Back-action-evading transducing scheme for cryogenic gravitational wave antennas

We present the design, development, and test of a resonant capacitive transducer for gravitational wave antennas suitable for back-action-evading measurements. We describe a detailed theoretical model of such a transducer, analyze the general requirements that it must satisfy, and report the results of some tests at low temperatures. We obtain on our prototype a good value of the mechanical merit factor (2.8×${10}^6$), a satisfactory geometrical balance, and a good stability of the electrical and geometrical parameters. The bridge readout circuit was balanced down to 0.8 ppm and an electrical quality factor ${\mathit{Q}}_{\mathit{e}}$≃6×${10}^3$ was measured for the electrical resonance at 123 kHz. The noise behavior of the system is in satisfactory agreement with the values predicted by our theoretical model.