Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators

TL;DR

This paper develops a semiclassical phase reduction approach to optimize entrainment stability and phase coherence in weakly forced quantum oscillators, demonstrating improved stability with tailored waveforms.

Contribution

It introduces a method to optimize periodic waveforms for quantum oscillators using classical optimization techniques applied to semiclassical phase equations.

Findings

Optimized waveforms improve entrainment stability over sinusoidal drives.

Phase coherence optimization shows minimal improvement.

Numerical analysis confirms the effectiveness of the optimization.

Abstract

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, 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.