Coherent states in a Rydberg atom: Classical mechanics

The interaction of a hydrogen or Rydberg atom with a circularly polarized microwave field leads to the creation of global equilibrium points that may be stable or unstable depending on the particulars of the applied field. The additional application of a magnetic field, perpendicular to the plane of polarization, can be used to manipulate both the nature and the stability of these points. We show that stable three-dimensional motion can be maintained that is localized at either a maximum or a minimum in the corresponding surface of zero velocity. At these equilibria, the zero-velocity surface may be locally quadratic in coordinates and stable harmonic-oscillator-like, nondispersive, coherent states can be supported. As the fields an varied, repeated order-chaos transitions may be observed, including various passages through rigorously integrable limits. Classical simulations are presented for a range of field strengths, and the effects of deviations of the microwave field from exactly circular polarization (i.e., elliptical polarization) are examined using a pulsating zero-velocity surface.