The soft-photon approximation in infrared-laser-assisted atomic ionization by extreme-ultraviolet attosecond-pulse trains

Abstract

We use the soft-photon approximation, formulated for finite pulses, to investigate the effects of the dressing pulse duration and intensity on simulated attosecond pump-probe experiments employing trains of attosecond extremeultraviolet pulses in conjunction with an IR probe pulse. We illustrate the validity of the approximation by comparing the modelled photoelectron distributions for the helium atom, in the photon energy region close to the N = 2 threshold, to the results from the direct solution of the time-dependent Schrödinger equation for two active electrons. Even in the presence of autoionizing states, the model accurately reproduces most of the background features of the ab initio photoelectron spectrum in the 1s channel. A splitting of the photoelectron harmonic signal along the polarization axis, in particular, is attributed to the finite duration of the probe pulse. Furthermore, we study the dependence of the sideband integrated signal on the pump-probe time delay for increasing IR field strengths. Starting at IR intensities of the order of ∼1 TW cm −2 , overtones in the sideband oscillations due to the exchange of three or more IR photons start to appear. We derive an analytical expression in the frequency-comb limit of the 3

Two-photon finite-pulse model for resonant transitions in attosecond experiments

“…In the same spirit, we can assume Os p + 2/3 ,2p 2 = O sp + 2/3 ,2p 2 , with which qs p + 2/3 ,2p 2 become derived quantities, thus reducing to 12 the total number of independent parameters. Finally, we assume q2 p 2 ,1s2p ≫ 1, so that the product O 1sε ℓ ,1s2p O 1s2p,1s 2 q2 p 2 ,1s2p comes as a single parameter γ2 p 2 ←1s2p←1s 2 , thus reducing the total number of parameters to 11. In one of our previous works [48], we developed a softphoton model for the non-resonant ionization of helium in which the continuum singlet states of the atom were approximated by the product of the 1s ground state of the He + parent-ion with free spherical waves,…”

Modulation of Attosecond Beating in Resonant Two-Photon Ionization

“…In the longpulse limit, the APT only comprises odd multiples H 2n+1 of the IR carrier frequency ω IR . The transition amplitudes for the two alternative A + γ H2n±1 ± γ IR → A + + e − paths, therefore, interfere giving rise to a sideband SB 2n whose intensity oscillates with frequency 2ω IR , ∆I 2n ∝ cos(ϕ 2n + 2ω IR τ ), where the ϕ 2n offset is given by the relative phase between the two consecutive H 2n±1 harmonics and the so-called relative atomic phase [9]. The RABBIT technique, therefore, can be used to reconstruct either the APT from the harmonic phases [10], if the atomic phases are known, or the atomic phases [11][12][13], if the APT shape is known.An appealing perspective is to use attosecond technologies to investigate photoionization processes governed by electron correlation [14][15][16][17].…”

Autoionizing states of atomic boron

“…Finally, the CC + LC bases examined in this work constitute a suitable space in which to conduct time-resolved studies of the correlated dynamics of three electrons triggered by subfemtosecond extreme-ultraviolet pulses. Therefore, this work, which demonstrates the possibility of building accurate scattering states within those same spaces, opens the way to the "exact" asymptotic analysis of correlated three-electron wave packets in the single-ionization continuum of three-electron systems, in a way similar to the one that has already been successfully employed for the helium atom [83][84][85][86]88]. …”

“…This is also confirmed by the agreement between the results of the present work and the few theoretical and experimental data available in the literature. Finally, explicit calculation of scattering states for two-electron systems has proved useful to analyze the asymptotic properties of the correlated electron wave packets generated in time-resolved simulations of photoionization events triggered by femtosecond and attosecond light pulses [83][84][85][86][87][88]. This work demonstrates that such approach can be extended to more complex systems, for which the representation of scattering states in terms of orthogonal single partial-wave channels is not possible, due to the correlated character of the parent ions, thus laying the foundations for a time-resolved study of the correlated motion of three electrons in the continuum.…”