  Matter-wave interferometry performed with massive objects elucidates their
wave nature and thus tests the quantum superposition principle at large scales.
Whereas standard quantum theory places no limit on particle size, alternative,
yet untested theories---conceived to explain the apparent quantum to classical
transition---forbid macroscopic superpositions. Here we propose an
interferometer with a levitated, optically cooled, and then free-falling
silicon nanoparticle in the mass range of one million atomic mass units,
delocalized over more than 150 nm. The scheme employs the near-field Talbot
effect with a single standing-wave laser pulse as a phase grating. Our
analysis, which accounts for all relevant sources of decoherence, indicates
that this is a viable route towards macroscopic high-mass superpositions using
available technology.
