OPTICAL MEASUREMENTS OF THE CONDENSATE PHASE

We propose a light-scattering scheme to measure the relative phase of atomic Bose-Einstein condensates and its diffusion rate. The proposal relies on the existence of two independent condensates coupled to a co mmon excited state. To this end, we consider a two-well ground-state p otential together with excited-state trap wave functions that extend o ver the whole region. When the first trap is driven by a weak monochro matic laser field, the light scattered from the second trap has a nonz ero mean-electric field amplitude with a phase shift proportional to t he difference of the condensate phases. When both condensates are driv en, the phases of the two laser fields can be adjusted to cancel the s cattering completely by a quantum interference. The particular value o f the laser phase difference that gives zero scattering determines the relative phase of the two condensates.