Effects of Geometry on Near Quantum Ground State Behaviour of Phonon-Trapping Acoustic Cavities

TL;DR

This paper investigates how curved phonon-trapping bulk acoustic wave cavities can enhance quantum ground state behavior, improve phonon confinement, and enable better observation of quantum effects at higher frequencies through unique geometric design.

Contribution

It demonstrates that non-trivial cavity geometry improves phonon trapping and zero-point fluctuation variance, overcoming frequency constraints and enhancing quantum effect observability in mechanical systems.

Findings

Curved BAW cavities improve phonon trapping efficiency.

Zero-point fluctuation variance becomes frequency-independent.

Enhanced coupling at high overtone numbers enables high-frequency quantum applications.

Abstract

This work presents some peculiarities of the near quantum ground state behaviour of curved (phonon trapping) Bulk Acoustic Wave (BAW) cavities when compared to a conventional mechanical resonator. The curved cavity system resolves the quandary of the conventional mechanical system where the Bose-Einstein distribution requires higher frequencies for lower quantum occupation factors contrary to the constraint of an inverse frequency dependence of the quantum fluctuations of displacement. We demonstrate how the non-trivial cavity geometry can lead to better phonon trapping, enhancing the variance of zero-point-fluctuations of displacement. This variance becomes independent of overtone number (or BAW resonance frequency) overcoming the constraint and allowing better observation of quantum effects in a mechanical system. The piezoelectric electro-mechanical coupling approach is qualitatively compared to the parametric optomechanical technique for the curved BAW cavities. In both cases the detectible quantity grows proportional to the square root of the overtone number, and thus the resonance frequency. Also, the phonon trapping improves with higher overtone numbers, which allows the electrode size to be reduced such that in the optimal case the parasitic capacitive impedance becomes independent of the overtone number, allowing effective coupling to very high frequency overtones.