Method of Higher-Order Operators for Quantum Optomechanics

TL;DR

This paper introduces a higher-order operator method for nonlinear quantum optomechanics, revealing symmetry breaking, resonance shifts, and providing explicit estimates for coherent phonon populations, with implications for precise measurement of optomechanical interactions.

Contribution

It presents a novel higher-order operator approach to analyze nonlinear optomechanics, including explicit phonon population estimation and solutions with linear Langevin equations.

Findings

Symmetry breaking in frequency shifts between red and blue side-bands.

Significant corrections to spring effect due to higher-order interactions.

A minimal basis yields exactly solvable Langevin equations.

Abstract

We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings. Similarly, a higher-order resonance shift exists appearing as changes in both of the optical and mechanical resonances. We provide the first known method to explicitly estimate the population of coherent phonons. We also calculate corrections to spring effect due to higher-order interactions and coherent phonons, and show that these corrections can be quite significant in measurement of single-photon optomechanical interaction rate. It is shown that there exists non-unique and various choices for the higher-order operators to solve the optomechanical interaction with different multiplicative noise terms, among which a minimal basis offers exactly linear Langevin equations, while decoupling one Langevin equation and thus leaving the whole standard optomechanical problem exactly solvable by explicit expressions. We finally present a detailed treatment of multiplicative noise as well as nonlinear dynamic stability phases by the method of higher-order operators. Similar approach can be used outside the domain of standard optomechanics to quadratic and all other types of nonlinear interactions in quantum physics.