Classical dynamics and localization of resonances in the high energy region of the hydrogen atom in crossed fields

TL;DR

This paper investigates classical and quantum behaviors of the hydrogen atom in crossed fields, focusing on resonance localization, bifurcations, and spectral signatures of stable orbits at high energies.

Contribution

It uncovers the bifurcation behavior of quasi-Penning orbits, identifies a stability apex and cusp bifurcation, and links classical orbits to quantum spectral features.

Findings

Identification of a stability apex in classical orbits.

Discovery of a cusp bifurcation near the apex.

Quantum signatures of stable orbits in spectra.

Abstract

When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom a saddle point appears, which is called the Stark saddle point. For energies slightly above the saddle point energy one can find classical orbits, which are located in the vicinity of this point. We follow those so-called quasi-Penning orbits to high energies and field strengths observing structural changes and uncovering their bifurcation behavior. By plotting the stability behavior of those orbits against energy and field strength the appearance of a stability apex is reported. A cusp bifurcation, located in the vicinity of the apex, will be investigated in detail. In this cusp bifurcation another orbit of similar shape is found, which becomes completely stable in the observed region of positive energy, i.e., in a region of parameter space, where the Kepler-like orbits located around the nucleus are already unstable. By quantum-mechanically exact calculations we prove the existence of signatures in quantum spectra belonging to those orbits. Husimi distributions are used to compare quantum-Poincar\'e sections with the extension of the classical torus structure around the orbits. Since periodic orbit theory predicts that each classical periodic orbit contributes an oscillating term to photoabsorption spectra, we finally give an estimation for future experiments, which could verify the existence of the stable orbits.