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

Abstract

The use of ultracold quantum gases, in particular bosonic and fermionic condensates, for simulating fundamental effects originating in condensed-matter physics has drawn much interest [1]. One of these effects is the spin-orbit coupling (SOC). This effect plays a major role in many phenomena and applications, including spin and anomalous Hall effects [2], topological insulators [3], spintronics [4], etc. In contrast to the complex picture found in solids, the experimental and theoretical description of SOC effects in Bose-Einstein condensate (BEC) is much simpler [5]. This has motivated our study of the impact of SOC on the immiscibility-miscibility transition in the localized complexes in BEC, which can emulate the phase transition between insulating and conducting states in semiconductor. For this purpose, we introduce a discrete model for binary SO-coupled BEC trapped in a deep one-dimensional optical lattice [6]. We consider two different types of coupling, with spatial derivatives acting inside each species, and between the species. Stable localized composite states of miscible and immiscible types are found to exist for both types of coupling. We also study how the transition between miscible and immiscible type of localized complexes depends on the SOC strength. Particularly interesting are the applications of our model to the SOC binary condensates built of infinitely heavy atoms and the binary BEC with effective atomic masses which have opposite signs.