Testing the generalized uncertainty principle with macroscopic mechanical oscillators and pendulums

• Published in: Physical review. D 2019-09, Vol.100 (6), Article 066020
• Main Authors: Bushev, P. A., Bourhill, J., Goryachev, M., Kukharchyk, N., Ivanov, E., Galliou, S., Tobar, M. E., Danilishin, S.
• Format: Article
• Language: English
• Subjects: Acoustic waves; Amplitudes; Change detection; Commutation; Commutators; Control stability; Dependence; Engineering Sciences; Experiments; Frequency stability; General Physics; General Relativity and Quantum Cosmology; Gravitational effects; Gravity; Mechanical oscillators; Oscillators; Other; Pendulums; Physics; Quantum gravity; Quartz; Resonant frequencies; Resonators; Sapphire; Uncertainty principles; Upper bounds
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.100.066020

Recent progress in observing and manipulating mechanical oscillators at quantum regime provides new opportunities of studying fundamental physics, for example to search for low energy signatures of quantum gravity. For example, it was recently proposed that such devices can be used to test quantum gravity effects, by detecting the change in the [x^,p^] commutation relation that could result from quantum gravity corrections. We show that such a correction results in a dependence of a resonant frequency of a mechanical oscillator on its amplitude, which is known as the amplitude-frequency effect. By implementing this new method we measure the amplitude-frequency effect for a 0.3 kg ultra-high-Q sapphire split-bar mechanical resonator and for an ∼10−5  kg quartz bulk acoustic wave resonator. Our experiments with a sapphire resonator have established the upper limit on a quantum gravity correction constant of β0 to not exceed 5.2×106, which is a factor of 6 better than previously measured. The reasonable estimates of β0 from experiments with quartz resonators yields β0