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Abstract

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 amplitude-frequency effect. By implementing of
this new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q
sapphire split-bar mechanical resonator and for 10 mg quartz bulk acoustic wave
resonator. Our experiments with sapphire resonator have established the upper
limit on quantum gravity correction constant of beta_0 to not exceed 5000000
which is factor of 6 better than previously detected. The reasonable estimates
of beta_0 from experiments with quartz resonators yields even more stringent
limit of 40000.