Bound states in Bose-Einstein condensates with radially-periodic spin-orbit coupling

TL;DR

This paper explores how radially-periodic spin-orbit coupling in Bose-Einstein condensates creates localized bound states and gap solitons, revealing a new mechanism for linear and nonlinear localization in quantum gases.

Contribution

It demonstrates that spatially periodic SOC can support localized modes and gap solitons in BECs, a phenomenon not observed with conventional periodic potentials.

Findings

Localized modes exist in spectral gaps due to SOC modulation.

Stable vortex gap solitons are found for vorticity from -2 to 3.

A new instability mechanism involving shifted complex eigenvalues is identified.

Abstract

We consider Bose-Einstein condensate (BEC) subject to the action of spin-orbit-coupling (SOC) periodically modulated in the radial direction. In contrast to the commonly known principle that periodic potentials do not create bound states, the binary BEC maintains multiple localized modes in the linear limit, with their chemical potential falling into spectral gaps of the (numerically found) radial band structure induced by the spatial modulation of the SOC. In the presence of the repulsive nonlinearity, the SOC modulation supports fundamental gap solitons of the semi-vortex types, as well as higher-order vortex gap solitons. The localization degree and stability of the gap solitons strongly depend on the location of their chemical potential in the gap. Stability intervals for vortex gap solitons in a broad range of the intrinsic vorticity, from -2 to 3, are identified. Thus, the analysis reveals the previously unexplored mechanism of linear and nonlinear localization provided by the spatially periodic modulation of SOC, which may be extended to other settings, such as those for optical beams and polaritons. Unlike the commonly known quartets of eigenvalues for small perturbations, in the present system the instability is accounted for by shifted complex eigenvalue pairs.