Measures of coherence for trapped matter waves

We define and discuss measures of coherence for matter waves. These charact erize the interference pattern arising from the overlap of one point of a m atter wave with another. We identify two coherence quantities, one related to the distance between the interfering parts of a matter wave, and one des cribing the influence of the position within the wave. We show that our coh erence properties are suitable for describing both single particles such as cold trapped ions, and many-particle systems such as Bose-Einstein condens ates and Fermi gases.