## 5 Time-Resolved Coherent Excitation and Decay of Strongly Correlated Autoionizing States
In summarizing the work of [14], we wrote:  
_\"The determination of the period of population transfer between the two main configurations is one of the crucial results of the present theory, for it suggests that a laser-generated probe in the attosecond range, which will excite (de-excite) the bright or dark configuration state to a higher (lower) state that can be registered, will allow the recording of the motion of two electrons as they occupy different configurations at different times. We note that the geometry of such configurations can be calculated in terms of appropriate mean values and of angular and radial probability densities.\"_ ([14], p. L276). The possibility of time-resolving, on hyperfast scales, the consequences of electron correlations and rearrangements in atoms and molecules is now an area of research that attracts interest both theoretically and experimentally. For example, the significance of the possibility of determining results of orbital rearrangements in molecules in future measurements with attosecond resolution was arguedby [PERSON] in a recent review [9]. I quote from Section 6 of [9], which is titled \"Future prospects: exploring electronic motions in complex systems\":  
_However, there is another observable of crucial importance: the expectation value of the electrons' spatial coordinates. Dynamic changes in the electrons' atomic-scale distribution... atomic-scale rearrangements of electron charge distributions occurring on the electronic timescale remain inaccessible in complex systems, such as biological molecules and solid-state nanostructures, to this day. Making them perceivable requires attosecond-duration multi-keV photon (X-ray) or electron pulses, permitting diffraction imaging with picometer spatial and attosecond temporal resolution._  
From the point of view of theory, fulfilling this prospect will require quantitatively time-resolving the occupation of orbital configurations in different geometries, analogous to the results for intra-atomic electron rearrangements [15]. Photoionization with Attosecond Resolution. Measurements on Neon and on Helium Agree with Theoretical Predictions  
I now turn to two new phenomena that were originally revealed during the '00s in studies of photoionization of helium and neon. Thus far, their understanding has been possible not only descriptively, but also quantitatively, thanks to achievements at both the experimental and the theoretical levels. As regards experiment, the development and implementation of novel pump-probe techniques have allowed the measurement of quantities that describe time-dependent electron dynamics with attosecond resolution. As regards theory, the same quantities were understood and predicted accurately, thanks to the development and implementation of formalisms that allow the calculation and use of the \(\Psi(t)\) that is appropriate for the solution of the problem. The solution of the METDSE has been obtained either nonperturbatively via the SSEA, or to first order in perturbation theory. In the latter case, we showed that the results of interest can be obtained from an analytic formula that uses N-electron wavefunctions and matrix elements [16]. Only a description of the essentials is given here. The main purpose is to point out that the experimental findings on helium [7, 8] and neon [10, 11] are in agreement with our theoretical results of 2007 [16] and 2010 [11] (see also the conclusion of [17]). Complete information can be found in the original publications [7, 8, 10, 11, 16], including the supporting online material of [11]. The same themes were also briefly reviewed in [3], which is based on an invited talk at the 2015 Sanibel conference. Time-Resolved Generation of the Photoionization Cross-Section Profiles of Doubly Excited and Inner-Hole Autoionizing N-Electron States on Hypershort Time Scales  
In the mid-'00s, in continuation of the initial work on attosecond electron dynamics [14, 15] discussed in Section 5, we completed two projects along the same direction.