Nambu-Goldstone Modes in Two Segregated Bose-Einstein Condensates Limited by a Hard Wall

Abstract

In the framework of the Gross-Pitaevskii theory, based on the double-parabola approximation method, we successfully found the expressions for dispersion relations of three NG modes of two immiscible Bose-Einstein condensates restricted by a hard wall (two phonons and a ripplon). For the first condensate component, which is not confined by a hard wall, we found one phonon and one ripplon. Meanwhile, for the second component confined by a hard wall, we found only one phonon (the dispersion relation depends on the position of the hard wall), and this manifests explicitly the finite-size effect.