Josephson Oscillations of Bose-Einstein Condensate in Double-Well Potential: Two-Mode Model and Beyond

Abstract

The Josephson oscillation of a Bose-Einstein condensate (BEC) in a double-well potential is typically characterized by the population imbalance between the two wells. Within the two-mode approximation, the dynamics of the center of mass of the condensate is predicted to coincide with that of the population imbalance. However, numerical simulations reveal a discrepancy between the dynamics of the center of mass and that of the population imbalance, indicating that the two-mode model fails to fully capture the dynamics of BEC Josephson oscillations. To address this limitation, a four-mode approximation is employed to describe the dynamics of the system. The four-mode model not only describes the dynamics of the population imbalance but also accounts for the oscillation of the center of mass, thereby explaining the origin of the discrepancy between the two-mode model and the simulation results. Moreover, we find that although higher-order excitation modes are always present in Josephson oscillations, the two-mode model can still describe the dynamics of the population imbalance. This phenomenon is explained by the interference of population oscillations between local states.