# Photoionization dynamics: Transition and scattering delays

J Caillat, Michel Vacher, R Gaillac, A Maquet, R Taïeb

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J Caillat, Michel Vacher, R Gaillac, A Maquet, R Taïeb. Photoionization dynamics: Transition and scattering delays. Journal of Physics: Conference Series, 2015, 635 (9), pp.092148 10.1088/1742-6596/635/9/092148. [hal-01265695](https://hal-01265695)

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Photoionization dynamics: Transition and scattering delays

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2015 J. Phys.: Conf. Ser. 635 092148

(http://iopscience.iop.org/1742-6596/635/9/092148)

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Photoionization dynamics:
Transition and scattering delays

J. Caillat<sup>a 1</sup>, M. Vacher<sup>b</sup>, R. Gaillac<sup>a</sup>, A. Maquet<sup>a</sup> and R. Taëeb<sup>a</sup>

<sup>a</sup> UPMC, CNRS, UMR 7614, Laboratoire de Chimie Physique – Matière et Rayonnement, Paris, France

<sup>b</sup> Department of Chemistry, Imperial College London, London, SW7 2AZ, UK

**Synopsis** The advent of attosecond science, with main objectives to probe and to control ultrafast dynamics in quantum systems, brought in the past few years a fresh look on photoemission. This very fundamental process was indeed recently revisited in the time domain, in a series of pioneering experiments [1] that were soon accompanied by an intense theoretical activity devoted to the interpretation of the reported "photoemission delays". At the conference, we will present some contributions of our group to this topic [2], with a focus on the characterization of photoemission dynamics in terms of "scattering delay" and "transition delay" as evidenced in numerical experiments performed on simple model systems.

Resolving electron motion in atoms and molecules on its natural attosecond (as) scale is way beyond the temporal resolution of available detection devices. The techniques developed to achieve such sub-fs resolution thus rely on interferometric setups, and the reported times are actually group delays derived from phase measurements, involving coherent photoemission processes. Therefore, the analysis of the experimental data and the related theoretical development ask for rigorous and unambiguous definitions and interpretations of these phases, and of the inferred group delays.

It is now accepted that a “scattering delay” [4] affects the dynamics of any photoemission process. However, the simplicity of the underlying physics is not fully recognized yet. Formally, such delays are imprinted in the phase shifts of the photoelectron wave-functions, which are commonly expressed on the basis of incoming waves. In this framework, the “scattering phase” associated to photoemission appears as the argument of the transition amplitude, thus obscuring the significance of the delay – which may be misinterpreted for example as a transition duration. Here, we will present the benefits of working with the continuum wave-functions selected by the transitions (SCWF) [3], which (i) carry all the information related to the continuum reached by photoabsorption, (ii) are defined independently of the arbitrary basis one chooses to work with and (iii) are real valued for single-photon transitions. They provide a clear-cut interpretation of the scattering delays.

In higher order processes, the SCWF comes
with an additional complex phase, as soon as the
transition is resonant. We will show that the
group delay associated with that phase can now
be interpreted as a “transition delay”, and how

it can be accessed experimentally in a straight-
forward reinterpretation of the RABBIT interfero-
metric technique, initially designed for the char-
acterization of coherent XUV pulses [5].

<figure><img src="image_2.png" /><figcaption>**Figure 1.** He⁺(2p₀) @ 17.06 eV. (a) Real valued SCWF . (b) Ionization delays against the detection direction θd: time-dependent simulations (circles); scattering group delays (full line). The delays are defined and computed with θd = 0 as reference.</figcaption></figure>

References

[1] S. Haessler *et al* 2009 *Phys. Rev. A* **80** 011404;
M. Schultze *et al* 2010 *Science* **25** 1658 ; K. Klun-
der *et al* 2011 *Phys. Rev. Lett.* **106** 143002

[2] J. Caillat *et al* 2011 *Phys. Rev. Lett.* **106** 093002;
R. Gaillac *et al* 2015 *submitted*; M. Vacher *et al*
2015 *in preparation*

[3] H. Park *et al* 1996 *J. Chem. Phys* **104** 4554

[4] E. P. Wigner 1955 *Phys. Rev.* **98** 145

[5] P. M. Paul *et al* 2001 *Science* **292** 1689

<footnote n="1">¹E-mail: jeremie.caillat@upmc.fr</footnote>