Bose-Einstein condensates with attractive interactions on a ring

TL;DR

This paper investigates phase transitions in a quasi-one-dimensional attractive Bose-Einstein condensate confined in a ring, revealing a transition from uniform to localized states as interaction strength increases, using mean-field and diagonalization methods.

Contribution

It introduces a combined mean-field and diagonalization approach to analyze phase transitions in attractive BECs on a ring, highlighting the transition mechanism.

Findings

System undergoes a phase transition from uniform to localized state.

Transition occurs as the coupling constant magnitude increases.

Both mean-field and diagonalization methods confirm the transition.

Abstract

Considering an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap, we find that the system undergoes a phase transition from a uniform to a localized state, as the magnitude of the coupling constant increases. Both the mean-field approximation, as well as a diagonalization scheme are used to attack the problem.