Strong correspondence principle and the classical-resonance overlap criterion for the onset of chaos

The overlap of classical resonances has been particularly successful in predicting ionization thresholds for hydrogen atoms in strong microwave fields, although not for low scaled frequencies. In this paper, we explicitly relate quantum mechanically computed matrix elements to the classical Fourier amplitudes used in the overlap criterion. The resulting twist to this demonstration of classical-quantum correspondence is that quantum matrix elements can be used to improve predictions of classical-resonance overlap for low scaled frequencies. Conversely, the classical amplitudes are shown to contain delicate cancellations in the quantum matrix elements. In the course of this demonstration, we also introduce a compact numerical method for evaluating high-order multiphoton matrix elements.