Quantum noise spectra for periodically-driven cavity optomechanics

TL;DR

This paper introduces a new method for calculating quantum noise spectra in periodically-driven cavity optomechanical systems, addressing limitations of existing approaches and enabling better analysis of experimental setups involving modulation.

Contribution

The authors develop a novel analytical approach for quantum noise spectra in modulated optomechanics, comparing it with existing methods and demonstrating its effectiveness in complex experimental scenarios.

Findings

New method accurately predicts noise spectra in modulated systems

Excellent agreement with stochastic simulations in thermal regimes

Predicts quantum squeezing and measurement of spectral components

Abstract

A growing number of experimental set-ups in cavity optomechanics exploit periodically driven fields. However, such set-ups are not amenable to analysis using simple, yet powerful, closed-form expressions of linearized optomechanics, which have provided so much of our present understanding of experimental optomechanics. In the present paper, we formulate a new method to calculate quantum noise spectra in modulated optomechanical systems, which we analyze, compare, and discuss with two other recently proposed solutions: we term these (i) frequency-shifted operators (ii) Floquet and (iii) iterative analysis. We prove that (i) and (ii) yield equivalent noise spectra, and find that (iii) is an analytical approximation to (i) for weak modulations. We calculate the noise spectra of a doubly-modulated system describing experiments of levitated particles in hybrid electro-optical traps. We show excellent agreement with Langevin stochastic simulations in the thermal regime and predict squeezing in the quantum regime. Finally, we reveal how experimentally inaccessible spectral components of a modulated system can be measured in heterodyne detection through an appropriate choice of modulation frequencies.