Cross-dimensional phase transition from an array of 1D Luttinger liquids to a 3D Bose-Einstein condensate

TL;DR

This study investigates the transition from a 2D array of 1D Bose gases to a 3D Bose-Einstein condensate, revealing how increased coupling induces a phase change and comparing experimental phase diagrams with theoretical models.

Contribution

It provides the first detailed experimental phase diagram of coupled 1D Bose gases transitioning to a 3D condensate, highlighting the effects of coupling strength and interactions.

Findings

Phase transition occurs at large positive chemical potential values.

Coupling strength increases shift the transition point.

Results align with theoretical predictions for low-dimensional systems.

Abstract

We study the thermodynamic properties of a 2D array of coupled one-dimensional Bose gases. The system is realized with ultracold bosonic atoms loaded in the potential tubes of a two-dimensional optical lattice. For negligible coupling strength, each tube is an independent weakly interacting 1D Bose gas featuring Tomonaga Luttinger liquid behavior. By decreasing the lattice depth, we increase the coupling strength between the 1D gases and allow for the phase transition into a 3D condensate. We extract the phase diagram for such a system and compare our results with theoretical predictions. Due to the high effective mass across the periodic potential and the increased 1D interaction strength, the phase transition is shifted to large positive values of the chemical potential. Our results are prototypical to a variety of low-dimensional systems, where the coupling between the subsystems is realized in a higher spatial dimension such as coupled spin chains in magnetic insulators.