Compactons in nonlinear Schrödinger lattices with spin‒orbit coupling under strong modulation

Abstract

This study aims to demonstrate the existence of compacton matter waves in binary mixtures of Bose-Einstein condensates trapped in deep optical lattices under periodic time modulation of the interspecies nonlinear interaction, described by coupled discrete nonlinear Schrödinger (DNLS) equations, in the presence of spin-orbit coupling (SOC). Averaging the coupled DNLS equations leads to a rescaling of SOC parameter that involves the density imbalance of the two components, which gives rise to density-dependent SOC parameter that strongly influence the existence and stability of compactons. The stability of compactons is investigated by linear stability analysis and direct numerical integrations of the coupled DNLS equations. Two types of SOC interactions are considered: intraspecies and interspecies SOC. In the case of intraspecies SOC, the SOC term restricts the parameter ranges for the existence of stable stationary compactons with one-, two- and three-site structures. However, it also provides a more stringent signature of their occurrence. In particular, compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balance or nearly balanced. In the case of interspecies SOC, similar parameter ranges restrictions are observed, however the existence of compactons is limited to only of one-site and next-nearest-neighbour two-site profiles. Notably, the linear stability analysis requires a more refined gain definition to reveal that there exists a critical point for the gain in which instability occurs if exceeded. Furthermore, the number of atoms in the two components does not necessarily to be balanced for compactons to appear. Therefore, in contrast to the intraspecies SOC case, the interspecies SOC compactons cannot be suggested as a tool for indirect measurements of the number of atoms and/or the interactions between the species.