We present first results from a number of experiments conducted on a 0.53-kg cylindrical dumbbell-shaped sapphire crystal. Here we report on an optomechanical experiment utilizing a modification to the typical cylindrical architecture. Mechanical motion of the crystal structure alters the dimensions of the crystal, and the induced strain changes the permittivity. These two effects result in parametric frequency modulation of resonant microwave whispering gallery modes that are simultaneously excited within the crystal. A microwave readout system is implemented, allowing extremely low noise measurements of this frequency modulation near our modes of interest, having a phase noise floor of $-165$ dBc/Hz at 100 kHz. Fine tuning of the crystal's suspension has allowed for the optimization of mechanical quality factors in preparation for cryogenic experiments, with a value of $Q=8\times {10}^7$ achieved at 127 kHz. This results in a $Q\times f$ product of ${10}^{13}$, equivalent to the best measured values in a macroscopic sapphire mechanical system. Results are presented that demonstrate the excitation of mechanical modes via radiation pressure force, allowing an experimental method of determining the transducer's displacement sensitivity $df/dx$ and calibrating the system. Finally, we demonstrate parametric backaction phenomenon within the system. These are all important steps towards the goal of achieving quantum limited measurements of a kilogram-scale macroscopic device for the purpose of detecting deviations from standard quantum theory resulting from quantum gravitational effects.

• Received 27 February 2015

DOI:https://doi.org/10.1103/PhysRevA.92.023817