2019/03/31 by P. A. Bushev, Pavel Bushev, Jeremy Bourhill +13 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Calculus (dental) #Classical mechanics #Engineering #Mathematics #Mechanical and Optical Resonators #Mechanical engineering #Mechanical system #Noncommutative and Quantum Gravity Theories #Physics #Quantum Mechanics and Applications #cond-mat.mes-hall #gr-qc #quant-ph
paper · pdf · doi:10.1103/physrevd.100.066020
published as Phys. Rev. D 100, 066020 (2019) · 3 figures
arxiv created 2019/08/23 · openalex publication_date 2019/09/20 · arxiv updated 2019/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 [\stackrel^x,\stackrel^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 \ensuremath∼10^\ensuremath-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 \ensuremathβ0 to not exceed 5.2\ifmmode×\else\texttimes\fi106, which is a factor of 6 better than previously measured. The reasonable estimates of \ensuremathβ0 from experiments with quartz resonators yields \ensuremathβ0<4\ifmmode×\else\texttimes\fi104. The datasets of 1936 measurements of a physical pendulum period by Atkinson [E. C. Atkinson, Proc. Phys. Soc. London 48, 606 (1936).] could potentially lead to significantly stronger limitations on \ensuremathβ0\ensuremath≪1. Yet, due to the lack of proper pendulum frequency stability measurement in these experiments the exact upper bound on \ensuremathβ0 cannot be reliably established. Moreover, pendulum based systems only allow one to test a specific form of the modified commutator that depends on the mean value of momentum. The electromechanical oscillators to the contrary enable testing of any form of generalized uncertainty principle directly due to a much higher stability and a higher degree of control.