Abstract

The strong coupling between quantum well excitons and cavity photons leads to the appearance of a new type of quasi-particles, the so-called microcavity polaritons. The energy dispersion of polaritons is very sharp owing to the photon component. At the same time, the polaritons are strongly interacting due to the exciton-exciton interaction and saturation. In this contribution, we present a microscopic theory for the nonlinear optics of the polariton matter. Microscopic equations are presented for two different regimes. The first regime concerns the coherent angle-resolved pump-probe spectroscopy We demonstrate that a parametric process leads to a giant angle-resonant amplification of the probe beam in very good agreement with recent experiments [1]. Analytical and numerical results show that the amplification has a threshold in the dependence on the pump intensity. The threshold intensity is such that the lower polariton blueshift is equal to its linewidth. The minimal threshold intensity is obtained when the idler energy matches the polariton dispersion. This is the reason for the angle-resonant character of the amplification. The second regime concerns the nonlinear emission from microcavities which are incoherently excited through a non-resonant pump. In this case, the nonlinear behavior is due to an incoherent population of excitons at the polariton bottleneck. We show that the three-polariton correlation leads to a huge nonlinearity in the lower polariton emission at k = 0 The phenomenology is quite reminiscent of the coherent case, because the threshold intensity and gain shift are determined by the polariton linewidth. Our results are in excellent agreement with the experiments by Le Si Dang et al. [2]. The present work represents a fascinating theoretical progress for the nonlinear optics of microcavities. Our microscopic equations allow to give a unified understanding of very different experiments [1, 2] and show in a clear way the intriguing nonlinear physics of the polariton matter.

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