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arXiv:1409.6485 · Physical Review A

Critical wetting, first-order wetting, and prewetting phase transitions in binary mixtures of Bose-Einstein condensates

Bert Van Schaeybroeck, Joseph O. Indekeu

Published Jan 23, 2015• 28 citations
arXivHTMLPDF

Abstract

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 $\ensuremath{\lambda}$ is assumed. The relevant surface excess energies are computed in an expansion in $\ensuremath{\lambda}/{\ensuremath{\xi}}_{i}$, where ${\ensuremath{\xi}}_{i}$ 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, $\ensuremath{\lambda}\ensuremath{\rightarrow}0$, exact results are derived for the prewetting and first-order wetting phase boundaries.

DOI
10.1103/physreva.91.013626

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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 \ensuremathλ\ensuremath{\lambda}\ensuremathλ is assumed. The relevant surface excess energies are computed in an expansion in \ensuremathλ/\ensuremathξi\ensuremath{\lambda}/{\ensuremath{\xi}}_{i}\ensuremathλ/\ensuremathξi​, where \ensuremathξi{\ensuremath{\xi}}_{i}\ensuremathξi​ is the healing length of condensate iii. Experimentally, the wetting transition may best be approached by varying the interspecies scattering length a12{a}_{12}a12​ using Feshbach resonances. In the hard-wall limit, \ensuremathλ\ensuremath→0\ensuremath{\lambda}\ensuremath{\rightarrow}0\ensuremathλ\ensuremath→0, exact results are derived for the prewetting and first-order wetting phase boundaries.
The possibility of wetting phase transitions in Bose-Einstein condensed gases is predicted on the basis of Gross-Pitaevskii theory. The surface of a binary mixture of Bose-Einstein condensates can undergo a first-order wetting phase transition upon varying the interparticle interactions, using, e.g., Feshbach resonances. Interesting ultra-low-temperature effects shape the wetting phase diagram. The prewetting transition is, contrary to general expectations, not of first order but critical, and the prewetting line does not meet the bulk phase coexistence line tangentially. Experimental verification of these extraordinary results is called for, especially now that it has become possible, using optical methods, to realize a planar "hard wall" boundary for the condensates.
In previous work within Gross-Pitaevskii (GP) theory for ultracold gases, wetting phase transitions were predicted for a phase-segregated two-component Bose-Einstein condensate (BEC) adsorbed at an optical wall. The wetting phase diagram was found to depend on intrinsic atomic parameters, being the masses and the scattering lengths, and on the extrinsic wall boundary condition. Here we study wetting transitions in GP theory without an optical wall in a setting with three phase-segregated BEC components instead of two. The boundary condition is removed by replacing the wall with the third component and treating the three phases on an equal footing. This leads to an unequivocal wetting phase diagram that depends only on intrinsic atomic parameters. It features first-order and critical wetting transitions, and prewetting phenomena. The phase boundaries are computed by numerical solution of the GP equations. In addition, useful analytic results are obtained by extending the established double-parabola approximation to three components.
To investigate the prewetting state of a Bose-Einstein condensate (BEC) mixture adsorbed on an optical hard wall at zero temperature, we consider a system in which condensate 1 coexists with condensate 2 with the chemical potential held fixed. Using the double parabola approximation (DPA) and solving the coupled Gross-Pitaevskii equations, we derive an analytical expression for the thermodynamic contact angle based on Youngs equation. Although the resulting formula is not algebraically simple, it reveals that complete wetting can occur before the bulk coexistence point is reached, indicating the presence of a continuous (second-order) prewetting transition. Our findings are in agreement with theoretical predictions in the literature and emphasize that the wetting film thickness grows smoothly without a discontinuous jump. This work provides useful guidance for the design of experiments aimed at observing wetting phenomena in Bose-Einstein condensates.
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 S\mathcal{S}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 $0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}$.
Nucleation and wetting transitions are studied in a three-component Bose-Einstein condensate mixture within Gross-Pitaevskii theory. For special cases of intermediate segregation between components 1 and 2, the nucleation phase transition of a surfactant film of component 3 is obtained by exact solution. Additional exact results for the nucleation transition are derived in the limit of strong segregation between components 1 and 2. In this limit the exact first-order wetting phase boundary is obtained using analytical and numerical methods, and is contrasted with the exact nucleation and wetting phase boundary derived previously for a two-component Bose-Einstein condensate mixture at a hard optical wall. Exact results for the three-component mixture are compared with results from the double-parabola approximation used in an earlier work.
The interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths ${\ensuremath{\xi}}_{1}$ and ${\ensuremath{\xi}}_{2}$ and by the interspecies repulsive interaction KKK. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case ${\ensuremath{\xi}}_{2}/{\ensuremath{\xi}}_{1}=1/2$ and K=3/2K=3/2K=3/2. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all ${\ensuremath{\xi}}_{1},\phantom{\rule{0.28em}{0ex}}{\ensuremath{\xi}}_{2}$, and KKK. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.