Interface potential and line tension for Bose-Einstein condensate mixtures near a hard wall

Within Gross-Pitaevskii (GP) theory we derive the interface potential V (e) which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance e. Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore nonequilibrium properties by using e as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, V (e) for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, V (e) is independent of e. This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using V (e) we study the three-phase contact line where the interface meets the wall under a contact angle 0. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension v. Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, v does not approach a nonzero positive constant for 0 -> 0, but instead approaches zero (from below) in the manner v proportional to -0 as would be expected for a critical wetting transition. This hybrid character of v is a consequence of the absence of a barrier in V (e) at wetting. For a typical V (e) = S exp(-e/xi), with S the spreading coefficient and xi a decay length, we conjecture that v = -2 (1 - ln 2) gamma xi sin 0 is exact within GP theory, with gamma the interfacial tension and 0 0 7t