  We discuss coherent atomic oscillations between two weakly coupled
Bose-Einstein condensates that are energetically different. The weak link is
notionally provided by a laser barrier in a (possibly asymmetric) multi-well
trap or by Raman coupling between condensates in different hyperfine levels.
The resultant boson Josephson junction dynamics is described by a double-well
nonlinear Gross-Pitaevskii equation. On the basis of a new set of Jacobian
elliptic function solutions, we describe the period of the oscillations as well
as associated quantities and predict novel observable consequences of the
interplay of the energy difference and initial phase difference between the two
condensate populations.
