Analytical Mean-Field Approach to the Phase Diagram
of Ultracold Bosons in Optical Superlattices

P. Buonsante1, V. Penna1, *, and A. Vezzani2

1 Dipartimento di Fisica and Unità INFM, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy


2 Dipartimento di Fisica & Unità INFM, Università degli Studi di Parma, Parco Area delle Scienze 7/a, I-43100 Parma, Italy

Received September 29, 2004

Abstract—We report a multiple-site mean-field analysis of the zero-temperature phase diagram for ultracold
bosons in realistic optical superlattices. The system of interacting bosons is described by a Bose–Hubbard
model whose site-dependent parameters reflect the nontrivial periodicity of the optical superlattice. An analytic
approach is formulated based on an analysis of the stability of a fixed point of the map defined by the self-con-
sistency condition inherent in the mean-field approximation. The experimentally relevant case of the two-period
one-dimensional superlattice is briefly discussed. In particular, it is shown that, for a special choice of the super-
lattice parameters, the half-filling insulator domain features an unusual loophole shape that the single-site
mean-field approach fails to capture.

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