COLLECTIVE EXCITATIONS OF A BOSE-EINSTEIN CONDENSATE TRAPPED IN A TWO-CHANNEL POTENTIAL

DOI: 10.18173/2354-1059.2026-0004

Abstract

In this paper, we investigate the collective excitations of an attractively interacting Bose–Einstein condensate confined in a two-channel potential. Using the Bogoliubov approximation, we derive the Bogoliubov–de Gennes equations and determine the excitation spectrum numerically. Two distinct modes are identified: the well-known Josephson mode, associated with periodic inter-channel tunneling, and a novel antisymmetric translational mode, describing out-of-phase oscillations of the condensate center of mass. Unlike conventional dipole oscillations, the latter arises from the interplay between inter-channel coupling and attractive nonlinearity and does not follow the Kohn theorem. We then employ the variational approximation to describe the condensate dynamics under these excitations and to extract the corresponding mode frequencies. The results are further validated by real-time simulations of the governing Gross–Pitaevskii equations, showing good agreement between analytical and numerical approaches.