Coherent population trapping of Bose-Einstein condensates: Detection of phase diffusion

Two Bose-Einstein condensates in different Zeeman sublevels can be decouple d from driving light fields in coherent population trapping. A condensate p air with a deterministic entanglement and a controllable value of the relat ive phase may be prepared by selecting the phase difference between the coh erent light fields. The rate of the condensate phase diffusion may be deter mined from the two-photon resonant absorption of radiation.