Interfaces between Bose–Einstein and Tonks–Girardeau atomic gases

Abstract

We consider 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 the TG component. An immiscibility condition for the binary system is derived in a general form. Under this condition, three types of BEC–TG interfaces 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 two DWs); 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 of DW states are produced in a generic form. BD complexes exist solely in the form of a TG drop embedded into the BEC background. On the contrary, BDSs exist as bound states of TG bright and BEC dark components, and vice versa.

Keywords

• domain wall
• immiscibility
• dark–bright soliton
• colloidal waveguide
• cubic–quintic nonlinearity
• Thomas–Fermi approximation