We report on a series of measurements of decoherence and wave-packet 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 nondecohered fraction in a time-of-flight image we observe oscillations for which both inhomogeneous and Doppler broadening are strongly suppressed. 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.
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