Stable two-dimensional soliton complexes in Bose-Einstein condensates with helicoidal spin-orbit coupling

TL;DR

This paper demonstrates that two-dimensional spinor Bose-Einstein condensates with helicoidal spin-orbit coupling can support stable soliton states and complexes, with their properties influenced by the SOC modulation and band spectrum.

Contribution

It introduces the existence and stability of fundamental solitons and bound complexes in 2D BECs with helicoidal SOC, revealing their spectral and stability characteristics.

Findings

Stable fundamental solitons exist above a threshold norm.

Bound soliton complexes can be stable, especially dipoles and quadrupoles.

Chemical potential behaviors are linked to the band spectrum and SOC strength.

Abstract

We show that attractive two-dimensional spinor Bose-Einstein condensates with helicoidal spatially periodic spin-orbit coupling (SOC) support a rich variety of stable fundamental solitons and bound soliton complexes. Such states exist with chemical potentials belonging to the semi-infinite gap in the band spectrum created by the periodically modulated SOC. All these states exist above a certain threshold value of the norm. The chemical potential of fundamental solitons attains the bottom of the lowest band, whose locus is a ring in the space of Bloch momenta, and the radius of the ring is a non-monotonous function of the SOC strength. The chemical potential of soliton complexes does not attain the band edge. The complexes are bound states of several out-of-phase fundamental solitons whose centers are placed at local maxima of the SOC-modulation phase. In this sense, the impact of the helicoidal SOC landscape on the solitons is similar to that of a periodic two-dimensional potential. In particular, it can compensate repulsive forces between out-of-phase solitons, making their bound states stable. Extended stability domains are found for complexes built of two and four solitons (dipoles and quadrupoles, respectively). They are typically stable below a critical value of the chemical potential.