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

In this paper rye 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. Given that we call expect to measure the SQL with one of these schemes, we analyze the properties of a microwave displacement measurement system based upon a high-Q parametric transducer and a double-frequency oscillator. Such a readout system represents a practical implementation of a black action evasion (BAE) displacement sensor allowing the discrimination between the quadratures of the mechanical oscillator. We determine the set of conditions which allows the enhanced sensitivity with respect to the desired quadrature and suppressed sensitivity to the unwanted quadrature. We find that tuning of the BAE system at the particular quadrature of interest can be performed by varying the phase relationship between the microwave carriers available from the double-frequency oscillator. We establish the importance of having the frequency and the phase-control servos to maintain the optimal tuning of the micro-wave BAE readout system, as both the mechanical oscillator and the double-frequency pump oscillator are always subject to various sources of environmental interference.