Sensitive multiphoton ionization

We present comprehensive results for the ionization of the one-dimensional model atom with one electron bound by an attractive δ-function potential in time-dependent external fields. We employ a high-order numerical method, allowing for high-resolution scans of the (essentially exact) ionization probability as a function of the external field parameters within reasonable computer time. We show that, for a sinusoidal external field with small frequency (multiphoton regime), the ionization depends sensitively on the field strength. This phenomenon is a generic multiphoton effect: The dominating peaks in the ionization rate as a function of the ponderomotive energy are separated by the photon energy. This structure is not sensitive to the pulse turn-on time, and, contrary to earlier beliefs, it also persists in the regime where tunneling is the dominant ionization process. (We obtain the tunneling background as the cycle-averaged dc rate.) The sensitive intensity dependence should be observable in photodetachment measurements with high resolution. A comparison with results recently presented by Greenwood and Eberly [Phys. Rev. A 43, 525 (1991)] for a one-dimensional finite-range model potential shows detailed agreement, demonstrating a surprising independence of the ionization on the short-range binding potential. Concerning time dependence, we report drastic deviations from the (usually excellently fulfilled) exponential decay law for the bound-state probability for cases where the latter becomes sufficiently small. In certain regions this function shows a sensitive dependence on time. In addition, we present evidence for exact zeros of the bound-state probability. Finally, we find the ionization rates in dc fields to agree excellently with those resulting from time-independent methods. Moreover, they yield a threshold field strength of some 80% of the experimental value for ${\mathrm{H}}^{\mathrm{-}}$.