Generic Structure of Multilevel Quantum Beats

Many transient signals from quantum systems result from beats among a large number of levels whose energies depend nonlinearly on the quantum number. Typical examples range from time-resolved laser femtochemistry to quantum optics of single atoms in cavities. Starting from rather general assumptions on the nature of the system, we derive approximate closed-form expressions, which describe such signals in the semiclassical limit. Our approach brings out in a most natural way the phenomenon of fractional revivals and full revivals and explains the oscillatory structures observed in recent experiments on atomic wave packets [Phys. Rev. Lett. 72, 3783 (1994)].