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

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 $MHz\mathrm{/}\mu$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${}^{11}V\mathrm{/}m$ and $1.8\times {10}^{-19}m{\sqrt{Hz}}^{-1}$, respectively.