Two-photon excitation of low-lying electronic quadrupole states in atomic clusters

Abstract

A simple scheme of population and detection of low-lying electronic quadrupole modes in free small deformed metal clusters is proposed. The scheme is analyzed in terms of the time-dependent local density approximation calculations. As a test case, the deformed cluster $\mathrm{Na}_{11}{}^{+}$ is considered. Long-living quadrupole oscillations are generated via resonant two-photon (two-dipole) excitation and then detected through the appearance of satellites in the photoelectron spectra generated by a probe pulse. Femtosecond pump and probe pulses with intensities $I=2\ifmmode\times\else\texttimes\fi{}{10}^{10}--2\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$ and pulse duration $T=200--500\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ are found to be optimal. The modes of interest are dominated by a single electron-hole pair and so their energies, being combined with the photoelectron data for hole states, allow us to gather full mean-field spectra of valence electrons near the Fermi energy. Besides, the scheme allows us to estimate the lifetime of electron-hole pairs and hence the relaxation time of electronic energy into ionic heat.