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Simulating Dirac models with ultracold atoms in optical lattices

We present a general model allowing quantum simulation of one-dimensional Dirac models with two- and four-component spinors using ultracold atoms in driven one-dimensional tilted optical latices. The resulting Dirac physics is illustrated by one of its well-known manifestations, zitterbewegung. This general model can be extended and applied with great flexibility to more complex situations.