Resonant quantum transport for kicked atoms : from classical stability to universal scaling laws

Abstract

New experimental, theoretical and numerical results are presented for stable resonant transport in a quantum system. Robust resonance behaviour is observed and a universal scaling law for the near resonant dynamics of the system is confirmed experimentally. The system under investigation is the atom-optics quantum kicked rotor, which is an experimental realisation of the paradigmatic standard map - a model system in the study of quantum chaos. The system is realised by subjecting ultra-cold Caesium atoms to periodic pulses (or "kicks") from an optical standing wave which is far detuned from any atomic transition. For certain kicking periods, the atoms experience enhanced growth in energy due to an effect called quantum resonance. The enhanced energy peaks at quantum resonance are shown to be surprisingly robust to random amplitude fluctuations on the kicking pulses (amplitude noise). To explain this unexpected stability of a quantum phenomenon, the e- classical dynamics of the kicked atoms is considered with the addition of amplitude noise. Additionally, a one parameter scaling law for the quantum resonance peaks is confirmed experimentally for the first time. Experimental measurements of the quantum resonance peaks are rescaled and shown to agree well with the analytical expression for the scaling function. Furthermore, a resonance phenomenon in the classical limit of the atom-optics kicked rotor is observed for the first time. For very small kicking periods ballistic energy growth is observed but for slightly larger periods dynamical freezing of atomic energy growth is observed. Finally, the effect of the initial momentum distribution on the resonant dynamics of the kicked rotor is investigated experimentally. Deviations from conventional theoretical results are shown to occur at very small kicking periods or for narrow initial momentum distributions due to the failure of the broad momentum distribution assumption used in the usual analytical theory. A modified theory which takes account of the exact initial momentum distribution is shown to successfully explain these deviations.