Properties of a monolithic sapphire parametric transducer: prospects of measuring the standard quantum limit

To measure the standard quantum limit (SQL) a high quality transducer must be coupled to a high quality mechanical system. Due to its monolithic nature, the monolithic sapphire transducer (MST) has high quality factors for both types of resonances. Single loop suspension is shown to yield a mechanical quality factor of 6 x 10(8) at 4 K and Whispering Gallery electromagnetic modes display a quality factor of 2 x 10(6) at 4 K. From standard analysis we show that the MST has the potential to measure the noise fluctuations of the mechanical oscillator at the SQL. Also, we point out a new way to determine if the transducer back-action is quantum limited. We show that if the fluctuations are at the quantum limit, then the amplitude of the oscillations will be amplified by the ratio of the ringdown time to the measurement time, which is an inherently easier measurement.