Kerr诱导的驱动van der Pol振子中同步与量子态恢复的控制

中文摘要 AI 辅助

我们研究了Kerr非线性如何改变压缩量子van der Pol振子中的量子同步。我们表明，Kerr相互作用产生一个振幅依赖的频率偏移，驱动鞍结分岔，将经典相空间结构从双稳态转变为单稳态动力学。在量子区域，这种转变表现为系统的频率牵引和谱展宽，而稳态Wigner函数揭示了量子态与半经典吸引子之间的连续对应关系，尽管存在有限的量子涨落。通过构建压缩-Kerr参数空间中的全局同步相图，我们发现维持相位锁定所需的临界压缩强度对Kerr非线性具有显著线性依赖。我们进一步证明，同步边界与超泊松和亚泊松光子统计之间的交叉不一致，表明同步和光子数统计表征了量子稳态的不同方面。这些结果为通过Kerr非线性控制量子同步提供了定量设计原则，并可能对捕获离子、超导电路和光机械平台具有潜在相关性。

英文摘要

We investigate how Kerr nonlinearity modifies quantum synchronization in a squeezed quantum van der Pol oscillator. We show that the Kerr interaction produces an amplitude-dependent frequency shift that drives a saddle-node bifurcation, transforming the classical phase-space structure from bistable to monostable dynamics. In the quantum regime, this transition manifests as systematic frequency pulling and spectral broadening, while the steady-state Wigner function reveals a continuous correspondence between the quantum state and the semiclassical attractor despite finite quantum fluctuations. By constructing global synchronization phase diagrams in the squeezing--Kerr parameter space, we uncover a remarkably linear dependence of the critical squeezing strength required to maintain phase locking on the Kerr nonlinearity. We further demonstrate that the synchronization boundary does not coincide with the crossover between super- and sub-Poissonian photon statistics, showing that synchronization and photon-number statistics characterize distinct aspects of the quantum steady state. These results provide quantitative design principles for controlling quantum synchronization through Kerr nonlinearity, with potential relevance to trapped-ion, superconducting-circuit, and optomechanical platforms.

发表机构

• University of Guilan（吉兰大学）
• Sirjan University of Technology（锡尔詹理工大学）

机构由 AI 辅助整理，请以论文原文为准。