Quality factor of a matter-wave beam

Imperfections in dilute atomic beams propagating in the paraxial regime and in potentials of cylindrical symmetry have been characterized experimentally through the measurement of a parameter analogous to a beam quality factor [Riou et al., Phys. Rev. Lett. 96, 070404 (2006)]. We propose a generalization of this parameter, which is suitable to describe dilute matter waves propagating beyond the paraxial regime and in fully general linear atom-optical systems. The presented quality factor shows that the atomic beam symmetry can be traded for a better transverse collimation.