Composite localized modes in discretized spin–orbit-coupled Bose–Einstein condensates

Abstract

We introduce a discrete model for binary spin-orbit-coupled (SOC) Bose-Einstein condensates (BEC) trapped in a deep one-dimensional optical lattice. Two different types of the couplings are considered, with spatial derivatives acting inside each species, or between the species. The discrete system with inter-site couplings dominated by the SOC, while the usual hopping is negligible, emulates condensates composed of extremely heavy atoms, as well as those with opposite signs of the effective atomic masses in the two components. Stable localized composite states of miscible and immiscible types are constructed. The effect of the SOC on the immiscibilitymiscibility transition in the localized complexes, which emulates the phase transition between insulating and conducting states in semiconductors, is studied.

Discrete and continuum composite solitons in Bose-Einstein condensates with the Rashba spin-orbit coupling in one and two dimensions

“…It is relevant, too, to study other types of the SO coupling. In particular, analysis demonstrates that discrete 1D solitons exist as well in the system with the mixed Rashba-Dresselhaus coupling, in which case an issue of major interest is the miscibility-immiscibility transition in the SO-coupled binary condensate, in its effectively discrete form [39].…”

Nonlinear localized flat-band modes with spin-orbit coupling

“…Besides the analytically found CLS solutions, other types of stationary solutions of the nonlinear system are found below by dint of a numerical procedure based on the Powell method [21]. The linear stability analysis of all found localized solutions was performed numerically, solving linearized equations for small perturbations which determine the stability eigenvalues (EVs).…”

“…(8). To this end, the nonlinear CLSs, belonging to the predicted stability and instability regions, with added a small amplitude random perturbation [21], were used as initial conditions. In the course of the evolution, stable nonlinear CLSs keep constant phase differences between adjacent lattice sites, see Fig.…”

“…The possibility to model these settings by discrete dynamics in a deep optical-lattice potential was demonstrated, in a general form, in Refs. [20,21]. We consider two types of nonlinearities produced by interactions between atoms in the BEC, viz., intra-and inter-component ones.…”

“…In a previous work [21], we studied the effect of the SOC on the dynamics of discrete solitons in a binary BEC trapped in a deep one-dimensional (1D) optical lattice. Among new findings related to the SOC were the tunability of the transition between different types of localized complexes, provided by the SOC strength, and the opening of a minigap in the spectrum induced by the SOC.…”