NONDESTRUCTIVE OPTICAL MEASUREMENT OF RELATIVE PHASE BETWEEN 2 BOSE-EINSTEIN CONDENSATES

We study the interaction of Light with two Bose-Einstein condensates a s an open quantum system. The two overlapping condensates occupy two d ifferent Zeeman sublevels and two driving light beams induce a coheren t quantum tunneling between the condensates. We derive the master equa tion for the system. It is shown via stochastic simulations that the m easurements of spontaneously scattered photons establish the relative phase between two Bose-Einstein condensates. even though the condensat es are initially in pure number states. These measurements are nondest ructive for the condensates, because only light is scattered and no at oms are removed from the system. Due to macroscopic quantum interferen ce the detection rate of photons depends strongly on the relative phas e between the condensates. This may provide a way to distinguish betwe en initial number states and initial symmetry-breaking states of rbe c ondensates.