Floquet approach to bichromatically driven cavity optomechanical systems

TL;DR

This paper introduces a Floquet method for analyzing time-periodic quantum Langevin equations, enabling efficient calculation of spectra in bichromatically driven cavity optomechanical systems, including those with quantum-squeezed states.

Contribution

The authors develop a Floquet-based framework to solve steady-state quantum Langevin equations with periodic driving, connecting correlation functions to spectra via a generalized Wiener-Khinchin theorem.

Findings

Provides a Fourier series expansion for two-time correlation functions.

Relates the zeroth Fourier component to measurable spectra.

Applies the method to bichromatic cavity optomechanics with quantum-squeezed states.

Abstract

We develop a Floquet approach to solve time-periodic quantum Langevin equations in steady state. We show that two-time correlation functions of system operators can be expanded in a Fourier series and that a generalized Wiener-Khinchin theorem relates the Fourier transform of their zeroth Fourier component to the measured spectrum. We apply our framework to bichromatically driven cavity optomechanical systems, a setting in which mechanical oscillators have recently been prepared in quantum-squeezed states. Our method provides an intuitive way to calculate the power spectral densities for time-periodic quantum Langevin equations in arbitrary rotating frames.