Interference between E2 and M1 amplitudes in two-colour frequency mixing in atoms

The relative contributions of the magnetic dipole interaction (M1) and the electric quadrupole interaction (E2) in the dipole-forbidden three-wave process of mixing two-colour radiation in free atoms may be determined from the dependence of the frequency-conversion efficiency on the incident-wave polarization. Analytical expressions are derived for the polarization dependence of amplitudes and cross sections of a double-resonant scattering of the sum- and difference-frequency photons. Numerical estimates are presented for the ratio of E2 and M1 three-photon amplitudes in ground-state indium and thallium atoms.