Boson Josephson junction with trapped atoms

We consider coherent atomic tunneling between two weakly coupled Bose-Einst ein condensates at T=0 in a double-well trap. The condensate dynamics of th e macroscopic amplitudes in the two wells is modeled by two Gross-Pitaevski i equations (GPE) coupled by a tunneling matrix element. Analytic elliptic function solutions are obtained for the time evolution of the inter-well fr actional population imbalance z(t) (related to the condensate phase differe nce) of the Boson Josephson junction (BJJ). Surprisingly, the neutral-atom BJJ shows (non-sinusoidal generalizations of) effects seen in charged-elect ron superconductor Josephson junctions (SJJ). The BJJ elliptic-function beh avior has a singular dependence on a GPE parameter ratio Lambda at a critic al ratio Lambda = Lambda(c), beyond which a novel 'macroscopic quantum self -trapping' effect sets in with a non-zero time-averaged imbalance [z] not e qual 0.