Static-field effects on the nonlinear quantum resonances and the ionization spectrum of a simple bound particle.

Abstract

A comparison of nonlinear classical resonances with the nonlinear quantum resonances has been well established for semiclassical systems. However, systems in which tunneling is present are no longer semiclassical and the correspondence between the classical and quantum systems breaks down. We examine nonlinear quantum resonances in a system consisting of a triangular potential well (formed by a static field plus an impenetrable wall) with an attractive \ensuremath{\delta}-function potential well and a weak external time-periodic force. In this system, tunneling is important and nonlinear quantum resonances that have no classical counterpart can occur. In the second part of this paper, we remove the impenetrable wall and consider this system to be a model of a bounded particle subject to a strong external static field and a weak periodic field. The presence of the static field leads to strong enhancement and suppression of the single-photon photodetachment rates for certain frequencies. This effect has been observed experimentally in the photodetachment of ${\mathit{H}}^{\mathrm{\ensuremath{-}}}$ ions and predicted by theoretical models. The model present here is particularly useful because the photodetachment spectrum can be obtained analytically and leads to greater insight into more realistic models.