# Quantum-enhanced mechanical sensing

A microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator is prepared in Fock states of up to seven phonons to estimate the displacement of a weak resonant signal of unknown phase. Such non-Gaussian quantum probes had shown metrological advantage only in lighter systems such as trapped ions, while squeezed-state advantages were restricted to a known quadrature. Two independent analyses of the measured phonon-number distributions agree on a Fisher information five times the vacuum value, beyond any classical probe of arbitrary energy; a neural network trained directly on calibration records reproduces the same sensitivity with half the systematic bias.

A microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator is prepared in Fock states of up to seven phonons to estimate the displacement of a weak resonant signal of unknown phase. Such non-Gaussian quantum probes had shown metrological advantage only in lighter systems such as trapped ions, while squeezed-state advantages were restricted to a known quadrature. Two independent analyses of the measured phonon-number distributions agree on a Fisher information five times the vacuum value, beyond any classical probe of arbitrary energy; a neural network trained directly on calibration records reproduces the same sensitivity with half the systematic bias.