  We recently demonstrated orders of magnitude enhancement of two-photon
absorption (2PA) in direct gap semiconductors due to intermediate state
resonance enhancement for photons of very different energies. It can be
expected that further enhancement of nondegenerate 2PA will be observed in
quantum wells (QWs) since the intraband matrix elements do not vanish near the
band center as they do in the bulk, and the density of states in QWs is larger
near the band edge. Here we present a perturbation-theory based theoretical
description of nondegenerate 2PA in semiconductor QWs, where both frequency and
polarization of two incident waves can vary independently. Analytical
expressions for all possible permutations of frequencies and polarizations have
been obtained, and the results are compared with degenerate 2PA in quantum
wells along with degenerate and nondegenerate 2PA in bulk semiconductors. We
show that using QWs in place of bulk semiconductors with both beams in the
TM-polarized mode leads to an additional order of magnitude increase in the
nondegenerate 2PA. Explicit calculations for GaAs QWs are presented.
