The dynamics of dipolariton states in a planar microcavity under pumping of the state corresponding to the intermediate dipolariton branch has been studied. Aperiodic conversion of pump dipolaritons into dipolaritons of idler and signal modes is shown to occur under exact-resonance conditions.
The system of nonlinear evolution equations was obtained for describing the time evolution of densities of pump, signal, and idler microcavity polaritons. It was shown that the period and amplitude of oscillations of the polariton densities essentially depend on the initial densities of polaritons, initial phase difference, and resonance detuning. For the definite relation between the parameters, the aperiodic evolution of the system is also possible; it represents the conversion of only the part of pump polaritons, by which the evolution of the system is finished. The significant dependence of the period and amplitude of polariton oscillations on the initial phase difference evidences the possibility of the phase controlling of the polariton dynamics. The damping of the system of coherent polaritons leads to the oscillatory decay of polariton density in time, the rate of which is defined by the polariton damping constants.
The polariton dynamics in a microcavity in the parametric oscillator mode, when two pump polaritons are transformed into signal and idler polaritons and vice versa, has been studied. A nonlinear differential equation is obtained, which describes the temporal evolution of pump-polariton density, the solution of which is expressed in terms of the Jacobi elliptical functions. The amplitude and period of polaritondensity oscillations are determined by the initial polariton densities and the resonance detuning. The possibility of self-trapping in exciton-polariton dynamics is predicted.
The threshold of triply resonant optical parametric oscillation in a semiconductor microcavity in the strong coupling regime is investigated. Because of the third-order nature of the excitonic nonlinearity, a variety of different behaviors is observed thanks to the interplay of parametric oscillation and optical bistability effects. The behavior of the signal amplitude and of the quantum fluctuations in approaching the threshold has been characterized as a function of the pump, signal, and idler frequencies.