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

Dec, 2011
21 pages
Published in:
  • New J.Phys. 14 (2012) 055004
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Abstract: (arXiv)
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.
Note:
  • 21 pages, 10 figures; revised version; corrected Figs. 2 and 8; added references
  • 67.85.Hj
  • 03.75.Lm
  • 03.65.Vf