The effect of decoherence at the resonances of the quantum delta-kicked rotor

In the last few years the quantum delta-kicked rotor realized with laser cooled atoms and a pulsed standing wave of light has become a vital test bed for ideas in quantum chaos. In this paper we present the results from experiments in which such a system is exposed to decoherence induced by spontaneous emission. In particular we examine the behavior when the pulsing period of the standing wave corresponds to one of the quantum resonances. We demonstrate theoretically that the mean energy growth is essentially unaffected by weak decoherence, but that the shapes of the momentum distributions are fundamentally altered. It is shown that since the mean energy calculated from experimental data is inevitably sensitive to certain nontrivial features of these distributions, the mean energy can give a misleading picture of the system dynamics. By considering this sensitivity we are now able to present an explanation for the observed decoherent enhancement of the quantum resonances observed by d'Arcy et al. [Phys. Rev. Lett. 8,074102 (2001)]. Thus we clarify both the nature of the coherent evolution, and the way in which decoherence disrupts it.