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VNU Journal of Science Mathematics - Physics

Critical Wetting Phase Transition in a Dilute Ternary Bose-Einstein Condensates

Nguyễn Văn Thụ, Dang Thanh Hai

Published Oct 12, 2025• 0 citations
Publisher

Abstract

We investigate the possibility of a critical wetting phase transition in a dilute ternary Bose-Einstein condensate using Gross-Pitaevskii theory within the framework of the double parabola approximation. By analytically determining the condensate wave functions, we derive the dependence of the surfactant layer thickness on the intrinsic atomic parameters. Our results reveal conditions under which a critical wetting transition may occur, highlighting a new aspect of interfacial phenomena in multicomponent quantum fluids.

DOI
10.25073/2588-1124/vnumap.5037

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We investigate the possibility of a critical wetting phase transition in a dilute ternary Bose-Einstein condensate using Gross-Pitaevskii theory within the framework of the double parabola approximation. By analytically determining the condensate wave functions, we derive the dependence of the surfactant layer thickness on the intrinsic atomic parameters. Our results reveal conditions under which a critical wetting transition may occur, highlighting a new aspect of interfacial phenomena in multicomponent quantum fluids.
We identify the adsorbed index as an experimentally accessible order parameter for the wetting phase transition in dilute ternary Bose–Einstein condensates (BECs). By tracking the nucleation and growth of a surfactant film of the third component at the interface between two immiscible condensates, we show that the adsorbed index exhibits a logarithmic divergence with the chemical-potential ratio in the prewetting phase. Numerical Gross–Pitaevskii calculations are consistent with analytical predictions from the double-parabola approximation, confirming the reliability of the approach. Unlike the conventional surfactant layer thickness, which becomes ill-defined near the nucleation point, the adsorbed index remains well defined throughout the entire prewetting-wetting regime and is directly proportional to the number of condensed atoms in the surfactant component, a quantity that is readily measurable in ultracold-atom experiments and tunable via Feshbach resonances. Our results offer a realistic opportunity to observe wetting transitions in multicomponent quantum gases.
Abstract The interfacial phenomena in multicomponent Bose-Einstein condensates include a rich variety of wetting transitions. Previous studies of a wall-less, three-component system have primarily fo-cused on the continuous (critical) wetting transition, leaving the phase diagram incomplete. In this work, we present a complete theoretical description of this system at zero temperature based on the Gross-Pitaevskii theory and a semi-analytical double-parabola approximation. We derive the analytical conditions for both discontinuous (first-order) and continuous (critical) wetting transitions by calculating the grand potential and the associated interfacial tensions. Synthesizing these results, we construct the complete wetting phase diagram and, crucially, identify the tricritical point where the first-order and critical transition lines meet. This complete phase diagram provides a quantitative roadmap for future experiments exploring complex interfacial phenomena in quantum fluids.
We investigate the thickness of the surfactant layer in dilute ternary Bose-Einstein condensates (BECs) using the Gross-Pitaevskii (GP) theory within the linear approximation. In this system, components 1 and 2 form strongly segregated phases, while component 3 wets their interface and acts as a surfactant. We demonstrate that, in the three-phase coexistence regime, the surfactant layer thickness is determined by intrinsic atomic parameters: specifically, healing lengths and coupling constants. Furthermore, we identify the critical wetting line within the parameter space. In the prewetting phase, we find that the surfactant layer thickness scales linearly with the chemical potential ratio on a logarithmic scale.
Within the framework of Gross-Pitaevskii theory, we investigate the effects of intraspecies interactions on the nucleation transition and the wetting phase diagram of dilute ternary Bose-Einstein condensate in the regime of strong segregation between two components. The analyses are carried out using both the analytical double-parabola approximation (DPA) and numerical computations. Our results show that the DPA provides a reliable approximation for describing the nucleation transition. For the wetting phase diagram, we find that the DPA is in excellent agreement with numerical results in symmetric systems, particularly in the completely symmetric case, whereas it fails to provide an adequate description for asymmetric systems.
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.