SAPPHIRE TEST-MASSES FOR MEASURING THE STANDARD QUANTUM LIMIT AND ACHIEVING QUANTUM-NONDEMOLITION

In this paper rye show that the available technology is sufficient to measure the Standard Quantum Limit (SQL) of a low loss acoustic oscill ator with a readout based on a microwave parametric transducer. The ex periment makes use of the low electrical and acoustical losses in mono crystalline sapphire and new low-noise microwave technology. The cryst al acts as an electrical vibration sensor and an acoustic oscillator i n one monolithic structure. We analyze two new types of such structure s: (1) The sapphire bar dielectric transducer and (2) the slotted sapp hire dielectric transducer. We show that with a 40-60 dB double-cavity phase-noise suppression system the SQL may be measured using the sapp hire 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 pa rametric readout. The principle of operation is demonstrated by some s imple room-temperature experiments with all results verified using fin ite-element analysis. Given that we call expect to measure the SQL wit h one of these schemes, we analyze the properties of a microwave displ acement measurement system based upon a high-Q parametric transducer a nd a double-frequency oscillator. Such a readout system represents a p ractical implementation of a black action evasion (BAE) displacement s ensor allowing the discrimination between the quadratures of the mecha nical oscillator. We determine the set of conditions which allows the enhanced sensitivity with respect to the desired quadrature and suppre ssed sensitivity to the unwanted quadrature. We find that tuning of th e BAE system at the particular quadrature of interest can be performed by varying the phase relationship between the microwave carriers avai lable from the double-frequency oscillator. We establish the importanc e of having the frequency and the phase-control servos to maintain the optimal tuning of the micro-wave BAE readout system, as both the mech anical oscillator and the double-frequency pump oscillator are always subject to various sources of environmental interference.