Nonlinear waves in coherently coupled Bose-Einstein condensates

TL;DR

This paper investigates how nonlinearity influences elementary excitations in a two-component Bose-Einstein condensate with coherent coupling, revealing stability properties and deriving effective equations like KdV and Gardner equations.

Contribution

It provides a detailed analysis of nonlinear effects on excitations in coherently coupled BECs, including stability conditions and effective nonlinear wave equations.

Findings

Upper branch exhibits modulational instability stabilized by resonance

Lower branch remains stable under studied conditions

Derived KdV and Gardner equations for weak nonlinearity regimes

Abstract

We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the elementary excitations. The spectrum has two branches which are affected in different ways. The upper branch experiences a modulational instability which is stabilized by a long wave-short wave resonance with the lower branch. The lower branch is stable. In the limit of weak nonlinearity and small dispersion it is described by a Korteweg-de Vries equation or by the Gardner equation, depending on the value of the parameters of the system.