  The development of quantum optomechanics now allows mechanical sensors with
femtogram masses to be controlled and measured in the quantum regime. If the
mechanical element contains isotopes that undergo nuclear decay, measuring the
recoil of the sensor following the decay allows reconstruction of the total
momentum of all emitted particles, including any neutral particles that may
escape detection in traditional detectors. As an example, for weak nuclear
decays the momentum of the emitted neutrino can be reconstructed on an
event-by-event basis. We present the concept that a single nanometer-scale,
optically levitated sensor operated with sensitivity near the standard quantum
limit can search for heavy sterile neutrinos in the keV-MeV mass range with
sensitivity significantly beyond existing constraints. We also comment on the
possibility that mechanical sensors operated well into the quantum regime might
ultimately reach the sensitivities required to provide an absolute measurement
of the mass of the light neutrino states.
