  Quantum non-Gaussian states of phononic systems coupled to light are
essential for fundamental studies of single-phonon mechanics and direct
applications in quantum technology. Although nonclassical mechanical states
have already been demonstrated, more challenging quantum non-Gaussianity of
such states remains limited. Using photon counting detection, we propose the
quantum non-Gaussian generation of few-phonon states of low-temperature
vibrating superfluid Helium. We predict the quantum non-Gaussian depth of such
phononic states and investigate their robustness under relevant mechanical
heating. As the quality of such phononic states is very high, we confirm a
single-phonon bunching capability to further classify such states for future
mechanical experiments. Moreover, we predict increasing capability for force
sensing and thermometry for increasing heralded phonon numbers.
