  In analogy to Glauber's analysis of optical coherence, we adopt an
operational approach to introduce different classes of atomic coherence
associated with different types of measurements. For the sake of concreteness
we consider specifically fluorescence, nonresonant imaging, and ionization. We
introduce definitions of coherence appropriate to them, which we call
electronic, density, and field coherence, respectively. We illustrate these
concepts in various descriptions of Bose-Einstein condensation, showing that
each of these descriptions makes different implicit assumptions on the
coherence of the system. We also study the impact of elastic collision on the
field and density coherence properties of atom lasers.
