Far Infrared absorption of non center of mass modes and optical sum rule in a few electron quantum dot with Rashba spin-orbit coupling

Spin-orbit interaction in a quantum dot couples far infrared radiation to non center of mass excitation modes, even for parabolic confinement and dipole approximation. The intensities of the absorption peaks satisfy the optical sum rule, giving direct information on the total number of electrons inside the dot. In the case of a circularly polarized radiation the sum rule is insensitive to the strength of a Rashba spin-orbit coupling due to an electric field orthogonal to the dot plane, but not to other sources of spin-orbit interaction, thus allowing to discriminate between the two.