Shot-to-shot displacement noise in state-expansion protocols with inverted potentials

Optically levitated nanoparticles are promising candidates for the generation of macroscopic quantum states of mechanical motion. Protocols to generate such states expose the particle to a succession of different potentials. Limited reproducibility of the alignment of these potentials across experimental realizations introduces additional noise. Here, we experimentally investigate and model how such shot-to-shot noise limits the coherence length of a levitated nanoparticle during a state-expansion protocol using a dark, inverted electrical potential. We identify electric stray fields and mechanical instabilities as major sources of shot-to-shot fluctuations. We discuss the resulting experimental requirements for state expansion protocols exploiting inverted potentials.