Interfaces between Bose–Einstein and Tonks–Girardeau atomic gases

Weconsider one-dimensional mixtures of an atomic Bose–Einstein condensate (BEC) and Tonks– Girardeau (TG) gas. The mixture is modeled by a coupled system of the Gross–Pitaevskii equation for the BEC and the quintic nonlinear Schrödinger equation for theTG component. An immiscibility condition for the binary system is derived in a general form. Under this condition, three types of BEC– TGinterfaces are considered: domain walls (DWs) separating the two components; bubble-drops (BDs), in the form of a drop of one component immersed into the other (BDs may be considered as bound states of twoDWs); and bound states of bright and dark solitons (BDSs). The same model applies to the copropagation of two optical waves in a colloidal medium. The results are obtained by means of systematic numerical analysis, in combination with analytical Thomas–Fermi approximations (TFAs). Using both methods, families ofDWstates are produced in a generic form. BD complexes exist solely in the form of a TGdrop embedded into the BEC background. On the contrary, BDSs exist as bound states of TGbright and BEC dark components, and vice versa.