Electric circuit model of microwave optomechanics

TL;DR

This paper develops a classical electric circuit model for microwave optomechanics, translating optical phenomena into electronic terms to facilitate measurement and design, and compares classical and quantum regimes.

Contribution

It introduces a comprehensive classical circuit model for microwave optomechanics that aligns with quantum descriptions at high occupation numbers.

Findings

Derived analytical expressions for back-action force and spectral densities.

Established correspondence between optical and electronic properties.

Compared classical and quantum models to identify quantum-specific features.

Abstract

We report on the generic classical electric circuit modeling that describes standard single-tone microwave optomechanics. Based on a parallel RLC circuit in which a mechanical oscillator acts as a movable capacitor, derivations of analytical expressions are presented, including key features such as the back-action force, the input-output expressions, and the spectral densities associated, all in the classical regime. These expressions coincide with the standard quantum treatment performed in optomechanics when the occupation number of both cavity and mechanical oscillator are large. Besides, the derived analytics transposes optical elements and properties into electronics terms, which is mandatory for quantitative measurement and design purposes. Finally, the direct comparison between the standard quantum treatment and the classical model addresses the bounds between quantum and classical regimes, highlighting the features which are truly quantum, and those which are not.