Abstract. The quantum resonances occurring with δ-kicked atoms when the kicking period is an integer multiple of the half-Talbot time are analysed in detail. Exact results about the momentum distribution at exact resonance are established, both in the case of totally coherent dynamics and in the case when decoherence is induced by spontaneous emission. A description of the dynamics when the kicking period is close to, but not exactly at resonance, is derived by means of a quasi-classical approximation where the detuning from exact resonance plays the role of the Planck constant. In this way scaling laws describing the shape of the resonant peaks are obtained. Such analytical results are supported by extensive numerical simulations, and explain some recent surprising experimental observations.

Mathematics Subject Classification: 81Q50, 81S30

PACS numbers: 05.45Mt, 03.65Yz, 72.15Rn, 42.50Vk

Print publication: Issue 4 (July 2003)
Received 17 December 2002
Published 23 May 2003