Classical and quantum-mechanical scaling of ionization from excited hydrogen atoms in single-cycle THz pulses

Abstract

Excited atoms, or nanotip surfaces, exposed to strong single-cycle terahertz radiation emit electrons with energies strongly dependent on the characteristics of the initial state. Here we consider scaling properties of the ionization probability and electron momenta of H($nd$) atoms exposed to a single-cycle pulse of duration 0.5--5 ps, with $n=9,12,15$. Results from three-dimensional quantum and classical calculations are in good agreement for long pulse lengths, independent of pulse strength. However, differences appear when the two approaches are compared at the most detailed level of density distributions. For the longest pulse lengths a mixed power law, $n$-scaling relation, $\ensuremath{\alpha}{n}^{\ensuremath{-}4}+(1\ensuremath{-}\ensuremath{\alpha}){n}^{\ensuremath{-}3}$ is shown to hold. Our quantum calculations show that the scaling relation puts its imprint on the momentum distribution of the ionized electrons as well: By multiplying the emitted electron momenta of varying initial $n$ level with the appropriate scaling factor the spectra fall onto a common momentum range. Furthermore, the characteristic momenta of emitted electrons from a fixed $n$ level are proportional to the pulse strength of the driving field.