Synthesizing arbitrary dispersion relations in a modulated tilted optical lattice

• URL: http://arxiv.org/abs/2107.11268v1
• Date: Fri, 23 Jul 2021 14:35:35 GMT
• Title: Synthesizing arbitrary dispersion relations in a modulated tilted optical lattice
• Authors: Jean Claude Garreau and V\'eronique Zehnl\'e
• Abstract summary: Dispersion relations are fundamental characteristics of the dynamics of quantum and wave systems. We show that adding a slow chirp to the lattice modulation allows one to reconstruct the dispersion relation from dynamical quantities. We generalize the technique to higher dimensions, and generate graphene-like Dirac points and flat bands in two dimensions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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