Environment-induced synchronization of two quantum oscillators

TL;DR

This paper demonstrates that two quantum harmonic oscillators can spontaneously synchronize their phases when strongly coupled to a common environment at zero temperature, revealing a quantum analog of classical synchronization.

Contribution

It provides a theoretical analysis of environment-induced quantum synchronization using an exact master equation and uncovers new dynamical regimes including long-lived oscillations.

Findings

Synchronization occurs at strong coupling to the environment.

Reduced damping and frequency locking are observed.

A regime with long-lived oscillations emerges.

Abstract

Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously when they are strongly coupled to a common bosonic quantum dissipative environment at zero temperature, in the absence of any driving mechanism. To do so, we compute the dynamics of the oscillators with an exact master equation obtained from a path integral formalism. Above some value of the system-environment coupling strength, we observe numerically a strongly reduced damping and a frequency locking in the dynamics of the oscillators. Beyond the synchronization mechanism, we also describe the rich phenomenology of the dynamics in the model and notably identify the additional emergence of a regime with long-lived oscillations.