Two stage superconducting quantum interference device amplifier in a high-Q gravitational wave transducer

We report on the total noise from an inductive motion transducer for a gravitational-wave antenna. The transducer uses a two-stage SQUID amplifier and has a noise temperature of 1.1 mK, of which 0.70 mK is due to back-action noise from the SQUID chip. The total noise includes thermal noise from the transducer mass, which has a measured Q of 2.60 X 10^6. The noise temperature exceeds the expected value of 3.5 \mu K by a factor of 200, primarily due to voltage noise at the input of the SQUID. Noise from flux trapped on the chip is found to be the most likely cause.