For three-dimensional many-electron time periodic Hamiltonians which are invariant under dynamical symmetry of order $N$ we prove that only the $(\mathrm{nN}\pm 1)\mathrm{th}$, $n=1,2,\dots ,$ harmonics are generated. We discuss the application of the dynamical symmetry based selection rules to the generation of high harmonics by thin crystals. The derived selection rules are demonstrated numerically for a one-dimensional model, showing that the dynamically symmetric systems can be used not only as “filters” of the very high harmonics but also as their “amplifiers.”

Interatomic (or intermolecular) Coulombic decay is a general, very efficient mode of decay of inner valence vacancies in clusters. The physically appealing interpretation of such decays as a transfer of a virtual photon between two cluster units rests on the neglect of the orbital overlap between them. We show that even in loosely bound van der Waals clusters the orbital overlap is a crucial factor. At the equilibrium geometry of a cluster, the overlap effect can bring about an enhancement of the decay rate by 2–3 orders of magnitude, making the process dramatically more efficient than implied by the simple estimations.

A new computational technique is introduced for the ab initio calculation of the rates of interatomic and intermolecular nonradiative decay processes occurring due to electronic correlation. These recently discovered phenomena are described theoretically using the configuration-interaction formalism first introduced by Fano [Phys. Rev. 124, 1866 (1961)] and later adapted to an Auger decay by Howat et al. [J. Phys. B 11, 1575 (1978)]. The boundlike and the continuumlike components of the wave function of the decaying state are constructed using a Green’s-function method known as algebraic diagrammatic construction. A combination of atomic and distributed Gaussian basis sets is shown to provide an adequate description of both boundlike and continuumlike wave-function components. The problem of the normalization of the continuum (final state) wave function is addressed using the Stieltjes imaging technique. The new method is applied to the calculation of the rates of interatomic decay in alkaline-earth–rare-gas clusters. The obtained results help to verify our earlier conclusions [Phys. Rev. Lett. 93, 263002 (2004)] regarding the validity of the virtual-photon transfer model for the interatomic Coulombic decay. In addition, we demonstrate that the process of electron-transfer-mediated decay is responsible for the finite lifetimes of the outer valence vacancies in alkaline-earth–rare-gas clusters.

The lifetime of interatomic Coulombic decay (ICD) [L. S. Cederbaum et al., Phys. Rev. Lett. 79, 4778 (1997)] in ${\mathrm{Ne}}_2$ is determined via an extreme ultraviolet pump-probe experiment at the Free-Electron Laser in Hamburg. The pump pulse creates a $2s$ inner-shell vacancy in one of the two Ne atoms, whereupon the ionized dimer undergoes ICD resulting in a repulsive ${\mathrm{Ne}}^{+}(2p^{-1})-{\mathrm{Ne}}^{+}(2p^{-1})$ state, which is probed with a second pulse, removing a further electron. The yield of coincident ${\mathrm{Ne}}^{+}-{\mathrm{Ne}}^{2+}$ pairs is recorded as a function of the pump-probe delay, allowing us to deduce the ICD lifetime of the ${\mathrm{Ne}}_2^{+}(2s^{-1})$ state to be $(150\pm 50)\mathrm{fs}$, in agreement with quantum calculations.

In quantum systems, coherent superpositions of electronic states evolve on ultrafast time scales (few femtoseconds to attoseconds; 1 attosecond = 0.001 femtoseconds = 10⁻¹⁸seconds), leading to a time-dependent charge density. Here we performed time-resolved measurements using attosecond soft x-ray pulses produced by a free-electron laser, to track the evolution of a coherent core-hole excitation in nitric oxide. Using an additional circularly polarized infrared laser pulse, we created a clock to time-resolve the electron dynamics and demonstrated control of the coherent electron motion by tuning the photon energy of the x-ray pulse. Core-excited states offer a fundamental test bed for studying coherent electron dynamics in highly excited and strongly correlated matter.