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

Abstract

Within Gross-Pitaevskii (GP) theory we derive the interface potential $V(\ensuremath{\ell})$ which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance $\ensuremath{\ell}$. Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore nonequilibrium properties by using $\ensuremath{\ell}$ as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, $V(\ensuremath{\ell})$ for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, $V(\ensuremath{\ell})$ is independent of $\ensuremath{\ell}$. This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using $V(\ensuremath{\ell})$ we study the three-phase contact line where the interface meets the wall under a contact angle $\ensuremath{\theta}$. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension $\ensuremath{\tau}$. Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, $\ensuremath{\tau}$ does not approach a nonzero positive constant for $\ensuremath{\theta}\ensuremath{\rightarrow}0$, but instead approaches zero (from below) in the manner $\ensuremath{\tau}\ensuremath{\propto}\ensuremath{-}\ensuremath{\theta}$ as would be expected for a critical wetting transition. This hybrid character of $\ensuremath{\tau}$ is a consequence of the absence of a barrier in $V(\ensuremath{\ell})$ at wetting. For a typical $V(\ensuremath{\ell})=\mathcal{S}\phantom{\rule{0.16em}{0ex}}exp(\ensuremath{-}\ensuremath{\ell}/\ensuremath{\xi})$, with $\mathcal{S}$ the spreading coefficient and $\ensuremath{\xi}$ a decay length, we conjecture that $\ensuremath{\tau}=\ensuremath{-}2\phantom{\rule{0.16em}{0ex}}(1\ensuremath{-}ln2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma}\phantom{\rule{0.16em}{0ex}}\ensuremath{\xi}\phantom{\rule{0.16em}{0ex}}sin\ensuremath{\theta}$ is exact within GP theory, with $\ensuremath{\gamma}$ the interfacial tension and $0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}$.