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

TL;DR

This paper extends the theory of two-color coherent control in bulk semiconductors by including excitonic effects, revealing Coulomb enhancement and a frequency-dependent phase shift in photocurrent and spin current responses.

Contribution

It introduces an analytic model incorporating electron-hole interactions into coherent control theory, highlighting Coulomb enhancement and phase shift phenomena near the band edge.

Findings

Coulomb interaction enhances two-photon coherent control processes.

A phase shift in photocurrent depends on photon energy and exciton binding energy.

Analytic solutions relate phase shifts to electron-hole wavefunction partial waves.

Abstract

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 may 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 $\mathbf{k}$ 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 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 0 over an energy range governed by the exciton binding energy. It is the difference between the partial wave phase shifts of the electron-hole envelope function reached by one- and two-photon pathways.