Cold atoms in real-space optical lattices

TL;DR

This paper develops a multi-orbital mean-field framework for describing various cold atom systems in real-space optical lattices, introducing dressed Wannier functions and providing illustrative examples.

Contribution

It derives energy functionals and equations for four types of cold atom systems, introducing dressed Wannier functions and spinors for the first time.

Findings

Dressed Wannier functions minimize energy including interactions.

Explicit equations for multi-orbital mean-field states.

Examples for spinless bosons and mixtures in 1D lattices.

Abstract

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.