Chaos and order in crossed fields

Abstract

Atoms with a single highly excited electron (so-called Rydberg atoms), when placed in external fields, become atomic-scale laboratories in which the quantum mechanics of strongly nonlinear systems can be tested. Especially the extensive symmetry breaking introduced to the Coulomb potential by crossed electric and magnetic fields leads to rich nonlinear dynamics and is also a source of great complexity. In this paper, we analyze the nonlinear dynamics aspects of this atomic system, such as periodic orbits, bifurcations, order-chaos transitions, and islands of stability. In particular, we present an approximate Hamiltonian that turns out to be very effective in bringing out the classical structures that support the complexity of the motion. We conclude with a coherent state analysis that allows a direct comparison of quantum and classical results.