Wilson Fermions and Axion Electrodynamics in Optical Lattices

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A. Bermudez, L. Mazza, M. Rizzi, N. Goldman, M. Lewenstein, M.A. Martin-Delgado
Phys. Rev. Lett. 105, 190404 (2010) http://link.aps.org/doi/10.1103/PhysRevLett.105.190404

The formulation of massless relativistic fermions in lattice gauge theories is hampered by the fundamental problem of species doubling, namely, the rise of spurious fermions modifying the underlying physics. A suitable tailoring of the fermion masses prevents such abundance of species, and leads to the so-called Wilson fermions. Here we show that ultracold atoms provide us with the first controllable realization of these paradigmatic fermions, thus generating a quantum simulator of fermionic lattice gauge theories. We describe a novel scheme that exploits laser-assisted tunneling in a cubic optical superlattice to design the Wilson fermion masses. The high versatility of this proposal allows us to explore a variety of interesting phases in three-dimensional topological insulators, and to test the remarkable predictions of axion electrodynamics.