Nonlinear modes and symmetry breaking in rotating double-well potentials

TL;DR

This paper investigates the behavior and stability of nonlinear modes in a rotating double-well potential, revealing symmetry-breaking transitions and identifying ground states in optical and BEC systems.

Contribution

It introduces a comprehensive analysis of nonlinear modes in a rotating double-well potential, highlighting symmetry-breaking phenomena and stability in both self-focusing and defocusing regimes.

Findings

Five and four trapped modes found in SF and SDF regimes.

Symmetry-breaking transitions of subcritical and supercritical types identified.

Ground states established in both regimes.

Abstract

We study modes trapped in a rotating ring carrying the self-focusing (SF) or defocusing (SDF) cubic nonlinearity and double-well potential $\cos^{2}\theta $, where $\theta $ is the angular coordinate. The model, based on the nonlinear Schr\"{o}dinger (NLS) equation in the rotating reference frame, describes the light propagation in a twisted pipe waveguide, as well as in other optical settings, and also a Bose-Einstein condensate (BEC)trapped in a torus and dragged by the rotating potential. In the SF and SDF regimes, five and four trapped modes of different symmetries are found, respectively. The shapes and stability of the modes, and transitions between them are studied in the first rotational Brillouin zone. In the SF regime, two symmetry-breaking transitions are found, of subcritical and supercritical types. In the SDF regime, an antisymmetry-breaking transition occurs. Ground-states are identified in both the SF and SDF systems.