Nonlinear standing waves in an array of coherently coupled Bose-Einstein condensates

TL;DR

This paper investigates various nonlinear standing wave solutions in coupled Bose-Einstein condensates, analyzing their stability and bifurcations, with implications for experimental realization in optical lattices.

Contribution

It introduces new families of solitary wave solutions in multi-component BECs and analyzes their stability and bifurcation behavior.

Findings

Overlapping dark solitons can decay into Josephson vortices.

Josephson vortex arrays exhibit mixed stability.

Stable solitary wave configurations exist under certain parameters.

Abstract

Stationary solitary waves are studied in an array of $M$ linearly-coupled one-dimensional Bose-Einstein condensates (BECs) by means of the Gross-Pitaevskii equation. Solitary wave solutions with the character of overlapping dark solitons, Josephson vortex - antivortex arrays, and arrays of half-dark solitons are constructed for $M>2$ from known solutions for two coupled BECs. Additional solutions resembling vortex dipoles and rarefaction pulses are found numerically. Stability analysis of the solitary waves reveals that overlapping dark solitons can become unstable and susceptible to decay into arrays of Josephson vortices. The Josephson vortex arrays have mixed stability but for all parameters we find at least one stationary solitary wave configuration that is dynamically stable. The different families of nonlinear standing waves bifurcate from one another. In particular we demonstrate that Josephson-vortex arrays bifurcate from dark soliton solutions at instability thresholds. The stability thresholds for dark soliton and Josephson-vortex type solutions are provided, suggesting the feasibility of realization with optical lattice experiments.