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A simple scheme of population and detection of low-lying electronicquadrupole modes in free small deformed metal clusters is proposed. The schemeis analyzed in terms of the TDLDA (time-dependent local density approximation)calculations. As test case, the deformed cluster $Na^+_{11}$ is considered.Long-living quadrupole oscillations are generated via resonant two-photon(two-dipole) excitation and then detected through the appearance of satellitesin the photoelectron spectra generated by a probe pulse. Femtosecond pump andprobe pulses with intensities $I = 2\cdot 10^{10} - 2\cdot 10^{11} W/cm^2$ andpulse duration $T = 200 - 500$ fs are found to be optimal. The modes ofinterest are dominated by a single electron-hole pair and so their energies,being combined with the photoelectron data for hole states, allow to gather newinformation about mean-field spectra of valence electrons in the HOMO-LUMOregion. Besides, the scheme allows to estimate the lifetime of electron-holepairs and hence the relaxation time of electronic energy into ionic heat.Comment: 4 pages, 4 figure

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