Wave modes trapped in rotating nonlinear potentials

TL;DR

This paper investigates various stable wave modes trapped in a rotating nonlinear potential ring, revealing multiple mode types and stability conditions in different nonlinear regimes, with applications to optics and Bose-Einstein condensates.

Contribution

It introduces a comprehensive analysis of trapped wave modes in a rotating nonlinear ring with modulated nonlinearity, identifying multiple stable modes and their transitions.

Findings

Multiple stable mode types identified in each nonlinear regime.

Analytical boundaries between symmetric and asymmetric modes derived.

Mode shapes and stability depend on the rotation and nonlinearity type.

Abstract

We study modes trapped in a rotating ring with the local strength of the nonlinearity modulated as cos(2\theta), where \theta is the azimuthal angle. This modulation pattern may be of three different types: self-focusing (SF), self-defocusing (SDF), and alternating SF-SDF. The model, based on the nonlinear Schrodinger (NLS) equation with periodic boundary conditions, applies to the light propagation in a twisted pipe waveguide, and to a Bose-Einstein condensate (BEC) loaded into a toroidal trap, under the action of the rotating nonlinear pseudopotential induced by means of the Feshbach resonance in an inhomogeneous external field. In the SF, SDF, and alternating regimes, four, three, and five different types of stable trapped modes are identified, respectively: even, odd, second-harmonic (2H), symmetry-breaking, and 2H-breaking ones. The shapes and stability of these modes, together with transitions between them, are investigated in the first rotational Brillouin zone. Ground-state modes are identified in each regime. Boundaries between symmetric and asymmetric modes are also obtained in an analytical form, by of a two-mode approximation.