Signatures of excitonic dark states in the time-resolved coherent response of a quantum well microcavity

We study the coherent time-resolved response of a semiconductor microcavity excited by an ultrashort light pulse. The cavity contains embedded quantum wells and quantum well excitons an strongly coupled to cavity photons. Two experimental situations are examined. We describe a linear regime when the exciting light pulse is weak. Further, a low-temperature pump-and-probe experiment in a nonlinear regime is analyzed, with a cw pump beam circularly polarized opposite to a weak ultrashort probe pulse in conditions yielding a bipolariton-mediated optical Stark effect. In both cases we examine the response of a single quantum well and contrast it with that of several quantum wells. In the latter case light is coupled only to a symmetric linear combination (bright exciton) of excitonic states in individual quantum wells. We find distinctive fingerprints of other linear combinations of exciton states (dark excitons). In the linear regime, in addition to a pattern of Rabi oscillations between the two polariton states, additional beating frequencies appear, related to dark states. In the nonlinear case, the bipolariton formalism outlined by Ivanov et al. [Phys. Rev. B 52, 11 017 (1995)] allows one to deduce a similar additional beating frequency and a splitting of bipolariton frequencies related to their dark or bright state character. This work identifies the effect of the microcavity parameters on its coherent response and determines the experimental conditions in which the influence of dark states may be observed.