Models of spin-orbit coupled oligomers

TL;DR

This paper investigates the stability and dynamics of eigenmodes in spin-orbit coupled oligomers made of binary Bose-Einstein condensates, revealing how spin-orbit coupling influences mode formation and stability across different oligomer sizes.

Contribution

It provides analytical and numerical analysis of eigenmodes in spin-orbit coupled oligomers, highlighting the impact of nonlinearity and system size on mode stability and existence.

Findings

Eigenmodes extend into nonlinear regimes with exact forms for certain oligomers.

Stability regions shrink as nonlinearity increases.

Trimer and pentamer modes are mostly stable, tetramers less so.

Abstract

We address the stability and dynamics of eigenmodes in linearly-shaped strings (dimers, trimers, tetramers, and pentamers) built of droplets of a binary Bose-Einstein condensate (BEC). The binary BEC is composed of atoms in two pseudo-spin states with attractive interactions, dressed by properly arranged laser fields, which induce the (pseudo-) spin-orbit (SO) coupling. We demonstrate that the SO-coupling terms help to create eigenmodes of particular types in the strings. Dimer, trimer, and pentamer eigenmodes of the linear system, which correspond to the zero eigenvalue (EV, alias chemical potential) extend into the nonlinear ones, keeping an exact analytical form, while tetramers do not admit such a continuation, because the respective spectrum does not contain a zero EV. Stability areas of these modes shrink with the increasing nonlinearity. Besides these modes, other types of nonlinear states, which are produced by the continuation of their linear counterparts corresponding to some nonzero EVs, are found in a numerical form (including ones for the tetramer system). They are stable in nearly entire existence regions in trimer and pentamer systems, but only in a very small area for the tetramers. Similar results are also obtained, but not displayed in detail, for hexa- and septamers.