Measurement of the Coherence of a Bose-Einstein Condensate

We present experimental and theoretical studies of the coherence properties of a Bose-Einstein condensate (BEC) using an interference technique. Two optical standing wave pulses of duration 100 ns and separation $\Delta t$ are applied to a condensate. Each standing wave phase grating makes small copies of the condensate displaced in momentum space. The quantum mechanical amplitudes of each copy interfere, depending on $\Delta t$ and on spatial phase variations across the condensate. We find that the behavior of a trapped BEC is consistent with a uniform spatial phase. A released BEC, however, exhibits large phase variation across the condensate.