Uniting Bose-Einstein condensates in optical resonators

The relative phase of two initially independent Bose-Einstein condensates c an be laser cooled to unite the two condensates by putting them into a ring cavity and coupling them with an internal Josephson junction. First, we sh ow that this phase cooling process already appears within a semiclassical m odel. We calculate the stationary states, find regions of bistable behavior , and suggest a Ramsey-type experiment to measure the buildup of phase cohe rence between the condensates. We also study quantum effects and imperfecti ons of the system.