Time-dependent approach to high-resolution spectroscopy: application to the photoabsorption spectrum of classically chaotic hydrogen atoms in magnetic fields

We present a new time-dependent approach for probing the dynamics and high-resolution spectroscopy of Rydberg systems in the presence of external fields. The procedure is based on the extension of a recent development of a generalized pseudospectral time-dependent method which allows for non-uniform spatial grid discretization, and long-time propagation of the time-dependent Schrِdinger equation with both high accuracy and efficiency. The method is demonstrated by a case study of the photoabsorption spectrum of atomic hydrogen in the presence of static magnetic fields. Excellent agreement of the time-dependent results with the high-resolution experimental spectrum is achieved line by line, covering both the classically regular and chaotic regimes.