Measurements of Relative Phase in Two-Component Bose-Einstein Condensates

We have measured the relative phase of two Bose-Einstein condensates using a time-domain, separated-oscillatory-field condensate interferometer. A single two-photon coupling pulse prepares the double-condensate system with a well-defined relative phase; at a later time, a second pulse reads out the phase difference accumulated between the two condensates. We find that the accumulated phase difference reproduces from realization to realization of the experiment, even after the individual components have separated spatially and their relative center-of-mass motion has damped.