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arXiv:2601.13968

Influence of intraspecies interactions on the nucleation and wetting phase diagram in dilute ternary Bose-Einstein condensates

Nguyen Van Thu

Published Jan 20, 2026• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2601.13968

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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.
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.
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.
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.
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.