Quantum limit cycles and synchronization from a measurement perspective

TL;DR

This paper investigates quantum limit cycles and synchronization using continuous measurement, revealing their classical-like behavior and linking theoretical measures to experimental observables.

Contribution

It introduces a measurement-based perspective on quantum limit cycles and synchronization, especially in the quantum van der Pol oscillator and two-level systems.

Findings

Quantum trajectories make quantum limit cycles observable.

Quantum synchronization measures relate to heterodyne detection outcomes.

Quantum limit cycles resemble classical ones under noise.

Abstract

Limit-cycle oscillators are the basic building blocks for synchronization; yet, the notion of a quantum limit cycle has remained unclear. Here, we study quantum limit cycles and synchronization in the presence of continuous heterodyne measurement. The resulting quantum trajectories, i.e., time evolutions of the quantum state conditioned on the measurement outcome, make the quantum limit cycles apparent. We focus on the paradigmatic model of the quantum van der Pol oscillator and on two-level systems. Our work provides insights into limit cycles in quantum systems, emphasizing their similarity to classical limit cycles subject to noise. Additionally, we connect theoretical measures of quantum synchronization to quantities experimentally accessible via heterodyne detection.