# Bose-Einstein condensate confined in a 1D ring stirred with a rotating delta link

## TL;DR

This paper investigates the stationary states, stability, and adiabatic manipulation of a Bose-Einstein condensate in a 1D ring with a rotating delta potential, revealing complex soliton and vortex structures.

## Contribution

It provides analytical solutions and stability analysis for the condensate with a rotating delta, introducing new methods to control solitons and vortices in ring traps.

## Key findings

- Energy spectrum exhibits swallowtail structures.
- Analytical wave functions derived using Jacobi elliptic functions.
- Proposed adiabatic cycles enable creation of vortices with arbitrary angular momentum.

## Abstract

We consider a Bose-Einstein condensate with repulsive interactions confined in a 1D ring where a Dirac delta is rotating at constant speed. The spectrum of stationary solutions in the delta comoving frame is analyzed in terms of the nonlinear coupling, delta velocity, and delta strength, which may take positive and negative values. It is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting in bright solitons, gray and dark solitonic trains, and vortices. Analytical expressions in terms Jacobi elliptic functions are provided for the wave functions and chemical potentials. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray solitons and vortices of arbitrary quantized angular momenta are obtained from the ground state by setting and unsetting a rotating delta.