Cold atoms in real-space optical lattices

Details Cold atoms in real-space optical lattices Cold atoms in real-space optical lattices

2006-12-06

arxiv.org/abs/cond-mat/0612170v1

Phys. Rev. A 76, 013611 (2007)

Physics

Condensed Matter

Other Condensed Matter

27 pages, 4 figures; [version minus figures published]

Scientific paper

10.1103/PhysRevA.76.013611

Cold atoms in optical lattices are described in {\it real space} by multi-orbital mean-field Ans\"atze. In this work we consider four typical systems: (i) spinless identical bosons, (ii) spinor identical bosons (iii), Bose-Bose mixtures, and (iv) Bose-Fermi mixtures and derive in each case the corresponding multi-orbital mean-field energy-functional and working equations. The notions of {\it dressed} Wannier functions and Wannier spinors are introduced and the equations defining them are presented and discussed. The dressed Wannier functions are the set of orthogonal, translationally-equivalent orbitals which minimizes the energy of the Hamiltonian including boson-boson (particle-particle) interactions. Illustrative examples of dressed Wannier functions are provided for spinless bosonic atoms and mixtures in one-dimensional optical lattices.

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