Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, pi oscillations, and macroscopic quantum self-trapping

We discuss the coherent atomic oscillations between two weakly coupled Bose -Einstein condensates. The weak link is provided by a laser barrier in a (p ossibly asymmetric) double-well trap or by Raman coupling between two conde nsates in different hyperfine levels. The boson Josephson junction (BJJ) dy namics is described by the two-mode nonlinear Gross-Pitaevskii equation tha t is solved analytically in terms of elliptic functions. The BJJ, beings a neutral, isolated system, allows the investigations of dynamical regimes fo r the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). T hese include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to pi (pi-phase oscillati ons); (ii) the average population imbalance is nonzero, in states with macr oscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJ J ac and plasma oscillations and the Shapiro resonance can also be observed . We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single uni versal curve for the inverse period of oscillations. Analogies with Josephs on oscillations between two weakly coupled reservoirs of He-3-B and the int ernal Josephson effect in He-3-A are also discussed. [S1050-2947(98)05912-5 ].