Chaos and Localisation

This thesis investigates quantum transport in the energy space of
two paradigm systems of quantum chaos theory. These are highly
excited hydrogen atoms subject to a microwave field, and kicked
atoms which mimic the delta-kicked rotor model. Both of these
systems show a complex dynamical evolution arising from the
interaction with an external time-periodic driving force. In
particular two quantum phenomena, which have no counterpart on the
classical level, are studied: the suppression of classical
diffusion, known as dynamical localisation, and quantum resonances
as a regime of enhanced transport for the delta-kicked rotor. The
first part of the thesis provides new support for the quantitative
analogy between energy transport in strongly driven highly excited
atoms and particle transport in Anderson-localised solids. A
comprehensive numerical analysis of the atomic ionisation rates
shows that they obey a universal power-law distribution, in
agreement with Anderson localisation theory. This is demonstrated
for a one-dimensional model as well as for the real
three-dimensional atom. We also discuss the implications of the
universal decay-rate distributions for the asymptotic time-decay of
the survival probability of the atoms. The second part of the
thesis clarifies the effect of decoherence, induced by spontaneous
emission, on the quantum resonances which have been observed in a
recent experiment with delta-kicked atoms. Scaling laws are
derived, based on a quasi-classical approximation of the quantum
evolution. These laws describe the shape of the resonance peaks in
the mean energy of an experimental ensemble of kicked atoms. Our
analytical results match perfectly numerical computations and
explain the initially surprising experimental observations.
Furthermore, they open the door to the study of the competing
effects of decoherence and chaos on the stability of the time
evolution of kicked atoms. This stability may be characterised by
the overlap of two identical initial states which are subject to
different time evolutions. This overlap, called fidelity, is
investigated in an experimentally accessible situation.