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We study superfluid (SF) states of strongly interacting Bose-Bose mixtureswith equal mass and intra-component interaction in optical lattices both in thepresence and absence of a barrier potential (BP). We show that the SF orderparameters obey the two-component nonlinear Schroedinger equation (NLSE) withnot only cubic but also quintic nonlinearity in the vicinity of the first-ordertransitions to the Mott insulators with even fillings. In the case of no BP, weanalyze solitary-wave (SW) solutions of the cubic-quintic NLSE. When the SFstate changes from a ground state to a metastable one, a standard dark SW turnsinto a bubble-like dark SW, which has a non-vanishing density dip and no piphase kink even in the case of a standing SW. It is shown that the former andlatter SW are dynamically unstable against an out-of-phase fluctuation and anin-phase fluctuation, respectively, and the dynamical instabilities areweakened when one approaches the transition point. We find that the size andthe inertial mass of the SW diverge at the first-order transition point. Wesuggest that the divergence of the inertial mass may be detected throughmeasurement of the relation between the velocity and the phase jump of the SW.In the presence of BP, we reveal that when the barrier strength exceeds acertain critical value, the SF state that was metastable without the barrier isdestabilized towards complete disjunction of the SF. The presence of thecritical BP strength indicates that the strong BP qualitatively changes thecriticality near the metastability limit of the SF state. We derive criticalbehaviors of the density, the compressibility, and the critical current nearthe metastability limit induced by the BP. It is also found that the relationbetween the supercurrent and the phase jump across the BP exhibits a peculiarbehavior, owing to the non-topological nature of the bubble-like SW.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Cubic-quintic nonlinearity in superfluid Bose-Bose mixtures in optical  lattices: Heavy solitary waves, barrier-induced criticality, and  current-phase relations