Boson Josephson junction with trapped atoms

Abstract

We consider coherent atomic tunneling between two weakly coupled Bose-Einstein condensates at T=0 in a double-well trap. The condensate dynamics of the macroscopic amplitudes in the two wells is modeled by two Gross-Pitaevskii equations (GPE) coupled by a tunneling matrix element. Analytic elliptic function solutions are obtained for the time evolution of the inter-well fractional population imbalance z(t) (related to the condensate phase difference) of the Boson Josephson junction (BJJ). Surprisingly, the neutral-atom BJJ shows (non-sinusoidal generalizations of) effects seen in charged-electron superconductor Josephson junctions (SJJ). The BJJ elliptic-function behavior has a singular dependence on a GPE parameter ratio Λ at a critical ratio Λ=Λ_c, beyond which a novel 'macroscopic quantum self-trapping' effect sets in with a non-zero time-averaged imbalance < z > ≠ 0.