Characterizing the coherence of Bose-Einstein condensates and atom lasers

For a dilute, interacting Bose gas of magnetically-trapped atoms at temperatures below the critical temperature T0 for Bose-Einstein condensation, we determine the second-order coherence function g (2) (r1 ; r2) within the framework of a finite-temperature quantum field theory. We show that, because of the different spatial distributions of condensate and thermal atoms in the trap, g (2) (r1 ; r2) does not depend on jr1 r2j alone. This means that the experimental determinations of g (2) reported to date give only its spatial average. Such an average may underestimate the degree of coherence attainable in an atom laser by judicious engineering of the output coupler.