Role of transverse excitations in the instability of Bose-Einstein condensates moving in optical lattices

TL;DR

This paper investigates how transverse excitations influence the stability of Bose-Einstein condensates in optical lattices, showing that while thresholds are unaffected, transverse modes affect the stability diagram and dynamics.

Contribution

It demonstrates that effective 1D models accurately predict instability thresholds but must include transverse excitations to fully describe the stability and dynamics.

Findings

Transverse excitations minimally affect instability thresholds.

Effective 1D models are sufficient for threshold prediction.

Transverse modes influence the stability diagram and radial dynamics.

Abstract

The occurrence of energetic and dynamical instabilities in a Bose-Einstein condensate moving in a one-dimensional (1D) optical lattice is analyzed by means of the Gross-Pitaevskii theory. Results of full 3D calculations are compared with those of an effective 1D model, the nonpolynomial Schrodinger equation, pointing out the role played by transverse degrees of freedom. The instability thresholds are shown to be scarcely affected by transverse excitations, so that they can be accurately predicted by effective 1D models. Conversely, transverse excitations turn out to be important in characterizing the stability diagram and the occurrence of a complex radial dynamics above the threshold for dynamical instability. This analysis provides a realistic framework to discuss the dissipative dynamics observed in recent experiments.