  Veselago pointed out that electromagnetic wave theory allows for materials
with a negative index of refraction, in which most known optical phenomena
would be reversed. A slab of such a material can focus light by negative
refraction, an imaging technique strikingly different from conventional
positive refractive index optics, where curved surfaces bend the rays to form
an image of an object. Here we demonstrate Veselago lensing for matter waves,
using ultracold atoms in an optical lattice. A relativistic, i.e. photon-like,
dispersion relation for rubidium atoms is realized with a bichromatic optical
lattice potential. We rely on a Raman $\pi$-pulse technique to transfer atoms
between two different branches of the dispersion relation, resulting in a
focusing completely analogous to the effect described by Veselago for light
waves. Future prospects of the demonstrated effects include novel sub-de
Broglie wave imaging applications.
