Hidden order in bosonic gases confined in one dimensional optical lattices

We analyze the effective Hamiltonian arising from a suitable power series expansion of the overlap integrals of Wannier functions for confined bosonic atoms in a 1d optical lattice. For certain constraints between the coupling constants, we construct an explicit relation between such an effective bosonic Hamiltonian and the integrable spin-$S$ anisotropic Heisenberg model. Therefore the former results to be integrable by construction. The field theory is governed by an anisotropic non linear $\sigma$-model with singlet and triplet massive excitations; such a result holds also in the generic non-integrable cases. The criticality of the bosonic system is investigated. The schematic phase diagram is drawn. Our study is shedding light on the hidden symmetry of the Haldane type for one dimensional bosons.Comment: 5 pages; 1 eps figure. Revised version, to be published in New. J. Phy

On the spin-liquid phase of one dimensional spin-1 bosons

We consider a model of one dimensional spin-1 bosons with repulsive density-density interactions and antiferromagnetic exchange. We show that the low energy effective field theory is given by a spin-charge separated theory of a Tomonaga-Luttinger Hamiltonian and the O(3) nonlinear sigma model describing collective charge and spin excitations respectively. At a particular ratio of the density-density to spin-spin interaction the model is integrable, and we use the exact solutions to provide an independent derivation of the low energy effective theory. The system is in a superfluid phase made of singlet pairs of bosons, and we calculate the long-distance asymptotics of certain correlation functions.Comment: 17 page

The physics of dipolar bosonic quantum gases

This article reviews the recent theoretical and experimental advances in the study of ultracold gases made of bosonic particles interacting via the long-range, anisotropic dipole-dipole interaction, in addition to the short-range and isotropic contact interaction usually at work in ultracold gases. The specific properties emerging from the dipolar interaction are emphasized, from the mean-field regime valid for dilute Bose-Einstein condensates, to the strongly correlated regimes reached for dipolar bosons in optical lattices.Comment: Review article, 71 pages, 35 figures, 350 references. Submitted to Reports on Progress in Physic