Comment on "Time Crystal in a Single-mode Nonlinear Cavity"

TL;DR

This paper critiques the classification of a driven quantum Van der Pol oscillator as a dissipative time crystal, arguing that its phase is unstable and oscillations are not robust, challenging previous claims in the literature.

Contribution

It clarifies the criteria for what constitutes a time crystal in open quantum systems, specifically challenging the robustness of oscillations in certain models.

Findings

Phase drifts due to dephasing and nonlinearities

Oscillations lack robustness in the quantum regime

Questions the validity of previous time crystal claims

Abstract

I argue that a single driven quantum Van der Pol oscillator should not be considered a dissipative time crystal, contrary to previous claims. In particular, I show that its phase is prone to randomly drift when considering dephasing or additional nonlinearities, and hence its oscillations are not robust in that sense. The arguments I provide are applicable to many other models studied in the literature for which the limit of persistent oscillations coincides with the classical limit. I hope that this comment will spark a discussion about what should or should not be considered a time crystal (at least in the context of open quantum systems) and clarify it to a point.