Cross-Kerr nonlinearity: a stability analysis

TL;DR

This paper investigates how cross-Kerr nonlinearity influences the stability and bistability of a nanomechanical resonator coupled with an electromagnetic cavity, revealing modifications to optical bistability regions.

Contribution

It provides a detailed analysis of the combined effects of radiation-pressure and cross-Kerr nonlinearities on system stability and bistability, highlighting how cross-Kerr coupling alters the bistable regions.

Findings

Cross-Kerr interaction reduces the optical bistable region.

Moderate cross-Kerr coupling extends the upper unstable branch.

Large cross-Kerr coupling diminishes the unstable branch.

Abstract

We analyse the combined effect of the radiation-pressure and cross-Kerr nonlinearity on the stationary solution of the dynamics of a nanomechanical resonator interacting with an electromagnetic cavity. Within this setup, we show how the optical bistability picture induced by the radiation-pressure force is modified by the presence of the cross-Kerr interaction term. More specifically, we show how the optically bistable region, characterising the pure radiation-pressure case, is reduced by the presence of a cross-Kerr coupling term. At the same time, the upper unstable branch is extended by the presence of a moderate cross-Kerr term, while it is reduced for larger values of the cross-Kerr coupling.