Transition from 3D to 1D in Bose Gases at Zero Temperature

TL;DR

This paper explores how strong transverse confinement causes a Bose gas to transition from three-dimensional to one-dimensional behavior, analyzing the physical signatures and phase diagram across regimes.

Contribution

It introduces a generalized Lieb-Liniger model with a variational approach to describe the dimensional crossover in Bose gases under confinement.

Findings

Sound velocity and mode frequency indicate the transition regime.

Derived phase diagram includes uniform, soliton, and collapsed phases.

Analyzed effects of negative scattering length in toroidal traps.

Abstract

We investigate the effects of dimensional reduction in Bose gases induced by a strong harmonic confinement in the transverse cylindric radial direction. By using a generalized Lieb-Liniger theory, based on a variational treatment of the transverse width of the Bose gas, we analyze the transition from a 3D Bose-Einstein condensate to the 1D Tonks-Girardeau gas. The sound velocity and the frequency of the lowest compressional mode give a clear signature of the regime involved. We study also the case of negative scattering length deriving the phase diagram of the Bose gas (uniform, single soliton, multi soliton and collapsed) in toroidal confinement.