Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials

Details Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials

2011-12-13

arxiv.org/abs/1112.2845v2

Physics

Condensed Matter

Quantum Gases

21 pages, 10 figures; revised version; corrected Figs. 2 and 8; added references

Scientific paper

We discuss a method for constructing generalized Wannier functions that are maximally localized at the minima of a one-dimensional periodic potential with a double-well per unit cell. By following the approach of (Marzari M and Vanderbilt D 1997 Phys. Rev. B 56, 12847), we consider a set of band-mixing Wannier functions with minimal spread, and design a specific two-step gauge transformation of the Bloch functions for a composite two band system. This method is suited to efficiently compute the tight-binding coefficients needed for mapping the continuous system to a discrete lattice model. Their behaviour is analyzed here as a function of the symmetry properties of the double-well (including the possibility of parity-breaking), in a range of feasible experimental parameters.

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