We have performed time-domain interferometry experiments with matter waves trapped in a harmonic potential above and below the Bose-Einstein phase transition, by means of the method of separated oscillating fields, with a variable time delay $T$. We observe the oscillations of the population between two internal Zeeman states versus the delay $T$ to be rapidly depleted both below and slightly above Bose-Einstein condensation. We give a quantitative explanation in terms of the phase evolution due to the entanglement between the internal and external degrees of freedom.

• Received 26 January 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.170401