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