We present a quantum model to calculate the dipole-dipole coupling between electronic excitations in the conduction band of semiconductor quantum wells. We demonstrate that the coupling depends on a characteristic length, related to the overlap between microscopic current densities associated with each electronic excitation. As a result of the coupling, a macroscopic polarization is established in the quantum wells, corresponding to one or few bright collective modes of the electron gas. Our model is applied to derive a sum rule and to investigate the interplay between tunnel coupling and Coulomb interaction in the absorption spectrum of a dense electron gas.
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