Thermal and back-action noises in dual-sphere gravitational-waves detectors

TL;DR

This paper analyzes the sensitivity limits of dual-sphere gravitational-wave detectors, focusing on thermal and back-action noises, and introduces a new method to accurately evaluate mechanical responses across a broad frequency range.

Contribution

It presents a novel approach to assess mechanical responses and noise contributions in dual-sphere detectors, enabling high sensitivity over a wide frequency band.

Findings

High sensitivities achievable with realistic parameters

New method improves accuracy of mechanical response estimates

Effective noise analysis across intermediate frequency domain

Abstract

We study the sensitivity limits of a broadband gravitational-waves detector based on dual resonators such as nested spheres. We determine both the thermal and back-action noises when the resonators displacements are read-out with an optomechanical sensor. We analyze the contributions of all mechanical modes, using a new method to deal with the force-displacement transfer functions in the intermediate frequency domain between the two gravitational-waves sensitive modes associated with each resonator. This method gives an accurate estimate of the mechanical response, together with an evaluation of the estimate error. We show that very high sensitivities can be reached on a wide frequency band for realistic parameters in the case of a dual-sphere detector.