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Journal of Experimental and Theoretical Physics Letters

Delay of Photoelectrons Emitted from the Ionized Ne 2s and 2p Shells Including Photoelectron Scattering

Larissa V. Chernysheva, V. G. Yarzhemsky

Published Aug 1, 2024• 3 citations
Publisher

Abstract

Formulas to calculate the atomic photoionization delay have been derived taking into account the interaction between the channels and the scattering of a photoelectron. The photoionization delay difference between Ne 2p and 2s shells has been calculated for photon energies up to 200 eV. The calculated delay difference at a photon energy of 105 eV is 18.5 as, which is approximately 8 as larger than delay differences previously calculated taking into account only the interactions between the channels and is in agreement within the experimental error with two existing experimental values.

DOI
10.1134/s0021364024602148

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Formulas to calculate the atomic photoionization delay have been derived taking into account the interaction between the channels and the scattering of a photoelectron. The photoionization delay difference between Ne 2p and 2s shells has been calculated for photon energies up to 200 eV. The calculated delay difference at a photon energy of 105 eV is 18.5 as, which is approximately 8 as larger than delay differences previously calculated taking into account only the interactions between the channels and is in agreement within the experimental error with two existing experimental values.
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Using the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) technique, a nonzero phase difference is observed in the two-photon ionization transition of krypton atoms into the ionization channels 2P1/2^{2}P_{1/2}2P1/2​ and 2P3/2^{2}P_{3/2}2P3/2​ when an electron is removed from the 4p4p4p shell. The phase difference is studied for excitation energies ranging from $\ensuremath{\approx}18\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ up to $\ensuremath{\approx}28\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$. The phase differences are found to depend on the relative directions of linear polarization of the photoionization laser pulses and the pulses inducing the subsequent continuum-continuum transition. The experimental results are compared to phase differences calculated on the basis of dipole matrix elements for photoionization and scattering phases known for krypton from earlier experiments. The results indicate that the RABBITT phase differences do not give an obvious direct access to time-delay differences in the primary photoionization step of the atom.
The role of Rydberg autoionizing states in interfering one- and two-photon ionization paths is theoretically investigated in atomic Ar. The angularly resolved photoionization cross sections for each individual path is provided. By varying the relative optical phase between the two pulses the phase difference between the two interfering paths is extracted. The retrieved phase difference and the photoelectron angular distributions exhibit a strong dependence on the photon energy in the vicinity of the resonant states. In contrast to previous results obtained in atomic Ne, the phase difference features a smooth dependence with photoelectron emission angle.
In the theoretical study of photoionization, certain properties of the photoelectrons are not defined in terms of any (even idealized) model for the electron-detection process, in contrast to the well-known Glauber theory of photon detection. Thus, for instance, the energy spectrum of the electron produced in atomic ionization is usually defined simply as the long-time probability for the electron to have a given energy. In this paper a formal model for an electron detector localized to a small region in space, similar to the DeWitt monopole detector, is set up in terms of which results analogous to those obtained for photon detection in the Glauber theory can be obtained. In addition, it is possible to define correlation functions describing the joint probability of detecting an electron and a photon. This correlation function is calculated here in the case of two-photon ionization of an atom modeled as having two discrete energy levels and an ionization continuum. When the atom is subjected to an incident driving field, both a photoelectron and scattered photons arising from the spontaneous decay of the upper of the two discrete levels are produced. Correlations between these photons and the photoelectron are studied here by considering the joint probability of detection of a photoelectron and a scattered photon for a monochromatic driving field.
We report a theoretical investigation of photoionization by a pair of coherent, ultrashort, fundamental and second-harmonic extreme-ultraviolet pulses, where the photon energies are selected to yield the same photoelectron energy for ionization of two different subshells. This choice implies that the fundamental energy is equal to the difference in energy of the ionic states and that they are therefore coupled by the fundamental photon. By deriving analytical expressions using the essential-states approach, we show that this Rabi coupling creates coherence between the two photoelectron wave packets, which would otherwise be incoherent. We analyze how the coupling is affected by the parameters, such as relative phase, pulse width, delay between the two pulses, Rabi coupling strength, and photoelectron energy. Our discussion mostly considers Ne 2p and 2s photoionization, but it is generally valid for many other quantum systems where photoionization from two different shells is observed.