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 TDLDA (timedependent local density approximation) calculations. As test case, the deformed cluster N a + 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 · 10 10 − 2 · 10 11 W/cm 2 and pulse duration T = 200 − 500 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 to gather new information about mean-field spectra of valence electrons in the HOMO-LUMO region. Besides, the scheme allows to estimate the lifetime of electron-hole pairs and hence the relaxation time of electronic energy into ionic heat.

Exploration of electronic quadrupole states in atomic clusters by two-photon processes

“…(t) = | d rφ [220] ( r, t)φ [220] ( r)| 2(3)turns out to contribute the complementing 99-97%. Similar relations were obtained for the direct two-photon (DTP) excitation of the quadrupole, described in[10]. During the…”

“…In principle, the photoionization can be also provided by the coherent synchrotron source with high-frequency photons. Then the two-photon ionization proposed in [10] can be replaced by more effective one-photon ionization. In this case, the characteristics of the pump and Stokes pulses can be taken again from [10], while the parameters of the probe irradiation need an independent adjusting.…”

“…A particularly interesting aspect emerges for low-frequency (infrared) quadrupole modes in small deformed clusters. It was found that these modes are dominated by a single electronhole (1eh) pair [9,10] and their spectra are close to the pure 1eh energy differences ǫ eh = ǫ e − ǫ h . As a result, measuring the energy ǫ eh in a two-photon process and the energy of the hole (occupied) state e h by PES [2,3,4], we gain information on the particle energy ǫ e .…”

“…It is worth noting that, unlike the dipole states with their high frequencies and strong collective mixing, the quadrupole states of interest mainly originate from the deformation splitting [9,10]. Their energy scale is thus quite small and they usually lie in the infrared region < 1eV .…”

“…However, to our knowledge, none has been applied so far in experimental investigations of atomic clusters. Some of these processes, namely the direct two-photon population (DTP) [10], the off-resonant stimulated Raman scattering (ORSR) [12], and the stimulated Raman adiabatic passage (STIRAP) [13,14], seem to be quite promising [15] and are thus worth a closer inspection. As is shown below, some particular cluster properties, e.g.…”