Surfactant layer thickness of ternary Bose-Einstein condensates

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.