Static and rotating domain-wall crosses in Bose-Einstein condensates

TL;DR

This paper introduces and analyzes stable cross-shaped domain wall patterns in two-dimensional Bose-Einstein condensates, including their stability, dynamics, and potential optical applications, expanding understanding of multi-component BEC structures.

Contribution

It presents the first detailed study of stable cross and propeller domain wall configurations in 2D BECs, including stability regions and dynamics, with implications for optical systems.

Findings

Stable cross patterns exist up to zero immiscibility parameter.

Propeller structures are stable in rotating traps.

Unstable multi-DW intersections evolve into vortex-antivortex arrays.

Abstract

For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by intersection of two domain walls (DWs) separating immiscible species, with opposite signs of the wave functions in each pair of sectors filled by the same species. The cross pattern remains stable up to the zero value of the immiscibility parameter $|\Delta |$, while simpler rectilinear (quasi-1D) DWs exist only for values of $|\Delta |$ essentially exceeding those in BEC mixtures (two spin states of the same isotope) currently available to the experiment. Both symmetric and asymmetric cross configurations are investigated, with equal or different numbers $N_{1,2}$ of atoms in the two species. In rotating traps, ``propellers'' (stable revolving crosses) are found too. A full stability region for of the crosses and propellers in the system's parameter space is identified, unstable crosses evolving into arrays of vortex-antivortex pairs. Stable rotating rectilinear DWs are found too, at larger vlues of $|\Delta |$. All the patterns produced by the intersection of three or more DWs are unstable, rearranging themselves into ones with two DWs. Optical propellers are also predicted in a twisted nonlinear photonic-crystal fiber carrying two different wavelengths or circular polarizations, which can be used for applications to switching and routing.