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Institute of Optics


Semiclassical Dynamics of Rydberg Electronic Wave Packets


Mark Mallalieu

This thesis develops theoretical techniques to clarify the correspondence between Kepler trajectories and Rydberg wave packet evolution. These methods provide criteria for determining when classical or nonclassical evolution can be expected, and lay the foundation for such studies for closely related systems which display nonintegrable dynamics.

A semiclassical propagator which is the WKB approximation to the Feynman propagator is applied to describe the dynamics of circular-orbit wave packets which are initially well localized in three dimensions. A sum over classical Kepler trajectories for the wave-packet autocorrelation function is obtained which is extremely accurate well past the classical regime of wave-packet evolution. The nonclassical nature of the wave-packet evolution at long times is associated with the interference between amplitudes from classical paths at different energies. The time scale of the wave-packet revivals is related to the shearing rate of the corresponding classical ensemble.

Electron interferometry between pairs of radial wave packets created by phase-coherent laser pulses is studied. It is shown how the quantal phases that wave packets acquire after propagation about the Kepler orbits can be measured with this method. A classical path representation of this measurement is found using a theory based on the Maslov formulation of WKB wave functions. The resulting semiclassical sum is used to show that the phase the wave packet acquires is a type of Berry's phase which is related to the Bohr-Sommerfeld action of Kepler orbits. This method is also used to study the correlated fractional wave packet states which occur when a wave packet revives into several replicas of the initial state.

Closed-form solutions to the semiclassical sums for the wave-packet autocorrelation functions are derived for times during fractional revivals. These solutions provide correspondences between the fractional wave packets and discrete sets of orbits. These sets have values of action variable which are multiples of rational fractions, and sometimes contain the Bohr orbits as a subset. Analytical solutions for the phases of the fractional wave packets are also obtained and found to be very accurate.

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Last modified 13 September 2006