Winding number dependence of Bose-Einstein condensates in a ring-shaped lattice

TL;DR

This paper investigates how the winding number affects the stationary states of a Bose-Einstein condensate in a ring-shaped lattice, revealing distinct regimes based on barrier height and particle number.

Contribution

It provides a detailed analysis of energy and angular momentum dependencies on winding number in different barrier regimes, highlighting new behaviors in BEC states.

Findings

Metastable vortex states exist up to a maximum winding number at low barriers.

Energy and angular momentum depend linearly/quadratically on winding number at low barriers.

At high barriers, energy and angular momentum vary sinusoidally with winding number.

Abstract

We study the winding number dependence of the stationary states of a Bose-Einstein condensate in a ring-shaped lattice. The system is obtained by confining atoms in a toroidal trap with equally spaced radial barriers. We calculate the energy and angular momentum as functions of the winding number and the barrier height for two quite distinct particle numbers. In both cases we observe two clearly differentiated regimes. For low barriers, metastable vortex states are obtained up to a maximum winding number which depends on the particle number and barrier height. In this regime, the angular momentum and energy show, respectively, almost linear and quadratic dependences on the winding number. For large barrier heights, on the other hand, stationary states are obtained up to a maximum winding number which depends only on the number of lattice sites, whereas energy and angular momentum are shown to be sinusoidal functions of the winding number.