  We propose an experiment that would demonstrate nonlinear Josephson-type
oscillations in the relative population of a driven, two-component
Bose-Einstein condensate. An initial state is prepared in which two condensates
exist in a magnetic trap, each in a different hyperfine state, where the
initial populations and relative phase between condensates can be controlled
within experimental uncertainty. A weak driving field is then applied, which
couples the two internal states of the atom and consequently transfers atoms
back and forth between condensates. We present a model of this system and
investigate the effect of the mean field on the dynamical evolution.
