Higher-Order Interactions in Quantum Optomechanics: Analysis of Quadratic Terms

TL;DR

This paper develops an analytical method using higher-order operators to study quadratic nonlinear interactions in quantum optomechanics, including both standard and non-standard interactions, especially relevant when mechanical frequency is comparable to optical frequency.

Contribution

The paper introduces a full operator analytical approach for quadratic interactions in quantum optomechanics, encompassing non-standard momentum-field interactions and applicable to high-frequency regimes.

Findings

Non-standard quadratic interactions could be observable under certain conditions.

The method provides an exactly closed commutator basis for second order operators.

Applicable to platforms like superconducting electromechanics and quantum circuits.

Abstract

This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second order operators which constitute an exactly closed commutators. We consider both types of standard position-field and the recently predicted non-standard momentum-field quadratic interactions, which is significant when the ratio of mechanical frequency to optical frequency is not negligible. This unexplored regime of large mechanical frequency can be investigated in few platforms including the superconducting electromechanics and simulating quantum cavity electrodynamic circuits. It has been shown that the existence of non-standard quadratic interaction could be observable under appropriate conditions.