  An ultralow-temperature binary mixture of Bose-Einstein condensates adsorbed
at an optical wall can undergo a wetting phase transition in which one of the
species excludes the other from contact with the wall. Interestingly, while
hard-wall boundary conditions entail the wetting transition to be of first
order, using Gross-Pitaevskii theory we show that first-order wetting as well
as critical wetting can occur when a realistic exponential optical wall
potential (evanescent wave) with a finite turn-on length $\lambda$ is assumed.
The relevant surface excess energies are computed in an expansion in
$\lambda/\xi_i$, where $\xi_i$ is the healing length of condensate $i$.
Experimentally, the wetting transition may best be approached by varying the
interspecies scattering length $a_{12}$ using Feshbach resonances. In the
hard-wall limit, $\lambda \rightarrow 0$, exact results are derived for the
prewetting and first-order wetting phase boundaries.
