Probing deformed commutators with micro- and nano-oscillators

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 minimal uncertainty in position measurements, which is encoded in deformed commutation relations. Once applied in the Heisenberg dynamics, they give effects potentially detectable in low energy experiments. For instance, an isolated harmonic oscillator becomes intrinsically nonlinear and its dynamics shows a dependence of the oscillation frequency on the amplitude, as well as the appearance of higher harmonics. Here we analyze the free decay of micro and nano-oscillators, spanning a wide range of masses, and we place upper limits to the parameters quantifying the commutator deformation.