Relaxation oscillations and frequency entrainment in quantum mechanics

TL;DR

This paper extends the understanding of frequency entrainment in quantum continuous-variable oscillators from weak to arbitrary nonlinearities, revealing quantum relaxation oscillations and their mechanisms.

Contribution

It introduces a framework for quantum frequency entrainment beyond weak nonlinearity, including the emergence of quantum relaxation oscillations.

Findings

Quantum oscillators can exhibit relaxation oscillations in the strong nonlinearity regime.

Two distinct mechanisms for relaxation oscillations are identified in phase space.

The weakly nonlinear steady state is recovered as a special case.

Abstract

Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary nonlinearities. The previously known steady state of such quantum oscillators in the weakly nonlinear regime (also known as a Stuart-Landau oscillator) is shown to emerge as a special case. Most importantly, the hallmark of strong nonlinearity--relaxation oscillations--is shown in quantum mechanics. Depending on the oscillator's nonlinearity, relaxation oscillations are found to occur via two distinct mechanisms in phase space.