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 common excited state. To this end, we consider a two-well ground-state potential together with excited-state trap wave functions that extend over the whole region. When the first trap is driven by a weak monochromatic laser field, the light scattered from the second trap has a nonzero mean-electric field amplitude with a phase shift proportional to the difference of the condensate phases. When both condensates are driven, the phases of the two laser fields can be adjusted to cancel the scattering completely by a quantum interference. The particular value of the laser phase difference that gives zero scattering determines the relative phase of the two condensates.