Sapphire test-masses for measuring the standard quantum limit and achieving quantum non-demolition

Abstract

In this paper we show that the available technology is sufficient to measure the Standard Quantum Limit (SQL) of a low loss acoustic oscillator, with a readout based on a microwave parametric transducer. The experiment makes use of the low electrical and acoustical losses in monocrystalline sapphire and new low-noise microwave technology. The crystal acts as an electrical vibration sensor and an acoustic oscillator in one monolithic structure. We analyze two new types of such structures: (1) The sapphire bar dielectric transducer and (2) the slotted sapphire dielectric transducer. We show that with a 40–60 dB double-cavity phase-noise suppression system the SQL may be measured using the sapphire bar. For the slotted structure, the phase noise requirements are less stringent because of its smaller resonant frequency and mass. We show that the SQL of this structure may be measured with a standard parametric readout. The principle of operation is demonstrated by some simple room-temperature experiments with all results verified using finite-element analysis.