## 5 Time-Resolved Coherent Excitation and Decay of Strongly Correlated Autoionizing States
[51] concerning the generation of attosecond pulses and trains of attosecond pulses. Specifically, in 2002, we published the proposal--which was supported by solutions of the METDSE from first principles--that the then emerging prospects of new electronic spectroscopic techniques that can interrogate electron dynamics on the attosecond time scale could find fertile ground in the study of strongly correlated excited states in the continuum and the ensuing electron rearrangements [14; 15]. It was pointed out that, whereas applying femtosecond spectroscopy provides information about nuclear motion, where the \"motion\" is described classically in terms of positions on potential energy surfaces, in the case of electrons in atoms or molecules, the time-resolution of electronic motion on the attosecond scale can be described in terms of properties of N-electron wave functions and their superpositions. The understanding and treatment of such dynamics engages the following concepts and computable quantities:  
* The main symmetry-adapted orbital configurations obtained in _state-specific_ self-consistent fields, the corresponding physically relevant transition amplitudes, and the \"geometries\" of the electron distributions in correlating configurations, and
* The dominant state-specific electron correlations as determined by the degree of configurational mixing [3,14]. As we wrote in [15], \"The problem was formulated around the following two questions, the first one being more general. _\"(1) Is it possible to probe the electronic structure in such a way as to extract from it meaningful information on dynamics that can be resolved within the attosecond regime? If so, what is an observable process that can reflect the concept of'motion' of electrons?_  
_(2) Considering the first question, given the quantum mechanical formalism of stationary states and of corresponding eigenfunctions of 3N coordinates, how are we to probe and reveal the possible connection of electronic structure to atomic dimensions, to hypershort time scales and to electron correlation?\"_ ([15], p. 2). The case for which the first calculations were carried out was the coherent preparation and decay of the strongly correlated low-lying \({}^{1}P^{o}\) DESs of helium. Their theoretical preparation was effected by letting two femtosecond pulses interact either with the ground state, \(1s^{2}\)\({}^{1}S\), or with the \(1s2s\)\({}^{1}S\) metastable state, so as to simultaneously excite two \({}^{1}P^{o}\) states, labeled by \(2s2p\) and \(2p3d\) configurations and undergoing hyperfast \"_electron correlation beats_\":  
\[He\!\left[ \begin{array}{c}1s^{2}\ {}^{1}S\\ \sigma,1s2s\ {}^{1}S\end{array} \right]\xrightarrow[ \begin{array}{c}\text{ femtosecond}\xrightarrow[]{ pulse}h_{1}\\ \rightarrow\\ \text{femtosecond}\xrightarrow[]{pulse}h_{2}\end{array} \left[ \begin{array}{ c}He\ (2s2p\ +1 sep)^{1}P^{o}\\ He\ (2p3d\ +1 sep)^{1}P^{o}\end{array} \right]\!.\]  
This system was chosen so as to define \"bright\", \"dark\", \"gray\", and \"bath\" electron configurations with respect to excitation, all playing roles in the overall physics [14]. I note that, according to the SPS theory of resonance states [21], the labels \"\(2s2p\)\" and \"\(2p3d\)\" correspond to two-electron wavefunctions that include the localized electron correlations to a high degree of accuracy. One of our proposals, which was supported by quantitative results, was that hyperfast electron rearrangements can be recognized in terms of time-dependent _geometries of the electron distributions_ as the dominant orbital configurations labeling the states correlate [3,14,15] (e.g., see [15], Figure 6). Evidently, a similar picture can exist in molecules, where one may expect that, tracked on attosecond scales, the main features of the electron distribution undergo some degree of oscillation from one nucleus to another.