Static Properties of Prewetting Phase in Binary Mixtures of Bose-Einstein Condensates

In this study, using the Gross-Pitaevskii (GP) theory under the double parabola approximation, we examine the static properties of the prewetting phase in a two-component Bose-Einstein condensates (BECs) adsorbed at an optical wall at zero temperature. The Schrödinger-like equation is solved analytically, providing an exact relation that describes the nucleation line. From the analytical solution of the ground state wave functions obtained from GP theory within double parabola approximation, the analytical relation for thickness of the prewetting layer is derived. Our results demonstrate that, in sufficiently large regions, this thickness is dependent on both the control parameter and the ground state energy of the condensate 2. Notably, in a logarithmic scale of the ground state energy, the thickness behaves as a linear function, with coefficients that depend solely on the control parameter. Furthermore, we analyze the thermodynamic contact angle, surface, and interfacial tensions. Remarkably, the analytical expressions for the cosine of the thermodynamic contact angle in the limits of the segregated-phase are obtained. These findings may contribute to the design of experiments aimed at observing the wetting phenomenon in BECs.