Negative refraction of ultra-cold atoms in optical lattices with nonuniform artificial gauge fields

We theoretically study the reflection and refraction of ultra-cold atoms in optical lattices exposed to a nonuniform artificial magnetic field. The introduction of the nonuniform artificial magnetic field to the optical lattice for suitable designer magnetic potential barrier can lead to a series of intriguing reflection and refraction phenomena of atoms, including reflection, positive refraction, negative refraction and atomic matter wave splitting. Both the occurrence and the distribution of these reflection and refraction scenarios can be coherently controlled by the nonuniform artificial magnetic field. In particular, the regions close to the boundary of reflection demonstrate two more interesting propagation modes, i.e., a reflected branch of atoms comprising a positive or negative refracted branch of atoms with almost same atom population will be excited simultaneously at the magnetic potential barrier. The results can be a guide for the coherent control of the matter waves in optical lattices and the design of new atom optics devices. (C) 2016 Elsevier B.V. All rights reserved.