Kato Yuzuru, Nakao Hiroya
Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan.
Phys Rev E. 2020 Jan;101(1-1):012210. doi: 10.1103/PhysRevE.101.012210.
Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase-reduction theory recently developed for quantum nonlinear oscillators [Y. Kato, N. Yamamoto, and H. Nakao, Phys. Rev. Res. 1, 033012 (2019)10.1103/PhysRevResearch.1.033012], two types of optimization problems, one for the stability and the other for the phase coherence of the entrained state, are considered. The optimal waveforms of the periodic amplitude modulation can be derived by applying the classical optimization methods to the semiclassical phase equation that approximately describes the quantum limit-cycle dynamics. Using a quantum van der Pol oscillator with squeezing and Kerr effects as an example, the performance of optimization is numerically analyzed. It is shown that the optimized waveform for the entrainment stability yields faster entrainment to the driving signal than the case with a simple sinusoidal waveform, while that for the phase coherence yields little improvement from the sinusoidal case. These results are explained from the properties of the phase sensitivity function.
在半经典区域研究了量子非线性振荡器对周期性调制弱谐波驱动的最佳同步。通过使用最近为量子非线性振荡器开发的半经典相位约化理论[Y. Kato, N. Yamamoto, and H. Nakao, Phys. Rev. Res. 1, 033012 (2019)10.1103/PhysRevResearch.1.033012]，考虑了两类优化问题，一类用于同步态的稳定性，另一类用于同步态的相位相干性。通过将经典优化方法应用于近似描述量子极限环动力学的半经典相位方程，可以导出周期性幅度调制的最佳波形。以具有压缩和克尔效应的量子范德波尔振荡器为例，对优化性能进行了数值分析。结果表明，与简单正弦波形的情况相比，用于同步稳定性的优化波形能更快地同步到驱动信号，而用于相位相干性的优化波形与正弦波形情况相比几乎没有改善。这些结果从相位灵敏度函数的性质得到了解释。
