Time-convolutionless reduced-density-operator theory of an arbitrary driven system coupled to a stochastic reservoir. II. Optical gain and line-shape function of a driven semiconductor

In this paper, recently developed time-convolutionless quantum-kinetic equations for electron-hole pairs near the band edge are used to derive the optical gain and the line-shape function of a driven semiconductor taking into account excitonic effects. The equation of motion for the interband pair amplitude is integrated directly assuming the quasiequilibrium or adiabatic approximation. It is shown that the line shape of the optical-gain spectra is Gaussian for the simplest non-Markovian quantum kinetics. On the other hand, the line-shape function becomes Lorentzian, which has been assumed in most practical calculations, in the Markovian limit. It is also shown that the optical gain is enhanced by (1) excitonic effects caused by the attractive electron-hole Coulomb interaction and (2) interference effects (or renormalized memory effects) between the external driving field and the stochastic reservoir of the system. Gain enhancement by the memory effects can be interpreted as the result of the violation of energy conservation on the time scale shorter than the correlation time.