Equivalence between an optomechanical system and a Kerr medium

TL;DR

This paper demonstrates that an optomechanical system exhibits optical bistability similar to a Kerr medium, with mechanical fluctuations affecting stability, and confirms the mechanical mode's role as a Kerr nonlinearity at low temperatures.

Contribution

It establishes the equivalence between an optomechanical system and a Kerr medium, analyzing stability conditions and confirming the nonlinearity through quantum steady state calculations.

Findings

Optomechanical system shows optical bistability similar to Kerr medium.

Mechanical fluctuations influence the stability of the upper branch.

Mechanical mode acts as a Kerr nonlinearity at low temperatures.

Abstract

We study the optical bistability of an optomechanical system in which the position of a mechanical oscillator modulates the cavity frequency. The steady-state mean-field equation of the optical mode is identical to the one for a Kerr medium, and thus we expect it to have the same characteristic behavior with a lower, a middle, and an upper branch. However, the presence of position fluctuations of the mechanical resonator leads to a new feature: the upper branch will become unstable at sufficiently strong driving in certain parameter regimes. We identify the appropriate parameter regime for the upper branch to be stable, and we confirm, by numerical investigation of the quantum steady state, that the mechanical mode indeed acts as a Kerr nonlinearity for the optical mode in the low-temperature limit. This equivalence of the optomechanical system and the Kerr medium will be important for future applications of cavity optomechanics in quantum nonlinear optics and quantum information science.