  We study the interaction of light with two Bose condensates as an open
quantum system. The two overlapping condensates occupy two different Zeeman
sublevels and two driving light beams induce a coherent quantum tunneling
between the condensates. We derive the master equation for the system. It is
shown that stochastic simulations of the measurements of spontaneously
scattered photons establish the relative phase between two Bose condensates,
even though the condensates are initially in pure number states. These
measurements are non-destructive for the condensates, because only light is
scattered, but no atoms are removed from the system. Due to the macroscopic
quantum interference the detection rate of photons depends substantially on the
relative phase between the condensates. This may provide a way to distinguish,
whether the condensates are initially in number states or in coherent states.
