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 onsite interaction it is possible to manipulate the motion of excitations above the Mott pha
se 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.
