  We report on a series of measurements of decoherence and wavepacket dephasing
between two colliding, strongly coupled, identical Bose-Einstein condensates.
We measure, in the strong excitation regime, a suppression of the mean-field
shift, compared to the shift which is observed for a weak excitation. This
suppression is explained by applying the Gross-Pitaevskii energy functional. By
selectively counting only the non-decohered fraction in a time of flight image
we observe oscillations for which both inhomogeneous and Doppler broadening are
suppressed, in quantitative agreement with a full Gross-Pitaevskii equation
simulation. If no post selection is used, the decoherence rate due to
collisions can be extracted, and is in agreement with the local density average
calculated rate.
