Fast quantum interference of a nanoparticle via optical potential control

We introduce and theoretically analyze a scheme to prepare and detect non-Gaussian quantum states of an optically levitated particle via the interaction with a light pulse that generates cubic and inverted potentials. We show that this allows operating on short time- and lengthscales, which significantly reduces the demands on decoherence rates in such experiments. Specifically, our scheme predicts the observation of interference of nanoparticles with a mass above $10^8$ atomic mass units delocalised over several nanometers, on timescales of milliseconds, when operated at vacuum levels around $10^{-10}$~mbar and at room temperature. We discuss the prospect of using this approach for coherently splitting the wavepacket of massive dielectric objects using neither projective measurements nor an internal level structure.