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VNU Journal of Science Mathematics - Physics

Adsorbed Index for Critical Wetting Phase Transition in Ternary Bose-Einstein Condensates

Nguyen Van Thu, Phạm Thế Song, Hoang Van Quyet

Published May 1, 2026• 0 citations

Abstract

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.

DOI: 10.25073/2588-1124/vnumap.5109

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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.

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.

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.

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.

By means of Gross-Pitaevskii theory we investigate the possibility of wetting phase transition in three-component Bose-Einstein condensates within the strong segregation between components 1 and 2. Third component plays the role of a surfactant, which can wet the interface formed by components 1 and 2. The case of symmetry of components 1 and 2, the equation for nucleation line and wetting phase diagram are studied. By linearizing the set of three-coupled Gross-Pitaevskii equations, the wave functions of the components are found. An analytical approximation for the surfactant thickness in the prewetting phase is presented. The results indicate that the surfactant thickness in the prewtting phase varies linearly with the chemical potential ratio in the logarithmic scale.

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.