Photoionization microscopy in the time domain: Classical atomic chronoscopy

The glory effect is one of the characteristic manifestations of the divergence of the classical scattering cross section, which occurs whenever the deflection function goes through zero for a nonzero impact parameter. This effect, companion of the more frequently discussed rainbow effect, occurs in particular in atomic photoionization in the presence of an external electric field, where it manifests itself by the appearance of an intense peak at the center of the photoelectron momentum distribution transversely to the field. Above the field-free ionization threshold where solely continuum Stark states exist (while quasibound ones are absent), the intensity of the glory signal, extracted from high-resolution momentum distribution images, oscillates as a function of energy. These oscillations exhibit a spectral frequency that increases with increasing energy, and Fourier analysis allows the extraction of time-dependent information from them. In this work we present a detailed analytical study of the dynamical aspects of classical electron trajectories in atomic Rydberg states in the presence of an external electric field. We demonstrate the strong connection between those classical properties and the spectral signatures of the glory signal. This close link provides a brilliant illustration of the correspondence principle in a complex situation where the quantum system is in the continuum and exhibits characteristic frequencies that vary with the excitation energy.