The effect of parallel static and microwave electric fields on excited hydrogen atoms

The classical dynamics of the hydrogen atom in parallel static and microwave electric fields are analysed. This work is motivated by recent experiments on excited hydrogen atoms in such fields, which show enhanced resonant ionization at certain combinations of field strengths. By analysing the dynamics using an appropriate representation and averaging approximations, a simple picture of the ionization process is obtained. This shows how the resonant dynamics are controlled by a separatrix that develops and moves through phase space as the fields are switched on and provides necessary conditions for a dynamical resonance to affect the ionization probability. In addition, these methods yield a simple approximate Hamiltonian that facilitates quantal calculations. Using high-order perturbation theory, we obtain a series expansion for the position of the dynamical resonance and an estimate for its radius of convergence. Because, unusually, the resonance island moves through the phase space, the position of the dynamical resonance does not coincide precisely with the ionization maxima. Moreover, there are circumstances in which the field switch-on time dramatically affects the classical ionization probability; for long switch times, it reflects the shape of the incipient homoclinic tangle of the initial state, making it impossible to predict the resonance shape. Additionally, for a similar reason, the resonance ionization time can reflect the timescale of the motion near the separatrix, which is therefore much longer than conventional static field Stark ionization. All these effects are confirmed using accurate Monte Carlo calculations using the exact Hamiltonian. The dynamical structures producing these effects are present in the quantum dynamics; so we conclude that, for sufficiently large principal quantum numbers, the effects seen here will also be observed in the quantum dynamics. New Journal of Physics 7 (2005) 138 PII: S1367-2630(05)95108-2 1367-2630/05/010138+44$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2 Institute of Physics DEUTSCHE PHYSIKALISCHE GESELLSCHAFT