A measurement-based protocol for the generation of delocalised quantum states of a mechanical system

Non-Gaussian mechanical states are a key resource for quantum-enhanced sensing and tests of macroscopic quantum physics. We propose a measurement-based protocol to herald delocalized, nonclassical states of a mechanical oscillator in cavity optomechanics by conditioning on Geiger photodetection of the optical output. We analyse under which conditions Stokes-induced optomechanical entanglement give rise to mechanical Wigner Function negativity upon detection. We develop and compare a blue-detuned pulsed scheme and a continuous-wave steady-state scheme employing temporal-mode filtering, and we quantify heralding rates and robustness to finite temperature under realistic detection efficiencies.