Precision Measurement of a low-loss Cylindrical Dumbbell-Shaped Sapphire Mechanical Oscillator using Radiation Pressure

Abstract: We present first results from a number of experiments conducted on a 0.53 kg cylindrical dumbbell-shaped sapphire crystal. This is the first reported optomechanical experiment of this nature utilising a novel 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 novel low-noise 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 optimisation of mechanical quality factors in preparation for cryogenic experiments, with a value of Q=8 x 10^7 achieved at 127 kHz. This results in a Q x 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 back-action phenomenon within the system. These are all important steps towards the overall goal of the experiment; to cool a macroscopic device to the quantum ground state at millikelvin temperatures.