Nonlinear modes in binary bosonic condensates with the pseudo-spin-orbital coupling

TL;DR

This paper explores nonlinear modes in binary Bose-Einstein condensates with spin-orbit and Zeeman couplings, revealing stable multi-domain structures and symmetry-breaking phenomena influenced by external fields and interactions.

Contribution

It introduces analytical and numerical analysis of stable multi-domain and asymmetric modes in SO-coupled BECs, highlighting the effects of linear couplings and external fields.

Findings

Multi-domain-wall structures are stable.

Single-domain-wall structures are unstable.

Zeeman splitting induces symmetry breaking.

Abstract

We consider a binary Bose-Einstein condensate (BEC) with nonlinear repulsive interactions and linear spin-orbit (SO) and Zeeman-splitting couplings. In the presence of the trapping harmonic-oscillator (HO) potential, we report the existence of even, odd, and asymmetric spatial modes. They feature alternating domains with opposite directions of the pseudo-spin, i.e., anti-ferromagnetic structures, which is explained by the interplay of the linear couplings, HO confinement, and repulsive self-interaction. The number of the domains is determined by the strength of the SO coupling. The modes are constructed analytically in the weakly nonlinear system. The dynamical stability of the modes is investigated by means of the Bogoliubov-de Gennes equations and direct simulations. A notable result is that the multi-domain-wall (DW) structures are stable, alternating between odd and even shapes, while the simplest single-DW structure is unstable. Thus, the system features a transition to the complex ground states under the action of the SO coupling. The addition of the Zeeman splitting transforms the odd modes into asymmetric ones via spontaneous symmetry breaking. The results suggest possibilities for switching the binary system between states with opposite (pseudo) magnetization by external fields, and realization of similar stable states and dynamical effects in solid-state and nonlinear-optical settings emulated by the SO-coupled BECs.