Interacting Bose gases in quasi-one dimensional optical lattices

TL;DR

This paper investigates the phase transitions and excitations in coupled one-dimensional bosonic tubes in optical lattices, revealing the emergence of anisotropic BEC, gapped modes, and Mott insulator transitions influenced by intertube coupling and periodic potentials.

Contribution

It provides a theoretical analysis of phase transitions, excitations, and phase diagrams in coupled 1D bosonic systems with optical lattices, including effects of periodic potentials and finite tube sizes.

Findings

Transition from incoherent Luttinger liquids to anisotropic BEC

Identification of a gapped mode alongside Goldstone mode

Deconfinement transition between Mott insulators and BEC

Abstract

We study a two-dimensional array of coupled one-dimensional (1D) tubes of interacting bosons. Such systems can be produced by loading ultra-cold atoms in anisotropic optical lattices. We investigate the effects of coupling the tubes via hopping of the bosons (i.e. Josephson coupling). In the absence of a periodic potential along the tubes, or when such potential is incommensurate with the boson density, the system undergoes a transition from an array of incoherent Tomonaga-Luttinger liquids at high temperature to an anisotropic Bose-Einstein condensate (BEC), at low temperature. We determine the transition temperature and long wave-length excitations of the BEC. In addition to the usual gapless (Goldstone) mode found in standard superfluids, we also find a gapped mode associated with fluctuations of the amplitude of the order parameter. When a commensurate periodic potential is applied along the tubes, they can become 1D Mott insulators. Intertube hopping leads to a deconfinement quantum phase transition between the 1D Mott insulators and the anisotropic BEC. We also take into account the finite size of the gas tubes as realized in actual experiments. We map out the phase diagram of the quasi-1D lattice and compare our results with the existing experiments on such systems.