Quantum dynamics of Dissipative Kerr solitons

TL;DR

This paper develops a quantum-mechanical model for dissipative Kerr solitons in ring microresonators, revealing their finite lifetime due to quantum fluctuations and identifying them as a class of dissipative time crystals.

Contribution

It introduces a quantum model using the truncated Wigner method to analyze quantum effects on Kerr solitons, extending classical descriptions to include quantum fluctuations.

Findings

Solitons have a finite lifetime caused by quantum fluctuations.

The Liouvillian spectrum indicates dissipative Kerr solitons are dissipative time crystals.

Quantum effects can be estimated through the Liouvillian eigenvalues.

Abstract

Dissipative Kerr solitons arising from parametric gain in ring microresonators are usually described within a classical mean-field framework. Here, we develop a quantum-mechanical model of dissipative Kerr solitons in terms of the truncated Wigner method, which accounts for quantum effects to lowest order. We show that the soliton experiences a finite lifetime due to quantum fluctuations originating from losses. Reading the results in terms of the theory of open quantum systems, allows to estimate the Liouvillian spectrum of the system. It is characterized by a set of eigenvalues with finite imaginary part and vanishing real part in the limit of vanishing quantum fluctuations. This feature shows that dissipative Kerr solitons are a specific class of dissipative time crystals.