Symmetry breaking of localized discrete matter waves induced by spin–orbit coupling

We study localized nonlinear excitations of a dilute Bose–Einstein condensate (BEC) with spin–orbit coupling in a deep optical lattice (OL). For this we introduce a tight-binding model that includes the spin–orbit coupling (SOC) at the discrete level in the form of a generalized discrete nonlinear Schrödinger equation. Existence and stability of discrete solitons of different symmetry types is demonstrated. Quite interestingly, we find three distinctive regions in which discrete solitons undergo spontaneously symmetry breaking, passing from on-site to inter-site and to asymmetric, simply by varying the interatomic interactions. Existence ranges of discrete solitons with inter-site symmetry depend on SOC and shrink to zero as the SOC parameter is increased. Asymmetric discrete solitons appear as novel excitations specific of the SOC. Possible experimental implementation of these results is briefly discussed.