# Sensitivity Characterisation of a Parametric Transducer for Gravitational Wave Detection Through Optical Spring Effect

## TL;DR

This paper characterizes a microwave parametric transducer with an optical spring effect designed to improve the sensitivity of the Mario Schenberg gravitational wave detector, demonstrating a frequency-displacement sensitivity of 726 MHz/μm at 4 K.

## Contribution

It introduces a novel microwave transducer design utilizing the optical spring effect for enhanced gravitational wave detection sensitivity.

## Key findings

- Frequency-displacement sensitivity of 726 MHz/μm at 4 K
- Transducer amplification gain of 5.5 × 10^{11} V/m
- Displacement noise level of 1.8 × 10^{-19} m/√Hz

## Abstract

We present the characterisation of the most recent parametric transducers designed to enhance the Mario Schenberg Gravitational Wave Detector sensitivity. The transducer is composed of a microwave re-entrant cavity that attaches to the gravitational wave antenna via a rigid spring. It functions as a three-mode mass-spring system; motion of the spherical antenna couples to a 50 $\mu m$ thick membrane, which converts its mechanical motion into a frequency shift of the cavity resonance. Through the optical spring effect, the microwave transducer frequency-displacement sensitivity was measured to be 726 $MHz/\mu$m at 4 K. The spherical antenna detection sensitivity is determined analytically using the transducer amplification gain and equivalent displacement noise in the test setup, which are 5.5 $\times$ 10$^{11} V/m$ and $1.8 \times 10^{-19} m\sqrt{Hz}^{-1}$, respectively.