Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials
arXiv:1112.2845 · doi:10.1088/1367-2630/14/5/055004
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.
21 pages, 10 figures; revised version; corrected Figs. 2 and 8; added references
References in corpus (14)
- Many-Body Physics with Ultracold Gases
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
- A lattice of double wells for manipulating pairs of cold atoms
- Cold Bosons in Optical Lattices
- Interference pattern and visibility of a Mott insulator
- Ultracold Fermions in a Graphene-Type Optical Lattice
- d-wave resonating valence bond states of fermionic atoms in optical lattices
- Quantum Many-Body Dynamics of Coupled Double-Well Superlattices
- Quantum Transport of Bosonic Cold Atoms in Double Well Optical Lattices
- Quantum phases of bosons in double-well optical lattices
- Delocalization and Heisenberg's uncertainty relation
- Cold atoms in double-well optical lattices
- Many-body Landau-Zener Transition in Cold Atom Double Well Optical Lattices
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