  The effect of decoherence, induced by spontaneous emission, on the dynamics
of cold atoms periodically kicked by an optical lattice is experimentally and
theoretically studied. Ideally, the mean energy growth is essentially
unaffected by weak decoherence, but the resonant momentum distributions are
fundamentally altered. It is shown that experiments are inevitably sensitive to
certain nontrivial features of these distributions, in a way that explains the
puzzle of the observed enhancement of resonances by decoherence [Phys. Rev.
Lett. 87, 074102 (2001)]. This clarifies both the nature of the coherent
evolution, and the way in which decoherence disrupts it.
