Crystalline phase for one-dimensional ultra-cold atomic bosons

TL;DR

This paper investigates the phase transition of one-dimensional ultra-cold bosonic gases from a Luttinger liquid to a crystalline phase, considering the effects of confinement-induced resonance and optical lattice interactions.

Contribution

It introduces a novel analysis combining sine-Gordon and Hubbard models to map the phase diagram of strongly interacting bosons in one dimension.

Findings

Identification of a phase transition to a crystalline phase

Demonstration of the role of effective range in interactions

Mapping of the phase diagram with optical lattice effects

Abstract

We study cold atomic gases with a contact interaction and confined into one-dimension. Crossing the confinement induced resonance the correlation between the bosons increases, and introduces an effective range for the interaction potential. Using the mapping onto the sine-Gordon model and a Hubbard model in the strongly interacting regime allows us to derive the phase diagram in the presence of an optical lattice. We demonstrate the appearance of a phase transition from a Luttinger liquid with algebraic correlations into a crystalline phase with a particle on every second lattice site.