Scaling properties of field ionization of Rydberg atoms in single-cycle THz pulses: 1D considerations

In recent experiments of single-cycle field ionization of excited Na(nd) atoms with principal quantum number n is an element of [6, 15] (Li and Jones 2014 Phys. Rev. Lett. 112 143006) it was shown that the maximum field intensity necessary to ionize 10% of the atoms decreases with increasing n according to an n(-3) power law dependence. This scaling property at the same ionization probability was confirmed in classical trajectory Monte Carlo calculations. In this work we note that the scaling relation in the experiment is much more general, it is in fact valid for all ionization probabilities. When applied to the emitted electron energies it places a very wide distribution of electron momenta from different initial states onto a narrow range. These aspects are investigated in a one-dimensional model with a 3D hydrogen-like spectrum. Calculations confirm the general n(-3) scaling relation for the ionization probability and that this particular scaling of the kinetic emission spectrum puts the ejected electron momenta on a narrow common scale. The ionization mechanism itself is identified as quantum mechanical tunneling and the nature of the tunneling process is the direct origin of the scaling law.