Probing deformed commutators with macroscopic harmonic oscillators

Abstract

A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated to a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters are roughly extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass $m_{\mathrm{P}}$ ($\approx 22\mu \mathrm{g}$), and compare it with a model of deformed dynamics. Previous limits to the parameters quantifying the commutator deformation are substantially lowered.

11 pages, 3 figures, reference added

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