Negative refraction of excitations in the Bose-Hubbard model

Ultracold atoms in optical lattices provide a unique opportunity to study Bose-Hubbard physics. In this work we show that by considering a spatially varying on-site interaction it is possible to manipulate the motion of excitations above the Mott phase in a Bose-Hubbard system. Specifically, we show that it is possible to "engineer" regimes where excitations will negatively refract, facilitating the construction of a flat lens.