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Measuring the Standard Quantum Limit Using a Sapphire Dielectric Bar Transducer

Clayton R. Locke, Michael Edmund Tobar, Eugene N. Ivanov, D. G. Blair

Published Jan 1, 1998• 0 citations
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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 6.10^8 at 4 K. From standard analysis we show the MST has the potential to measure 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 oscillation will be amplified by the ratio of the ringdown time to the measurement time, which is an inherently easier measurement.

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The construction and operation of a high-quality factor microwave sapphire resonator transducer 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.

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Optics Communications•May 1, 1992•18 citations
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 6.10^8 at 4 K. From standard analysis we show the MST has the potential to measure 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 oscillation will be amplified by the ratio of the ringdown time to the measurement time, which is an inherently easier measurement.
The construction and operation of a high-quality factor microwave sapphire resonator transducer 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.