Non-equilibrium screening and plasmons in a coherently pumped semiconductor

The dielectric function of a coherently pumped semiconductor is calculated in the RPA to arbitrary order in the pump field. The theory starts with the longitudinal intraband polarization function. The diagonal and off-diagonal retarded one-particle Green's functions as well as the distribution functions are derived by means of the non-equilibrium Keldysh formalism. Exact analytical expressions follow within the collisionless regime and the rotating wave approximation. In this regime of the optical Stark effect the wavevector and frequency dependences of the resulting dielectric function are discussed for several values of the Rabi frequency and detuning between the pump frequency and energy gap. In the high-frequency limit the electron-hole pairs excited virtually exhibit the same Drude behaviour as real free carriers. For small frequencies and wavevectors there are remarkable discrepancies. The metallic properties of the virtual two-component plasma are depressed due to a finite transition energy. Moreover, contrary to what is found in the equilibrium case plasmons are strongly Landau damped already, even for vanishing wavevectors. Nevertheless, a screening function within the plasmon pole approximation is prepared.