Excitonic effects on the two-color coherent control of interband transitions in bulk semiconductors

Quantum interference between one- and two-photon absorption pathways allows coherent control of interband transitions in unbiased bulk semiconductors; carrier population, carrier spin polarization, photocurrent injection, and spin-current injection can all be controlled. We extend the theory of these processes to include the electron-hole interaction. Our focus is on photon energies that excite carriers above the band edge, but close enough to it so that transition amplitudes based on low-order expansions in k are applicable; both allowed-allowed and allowed-forbidden two-photon transition amplitudes are included. Analytic solutions are obtained using the effective-mass theory of Wannier excitons; degenerate bands are accounted for, but envelope-hole coupling is neglected. We find a Coulomb enhancement of each two-color coherent control process and relate it to the Coulomb enhancements of one- and two-photon absorption. In addition, we find a frequency-dependent phase shift in the dependence of photocurrent and spin current on the optical phases. The phase shift decreases monotonically from pi/2 at the band edge to zero over an energy range governed by the exciton binding energy. The phase shift is the difference between the partial-wave phase shifts of the electron-hole envelope function reached by one- and two-photon pathways.