Computation of tunneling rates in time-dependent electric fields: Electrons on the surface of liquid helium, a one-dimensional hydrogen atom

Abstract

We have solved, by numerical methods, the time-dependent Schrödinger equation for the known potential of electrons over the surface of liquid helium. The computed tunneling rates for a static field agreed with experimental measurements of the rates. We describe here the extension of the computation to time-dependent electric fields. The results provide quantitative details of the amplitude and frequency dependence of the tunneling rates. They show very large photoassisted enhancements of the tunneling rates. In addition, we find a modulation of the tunneling rates at the frequency of the applied field. The modulation amplitude decreases sharply at frequencies that are integer fractions of the frequency corresponding to the energy difference between the electron ground state and the top of the barrier. We find no evidence of finite transit-time effects.