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In the recent work of Herath et al. [Phys. Rev. Lett. 109, 043004 (2012)] thefirst experimental observation of a dependence of strong-field ionization rateon the sign of the magnetic quantum number m (of the initial bound state(n,l.m)) was reported. The experiment with nearly circularly polarized lightcould not distinguish which sign of m favors faster ionization. We perform abinitio calculations for the hydrogen atom initially in one of the four boundsub states with the principal quantum number n=2 and irradiated by a shortcircularly polarized laser pulse of 800nm. In the intensity range of 10^12 to10^13 Watts/cm^2 excited bound states play a very important role, but also upto some 10^15 Watts/cm^2 they can not be neglected in a full description of thelaser-atom interaction. We explore the region that with increasing intensityswitches from multiphoton to over the barrrier ionization and we find unlike intunneling-type theories, that the ratio of ionization rates for electronsinitially counter-rotating and co-rotating (with respect to the laser field)may be higher or lower than one.

Ionization and excitation of the excited hydrogen atom in strong circularly polarized laser fields