Understanding two-photon double ionization of helium from the perspective of the characteristic time of dynamic transitions

Abstract

By using the B-spline numerical method, we investigate a two-photon double-ionization (TPDI) process of helium in a high-frequency laser field with its carrier frequency ranging from 1.6 to 3.0 a.u. and the pulse duration ranging from 75 to 160 attoseconds. We found that there exists a characteristic time tc for a TPDI process, such that the pattern of energy distribution of two ionized electrons presents a peak or two, depending respectively on whether the pulse duration is shorter or longer than tc. Especially, when the pulse duration is larger than tc, the TPDI spectrum shows a double-peak structure which is attributed to the fact that most of the electron–electron Coulomb interaction energy is acquired by a single electron during their oscillation around the nucleus before the two electrons leave, and hence the double-peak structure cannot be identified as a signal of sequential ionization. Additionally, if the carrier frequency is less than the ionization energy of He+, i.e. that carrier frequency is in the so called correlated region, tc is not a fixed value, and it increases as the carrier frequency decreases; while if the carrier frequency is greater than the ionization energy of He+, i.e. the carrier frequency is in the so called non-correlated region, tc is fixed at about 105 attoseconds. We further found that, for a helium-like ion in its ground state, the characteristic time for when the carrier frequency is larger than the ionization energy of the second electron has a key relation with the Coulomb interaction energy between the two electrons, which can be expressed as , a type of quantum mechanical uncertainty relation between time and energy. In addition, this relation can be attributed to the existence of a minimal evolution time from the ground state to a double ionization state with two electrons carrying different energies. These results may shed light on a deeper understanding of many-electron quantum dynamical processes.