Interpretation of time delay in the ionization of two-center systems

Abstract

We consider the time delay of electron detachment from a Coulomb center and two-center systems in the process of ionization. It is shown that the attosecond streaking, most usual method of time delay measure, can be formally described by placing a virtual detector of the arrival time delay at a certain distance from the center of the system. This approach allows derivation of a simple formula for Coulomb-laser coupling that perfectly agrees with the results of numerical solution of the time-dependent Schrödinger equation. The dependence of the time delay upon the energy, the angular momentum projection, and the azimuthal quantum number is studied for the ionization of molecular hydrogen ion. Finally, we propose a physical interpretation of singularities, arising when the formal expression for the time delay is applied to the ionization of molecular hydrogen.

Attosecond chronoscopy of photoemission

“…The pronounced peak in the EWS time delay, more precisely in magnitude | EWS |, near the point of destructive Cohen-Fano interferences can be viewed as a molecular analogue of the enhancement of EWS near a Cooper minimum (see Section V). Indeed, the suppression of the dipole transition by the two-center interference can be in some cases directly associated with a zero (or Cooper minimum) in a single spheroidal partial wave amplitude of the Coulomb two-center problem Serov et al, 2013). This structural similarity implies, however, that the experimental observation may face a similar challenge as peaks in the EWS time shift are associated with (near) zero emission probability.…”

“…The time encoded in the wavepacket of the receding electron carries information on the initial localization within the molecule as well on the near-field of neighboring atomic constituents. The simplest prototypical case is the photoionization of a diatomic molecule (Fernández et al, 2007;Hu et al, 2009;Guan et al, 2011;Ivanov et al, 2012;Bian and Bandrauk, 2012;Serov et al, 2013;Carpeggiani et al, 2014;Ning et al, 2014;Chacon et al, 2014). Among the fundamental questions to be addressed are: Does it take a longer time for the electron to escape from the multicenter molecular core than from the one-center atomic core?…”

“…containing, in addition to C EWS , a contribution due to the logarithmic distortion of the wavefront Thumm, 2010, 2011c;Nagele et al, 2011;Ivanov and Smirnova, 2011;Dahlström et al, 2013Dahlström et al, , 2012bPazourek et al, 2013;Su et al, 2013b,c;Serov et al, 2013) in the context of attosecond time-resolved photoemission. It gives the time delay relative to a free wavepacket, however, with the drawback that its value depends on the radial coordinate and diverges as → ∞.…”

Angular anisotropy of time delay in XUV+IR photoionization ofH2+

“…For more complex targets like molecules, the angular dependence of the time delay brings particularly useful information as it is sensitive to the orientation of the molecular axis [7].…”

Asymmetry of Wigner's time delay in a small molecule

“…While the Wigner time is included in the measured time, some other factors such as the polarization of the initial state [14], multielectron effects [15], and, more important, the laser-Coulomb coupling are included in the experimental observable [12,14,16]. Recent work has also theoretically addressed the time delay in small molecules such as hydrogen molecules [13] and other two-center molecules [17], emphasizing the consequences of having two centers.…”