Quantum interference control of free-carrier density in GaAs

We have carried out theoretical and experimental investigations of optical phase controlled-free carrier injection in semiconductors via quantum interference between different absorption pathways connecting the same initial and final states in the valence and conduction bands. The interference schemes are theoretically modeled within a Fermi Golden rule approximation which also allows for a description in terms of the susceptibility formalism of nonlinear optics. Two different types of schemes involving interference between n and m multiphoton absorption events are considered depending on whether $n+m$ is even or odd. If $n+m$ is odd, phase control of carrier density can be observed only in a noncentrosymmetric crystal; if $n+m$ is even, interference can be observed in both centrosymmetric and noncentrosymmetric materials. The interference contribution to the density control is related to the imaginary part of the nonlinear electric susceptibility ${\chi }_{n+m-1}.$ Experimentally we have investigated carrier density control effects in GaAs at room temperature using nominally 150 fs optical pulses and considered an example for each of the two schemes: one-photon vs two-photon absorption with 0.775 and $1.55\mu \mathrm{m}$ pulses and one-photon vs three-photon absorption with 0.675 and $2.03\mu \mathrm{m}$ pulses. The main experimental features, including degree of phase control, are in good agreement with theory. We extract the relative magnitude of the imaginary and real components of ${\chi }_2$ and ${\chi }_3$ for GaAs at $1.55\mu \mathrm{m}$ and $2.03\mu \mathrm{m},$ respectively.