Probing the effect of orbital deformation on the atomic tunneling-ionization-time distribution by phase-of-the-phase spectroscopy

Abstract

We theoretically studied the tunneling ionization time of atomic ${p}_{\ifmmode\pm\else\textpm\fi{}}$ orbitals by introducing a weak linearly polarized second-harmonic field to the attoclock frame. In our scheme, the ionization time is retrieved by analyzing the relative phase dependence of ionization yield, where one can be free from handling the Coulomb interaction on the emitted electron. By solving the time-dependent Schr\"odinger equation, we verified that at low laser intensity the ionization time delays are both close to zero for the $2{p}_{\ifmmode\pm\else\textpm\fi{}}$ orbitals, though their offset angles in the photoelectron angular distributions are different. As the laser intensity increases, the atomic orbitals are deformed significantly, which affects the tunneling-ionization-time distribution. With our scheme, the orbital deformation-induced ionization time delay is unambiguously determined. Furthermore, the depletion of the ground state at the high laser intensity enhances the relative contribution of early ionization events and thus the ionization peak shifts to the earlier time. This effect is also directly revealed by our scheme.