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

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.