Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system

TL;DR

This paper derives an effective Hamiltonian for an optomechanical system using the Born-Oppenheimer approximation, revealing a Kerr nonlinearity and squeezing effects, and proposes a quantum-nondemolition measurement setup to monitor such systems.

Contribution

It introduces a novel effective Hamiltonian approach to analyze Kerr nonlinearity and squeezing in optomechanical systems, enabling new measurement techniques.

Findings

Kerr effect induced in the vacuum state of the system

Squeezing effect observed in the cavity field spectrum

Proposed quantum-nondemolition measurement setup

Abstract

Using the Born-Oppenheimer approximation, we derive an effective Hamiltonian for an optomechanical system that leads to a nonlinear Kerr effect in the system's vacuum. The oscillating mirror at one edge of the optomechanical system induces a squeezing effect in the intensity spectrum of the cavity field. A near-resonant laser field is applied at the other edge to drive the cavity field, in order to enhance the Kerr effect. We also propose a quantum-nondemolition-measurement setup to monitor a system with two cavities separated by a common oscillating mirror, based on our effective Hamiltonian approach.