Stabilization of Multidimensional Solitons by Spin–Orbit Coupling (SOC)

Abstract

The possibility of using spinorbit coupling (SOC) for the stabilization of 2D solitons in two-component BEC was first predicted by Sakaguchi et al. [Phys. Rev. E 89, 032920 (2014)]. Then, a possibility to create metastable 3D solitons in the same setting was reported by Zhang et al. [Phys. Rev. Lett. 115, 253902 (2015)]. Many interesting theoretical results were predicted in subsequent works, although they have not yet been realized in the experiment. In this chapter, the theoretical predictions are summarized, following, in particular, review articles by Sakaguchi and Malomed [Phys. Rev. A 97, 013607 (2018)] and by Malomed [Europhys. Lett. 122, 36001 (2018)]. Basic results included in the chapter represent absolutely stable 2D two-component solitons (ground states) of the semi-vortex (SV) and mixed-mode (MM) types, supported by the SOC in the Rashba and combined Rashba–Dresselhaus forms, as well as mobility of such solitons and collisions between them. The SVs are compound states with zero vorticity in one component and vorticity S = ±1 in the other, while MMs mix the zero-vorticity terms and ones with S = ±1 in both components. Also considered are effects of the Zeeman splitting (ZS) between the components—in particular, stable 2D gap solitons of the SV type, produced by the interplay of the ZS and SOC, while the kinetic-energy terms may be neglected. Finally, it is demonstrated that the SOC maintains three-dimensional metastable solitons, of both the SV and MM types, in two-component BEC with the attractive intrinsic nonlinearity.