Synthesizing arbitrary dispersion relations in a modulated tilted optical lattice
arXiv:2107.11268 · doi:10.1103/PhysRevA.105.013318
Abstract
Dispersion relations are fundamental characteristics of the dynamics of quantum and wave systems. In this work we introduce a simple technique to generate arbitrary dispersion relations in a modulated tilted lattice. The technique is illustrated by important examples: the Dirac, Bogoliubov and Landau dispersion relations (the latter exhibiting the roton and the maxon). We show that adding a slow chirp to the lattice modulation allows one to reconstruct the dispersion relation from dynamical quantities. Finally, we generalize the technique to higher dimensions, and generate graphene-like Dirac points and flat bands in two dimensions.
arXiv comment9 pages, 6 color figures, submitted to Phys. Rev. A
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