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We discuss coherent atomic oscillations between two weakly coupledBose-Einstein condensates that are energetically different. The weak link isnotionally provided by a laser barrier in a (possibly asymmetric) multi-welltrap or by Raman coupling between condensates in different hyperfine levels.The resultant boson Josephson junction dynamics is described by a double-wellnonlinear Gross-Pitaevskii equation. On the basis of a new set of Jacobianelliptic function solutions, we describe the period of the oscillations as wellas associated quantities and predict novel observable consequences of theinterplay of the energy difference and initial phase difference between the twocondensate populations.

Quantum Oscillations between weakly coupled Bose-Einstein Condensates: Evolution in a Non-degenerate Double Well