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 |r ₁-r₂| 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.