  Two internal hyperfine states of a Bose-Einstein condensate in a dilute
magnetically trapped gas of ${}^{87}$Rb atoms are strongly coupled by an
external field that drives Rabi oscillations between the internal states. Due
to their different magnetic moments and the force of gravity, the trapping
potentials for the two states are offset along the vertical axis, so that the
dynamics of the internal and external degrees of freedom are inseparable. The
rapid cycling between internal atomic states in the displaced traps results in
an adiabatic transfer of population from the condensate ground state to its
first antisymmetric topological mode. This has a pronounced effect on the
internal Rabi oscillations, modulating the fringe visibility in a manner
reminiscent of collapses and revivals. We present a detailed theoretical
description based on zero-temperature mean-field theory.

Condensed Matter