Optimization of static potentials for large delocalization and non-Gaussian quantum dynamics of levitated nanoparticles under decoherence

Levitated nanoparticles provide a controllable and isolated platform for probing fundamental quantum phenomena at the macroscopic scale. In this work we introduce an optimization method to determine optimal static potentials for the generation of largely delocalized and non-Gaussian quantum states of levitated nanoparticles. Our optimization strategy accounts for position-dependent noise sources originating from the fluctuations of the potential. We provide key figures of merit that allow for fast computation and capture relevant features of the dynamics, mitigating the computational demands associated with the multiscale simulation of this system. Specifically, we introduce coherence length and coherent cubicity as signatures of large delocalization and quantum non-Gaussian states, respectively. As a proof of principle, we apply the optimization approach to a family of quartic potentials and show that the optimal configuration depends on the strength and nature of the noise in the system. Additionally, we benchmark our results with a full quantum dynamics simulations of the system for the optimal potentials.