Josephson Tunneling of Excited States in a Double-Well Potential

Abstract We study the dynamics of matter waves in an effectively one-dimen-sional Bose–Einstein condensate in a double well potential. We consider in par-ticular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. The validity regions of the two-mode approximation are discussed.