strategies and the development of quantum information platforms.
