NONPERTURBATIVE SCALING BEHAVIOR OF THE COHERENT SEMICONDUCTOR BLOCH EQUATIONS IN THE LOW-DENSITY REGIME

The set of phenomenological model equations which we proposed to determine the scaling behavior of the low-density Rabi oscillations [Phys. Rev. B 48, 17 811 (1993)] is justified from the coherent part of the semiconductor Bloch equations in lowest order in the light-matter coupling. In contrast to similar short-time studies, it is shown that for resonant excitation of an excitonic state the Rabi oscillations can be described by a Ginzburg-Landau type equation which includes only the exciton-exciton interaction of the resonantly excited state but no state-filling terms or contributions from detuned excitonic or continuum resonances. Explicit calculations are performed for the bulk two-band jellium model and for a one-dimensional two-band Hubbard model.