Parametric back-action effects in a high-Q cyrogenic sapphire transducer

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Abstract
The construction and operation of a high‐quality factor microwavesapphireresonatortransducer coupled to a 1 kHz niobium membrane acoustic oscillator are presented in this paper. A four‐stage passive vibration isolation system was included in the design to permit the measurement of the transducer’s parametric properties. The isolation system was shown to sufficiently suppress mechanical noise above 100 Hz and an upper limit to the displacement sensitivity of the transducer was measured to be 3.0±0.6×10−16 m/√Hz. The parametric behavior of the transducer with a single pump readout was measured for several transducer configurations, and the results were found to be in good agreement with theory. The measurements presented here display for the first time the complete parametric behavior in a high electrical Q system, where the transducer’s bandwidth is less than the mechanical oscillator’s frequency. The high stability and low losses of our system may allow the transducer to be configured as a back‐action evasion or quantum nondemolition device.