Many-body state and dynamic behaviour of the pair-correlation function of a small Bose-Einstein condensate confined in a ring potential

TL;DR

This paper studies the many-body quantum states and the dynamic pair-correlation functions of a small Bose-Einstein condensate in a ring potential, revealing behaviors related to quantum time crystals and the effects of atom number and interaction type.

Contribution

It provides a detailed analysis of the dynamic pair-correlation function in finite Bose-Einstein condensates, linking it to quantum time crystals and exploring the impact of atom number and interaction strength.

Findings

Periodic temporal behavior of pair-correlation function in small condensates with repulsive interactions

Disappearance of time-crystalline behavior as atom number increases

Time-crystalline behavior persists only in large atom number limit for attractive interactions

Abstract

We investigate the many-body state and the static and the dynamic behaviour of the pair-correlation function of a Bose-Einstein condensate with a finite atom number, which is confined in a quasi-one-dimensional toroidal/annular potential, both for repulsive, and for attractive interactions. We link the dynamic pair-correlation function that we evaluate with the problem of quantum time crystals. For weak repulsive interatomic interactions and a finite number of atoms the pair-correlation function shows a periodic temporal behaviour, which disappears in the limit of a large atom number, in agreement with general arguments. Finally we provide some insight into older results of attractive interactions, where the time-crystalline behaviour exists only in the limit of a large atom number.