Time-convolutionless reduced-density-operator theory of an arbitrary driven system coupled to a stochastic reservoir: Quantum kinetic equations for semiconductors

In this paper two things are done. (1) A projection-operator formalism is used to derive the time-convolutionless stochastic equation of motion for the reduced density operator from the quantum Liouville equation for an arbitrary driven system coupled to a stochastic reservoir. As an initial condition, decoupling of the system and reservoir for the total-density operator is assumed in the formulation. Perturbation expansions of the generalized collision operator are carried out in powers of the driving field within the Born approximation for the interaction of the system with the reservoir. The time-convolutionless form of the equation for the reduced density operator allows one to include the memory effects systematically. (2) Time-convolutionless quantum kinetic equations for interacting electron-hole pairs near the band edge in semiconductors under an arbitrary optical field are obtained from the equation of motion for the reduced density operator. These equations generalize the semiconductor Bloch equations to incorporate the non-Markovian relaxation and the interference effects between the external driving field and the stochastic reservoir of the system and are valid to any time scale. It is shown that the interference term modulates the interband polarization and includes the renormalized memory effects.