Gauge-invariant two-photon transitions in quantum wells

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Abstract
We calculate the two-photon transition rates for a semiconductor quantum well within a two-band model in the effective-mass approximation. The results are presented for polarizations of the beams parallel and orthogonal to the growth axis of the quantum well. Since the model Hamiltonian describing the electronic states contains a nonlocal potential, the interaction with the electromagnetic field has to be generalized to preserve the gauge independence of the physical quantities. We also evaluate the rate in the velocity gauge ‘‘A⋅p,’’ which leads to a gauge-dependent result. Finally we discuss the possibility to discriminate between the different interactions by comparison with experiment.