On the effective Dirac dynamics of ultracold atoms in bichromatic optical lattices

TL;DR

This paper demonstrates how ultracold atoms in bichromatic optical lattices can simulate Dirac dynamics, enabling the observation of phenomena like Klein tunneling with current experimental setups.

Contribution

It provides a rigorous derivation of Dirac dynamics beyond tight-binding approximation in optical lattices and shows how to realize Klein tunneling experimentally.

Findings

Dirac points can be engineered in bichromatic optical lattices.

The Dirac equation accurately describes atom dynamics near band crossings.

Klein tunneling can be observed with current experimental configurations.

Abstract

We study the dynamics of ultracold atoms in tailored bichromatic optical lattices. By tuning the lattice parameters, one can readily engineer the band structure and realize a Dirac point, i.e. a true crossing of two Bloch bands. The dynamics in the vicinity of such a crossing is described by the one-dimensional Dirac equation, which is rigorously shown beyond the tight-binding approximation. Within this framework we analyze the effects of an external potential and demonstrate numerically that it is possible to demonstrate Klein tunneling with current experimental setups.