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arXiv:2104.00313 · Physical Review A

Surfactant behavior in three-component Bose-Einstein condensates

Keisuke Jimbo, Hiroki Saito

Published Jun 28, 2021• 11 citations
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Abstract

In classical fluids, surfactants enter the interface between two immiscible fluids and reduce the interfacial tension. We show that a similar situation can be realized in a three-component Bose-Einstein condensate (BEC), in which a phase-separated two-component BEC forms an interface and the third component enters the interface. We derive an expression for the interfacial tension of this system, and numerically show that the third component can reduce the interfacial tension, i.e., the third component plays the role of a surfactant. The stability of such an interface is corroborated by the Bogoliubov analysis. We also consider a system that has a spatial gradient in the interfacial tension, and we show that interfacial flow is induced, which resembles the Marangoni flow in classical fluids.

DOI
10.1103/physreva.103.063323

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In classical fluids, surfactants enter the interface between two immiscible fluids and reduce the interfacial tension. We show that a similar situation can be realized in a three-component Bose-Einstein condensate (BEC), in which a phase-separated two-component BEC forms an interface and the third component enters the interface. We derive an expression for the interfacial tension of this system, and numerically show that the third component can reduce the interfacial tension, i.e., the third component plays the role of a surfactant. The stability of such an interface is corroborated by the Bogoliubov analysis. We also consider a system that has a spatial gradient in the interfacial tension, and we show that interfacial flow is induced, which resembles the Marangoni flow in classical 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.
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.
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 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.