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Physical Review A

Time-dependent perturbation theory beyond the dipole approximation for two-photon ionization of atoms

Mu-Xue Wang, Hao Liang, Xiang-Ru Xiao, Si-Ge Chen, Liang-You Peng

Published Feb 5, 2019• 8 citations
Publisher

Abstract

We develop a time-dependent perturbation theory (PT) beyond the dipole approximation to analyze the two-photon ionization dynamics of atoms exposed to short laser pulses with an arbitrary polarization. In a wide range of laser parameters, the good performance of the PT method is validated by comparing the results of a number of physical quantities with those calculated by numerically solving the time-dependent Schr\"odinger equation beyond the dipole approximation. Subsequent applications of the PT method in the nonresonant regime allow us to unveil the important role of the interferences between the dipole and nondipole transition pathways to the photoelectron momentum shift along the laser-propagation direction. In particular, we find that the ratio of the probability of each dipole transition channel to the total ionization probability oscillates with the increase of the photon energy. The interferences among different pathways and the oscillatory behavior of the ratios jointly lead to a series of minima in the linear momentum transfer for the case of the linear polarization.

DOI
10.1103/physreva.99.023407

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Journal of Physics B Atomic Molecular and Optical Physics•Dec 14, 1995•5 citations
We develop a time-dependent perturbation theory (PT) beyond the dipole approximation to analyze the two-photon ionization dynamics of atoms exposed to short laser pulses with an arbitrary polarization. In a wide range of laser parameters, the good performance of the PT method is validated by comparing the results of a number of physical quantities with those calculated by numerically solving the time-dependent Schr"odinger equation beyond the dipole approximation. Subsequent applications of the PT method in the nonresonant regime allow us to unveil the important role of the interferences between the dipole and nondipole transition pathways to the photoelectron momentum shift along the laser-propagation direction. In particular, we find that the ratio of the probability of each dipole transition channel to the total ionization probability oscillates with the increase of the photon energy. The interferences among different pathways and the oscillatory behavior of the ratios jointly lead to a series of minima in the linear momentum transfer for the case of the linear polarization.
Synopsis We develop a time-dependent perturbation theory beyond the dipole approximation to analyze the two-photon ionization dynamics of atoms exposed to short laser pulses with an arbitrary polarization. Subse-quent applications of the PT method in the nonresonant regime allow us to analyze one of the most important nondipole effects, i.e., the linear-momentum-transfer law in the two-photon ionization process and to unveil the important role of the interferences between the dipole and nondipole transition pathways to the photoelectron momentum shift along the laser-propagation direction.
Abstract Beyond the widely adopted dipole approximation, nondipole effects play an important role in completely understanding the electronic dynamics in light–matter interaction. We present a two-photon interferometric scheme to theoretically study the under-threshold nondipole transition phase over a broad energy range. It is found a significant difference between the nondipole and dipole two-photon transition phases near the Cooper minimum, which originates from the multichannel interference in the nondipole transition. Through the angular dependence of transition phase, we uncover the competition among partial waves in nondipole ionization. This work advances the fundamental understanding of nondipole dynamics in two-photon ionization, and opens a route toward the complete reconstruction of nondipole photoelectron wave packets.
When an atom is driven by a laser field with a photon energy that is nearly resonant with an atomic transition, it can undergo periodic population transfers between the ground and excited state, known as Rabi oscillations [1], [2]. The aim of this work is to study photoionization from atoms for parameters accessible to a free-electron laser (FEL) [3]. Using time dependent perturbation theory to model photoionization from a Rabi oscillating atom, we have shown that in addition to the expected pathway of ionization from the excited state, non-resonant two-photon ionization will have a comparable amplitude at intensities on the order of 1013W/cm2[3].
We study nondipole effects in multiphoton ionization of a two-dimensional hydrogen-like atom by a flat-top laser pulse of varied intensity. For this purpose, we solve numerically a two-dimensional Schrödinger equation treating a propagating laser pulse exactly. The resulting distributions are then compared to those calculated in the dipole approximation. A directional dependence of the energy-angular photoelectron distributions is demonstrated numerically in the case of a propagating laser pulse of a moderate and a high intensity. It is analytically interpreted based on the leading order relativistic expansion of the electron Volkov state, showing a significant contribution of the electron recoil to that behavior. In contrast, the retardation correction originating from the space- and time-dependence of the laser field leads to a tiny redshift of the photoelectron energy spectra. Other features of ionization distributions are also analyzed, including the sidelobes and the double-hump structures of multiphoton peaks, or their disappearance for intense propagating laser pulses.
We calculate two-dimensional photoelectron momentum distributions and energy spectra after multiphoton ionization of Li atoms subject to intense laser fields in the one-photon Rabi-flopping regime. The time-dependent Schr\"odinger equation is solved within the single-active-electron approximation using a model potential which reproduces accurately the binding energies and dipole matrix elements of the Li atom. Interaction with the external electromagnetic field is treated within the dipole approximation. We show that the Rabi oscillations of the population between the ground 2s2s2s state and the excited 2p2p2p state in the one-photon resonance regime are reflected in the energy spectra of emitted photoelectrons, which manifest interference structures with minima. Transformations of the interference structures in the photoelectron energy spectra caused by the variation of the laser peak intensity and pulse duration are analyzed.
For pt.I see ibid., vol.28, p.5057-75 (1995). In the previous paper, a non-perturbative time-dependent theory of resonant multiphoton ionization by both smooth and rectangular pulses was derived, and as a first step, applied to the two-photon ionization of caesium in weak fields. In the present paper, we continue the analysis of the same system, extending the weak-field results and considering the case of stronger fields. At higher intensities the spectra exhibit energy modulations of a different character from those predicted for low power. Here, for stronger fields, the structure arises from Rabi oscillations, which, for the smooth pulses assumed here, are triggered by time-dependent Stark shifts. In order to obtain a better understanding of the energy oscillations, we also look at the photoelectron energy spectrum produced by a rectangular pulse, a problem which is solved exactly. We show that there are other sources of strong-field structure.