  We analyze particular two-photon processes as possible means to explore
electronic quadrupole states in free small deformed atomic clusters. The
analysis is done in the time-dependent local density approximation (TDLDA). It
is shown that the direct two-photon population (DTP) and off-resonant
stimulated Raman (ORSR) scattering can be effectively used for excitation of
the quadrupole states in high-frequency (quadrupole plasmon) and low-frequency
(infrared) regions, respectively. In ORSR, isolated dipole particle-hole states
as well as the tail of the dipole plasmon can serve as an intermediate state. A
simultaneous study of low- and high-frequency quadrupoles, combining DTP and
ORSR, is most effective. Femtosecond pulses with intensities $I = 2\cdot
10^{10} - 2\cdot 10^{11} W/cm^2$ and pulse durations $T = 200 - 500$ fs are
found to be optimal. Since the low-lying quadrupole states are dominated by one
single electron-hole pair, their energies, being combined with the
photoelectron data for hole states, allow to get the electron spectrum above
the Fermi level and thus greatly extend our knowledge on the single particle
spectra of clusters. Besides, the developed schemes allow to estimate the
lifetime of the quadrupole states.
