Suspension-thermal noise in spring-antispring systems for future gravitational-wave detectors

TL;DR

This paper analyzes the suspension thermal noise in spring-antispring systems, especially the Roberts linkage, revealing that thermal noise depends on system size rather than resonance frequency, impacting future gravitational-wave detector designs.

Contribution

It provides a detailed calculation of suspension thermal noise in spring-antispring systems, highlighting the size dependence and implications for low-frequency gravitational-wave detectors.

Findings

Thermal noise spectrum resembles that of a simple pendulum.

Thermal noise is primarily determined by system dimensions.

Strict size requirements are necessary for future low-frequency detectors.

Abstract

Spring-antispring systems have been investigated as possible low-frequency seismic isolation in high-precision optical experiments. These systems provide the possibility to tune the fundamental resonance frequency to, in principle, arbitrarily low values, and at the same time maintain a compact design of the isolation system. It was argued though that thermal noise in spring-antispring systems would not be as small as one may naively expect from lowering the fundamental resonance frequency. In this paper, we present a detailed calculation of the suspension thermal noise for a specific spring-antispring system, namely the Roberts linkage. We find a concise expression of the suspension thermal noise spectrum, which assumes a form very similar to the well-known expression for a simple pendulum. It is found that while the Roberts linkage can provide strong seismic isolation due to a very low fundamental resonance frequency, its thermal noise is rather determined by the dimension of the system. We argue that this is true for all horizontal mechanical isolation systems with spring-antispring dynamics. This imposes strict requirements on mechanical spring-antispring systems for the seismic isolation in potential future low-frequency gravitational-wave detectors as we discuss for the four main concepts: atom-interferometric, superconducting, torsion-bars, and conventional laser interferometer.