Measures of coherence for trapped matter waves

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