Dynamics of the Formation of Bright Solitary Waves of Bose-Einstein Condensates in Optical Lattices

TL;DR

This paper investigates the formation and stability of bright solitary waves in Bose-Einstein condensates within optical lattices, highlighting the role of dissipation, wavepacket width, and lattice geometry in their dynamics.

Contribution

It provides a detailed numerical analysis of solitary wave formation in ring-shaped optical lattices, emphasizing dissipation mechanisms and stability criteria linked to energy band properties.

Findings

Condensate radiation is key in relaxation to self-trapped states.

Stability depends on specific wavepacket widths in reciprocal space.

Solitary waves are unstable under collisions, indicating non-solitonic behavior.

Abstract

We present a detailed description of the formation of bright solitary waves in optical lattices. To this end, we have considered a ring lattice geometry with large radius. In this case, the ring shape does not have a relevant effect in the local dynamics of the condensate, while offering a realistic set up to implement experiments with conditions usually not available with linear lattices (in particular, to study collisions). Our numerical results suggest that the condensate radiation is the relevant dissipative process in the relaxation towards a self-trapped solution. We show that the source of dissipation can be attributed to the presence of higher order dispersion terms in the effective mass approach. In addition, we demonstrate that the stability of the solitary solutions is linked with particular values of the width of the wavepacket in the reciprocal space. Our study suggests that these critical widths for stability depend on the geometry of the energy band, but are independent of the condensate parameters (momentum, atom number, etc.). Finally, the non-solitonic nature of the solitary waves is evidenced showing their instability under collisions.