Classical chaos in one-dimensional hydrogen in strong dc electric fields

We analyze the effect of a dc electric field on classical chaos in one-dimensional hydrogen in a microwave field in the n nonmixing regime and also in the inter-n-mixing regime where significant dc field-induced ionization occurs. We study the ac field-induced nonlinear classical resonances, the threshold of chaos, and the number of states trapped in the resonances. In the strong-n-mixing and ionizing regime (unclamping dc field), we find the chaotic dynamics depend sharply on the dc field and the number of states trapped in the resonances, allowing the system to undergo a transition from a regime of classical behavior to a regime of uniquely quantum behavior as the dc field is changed. We show that ionization by classical chaos competes favorably with ionization by tunneling in the transition region, and that tunneling allows very sensitive spectroscopy of this region.