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

TL;DR

This paper presents a method to construct maximally localized Wannier functions for one-dimensional double-well periodic potentials, enabling efficient mapping of continuous ultracold atom systems to discrete lattice models.

Contribution

It introduces a specific two-step gauge transformation approach for band-mixing Wannier functions in double-well systems, extending prior methods to handle complex symmetry properties.

Findings

The method effectively computes tight-binding coefficients for various double-well configurations.

Localization properties depend on the symmetry and parity-breaking of the double-well potential.

The approach is applicable within experimentally feasible parameter ranges.

Abstract

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.