Superconducting inductance-bridge transducer for resonant-mass gravitational-radiation detector

The sensitivity of cryogenic gravitational-radiation detectors is presently limited by the performance of the transducers. A superconducting ac-pumped inductance bridge is proposed as a new transducer for resonant-mass gravitational-radiation detectors. The impedance matrix of the transducer is computed to determine the input, output, and transfer characteristics of the electromechanical system. It is shown that the dissipative forces exerted on the proof mass by the bridge circuit through the two sidebands cancel each other almost exactly so that the Brownian-motion level is nearly unaffected by the electric sensing circuit. This implies that an effective energy coupling coefficient near unity could be used without being limited by the electrical Nyquist noise. With the parametric up conversion of the signal, the inductance bridge can be coupled to a nearly quantum-limited dc superconducting quantum interference device (SQUID). The sensitivity of the gravitational-radiation detector employing the new superconducting transducer is computed as a function of transducer parameters. It is shown that the proposed transducer, with modest values for its parameters, is capable of matching a high-Q gravitational-radiation antenna, cooled to 50 mK, to a nearly quantum-limited dc SQUID