Heterodyne spectroscopy of polariton spinor interactions

We report on spinor polariton interactions in GaAs based microcavities. This investigation is carried out by means of heterodyne polarized pump-probe spectroscopy. We show the dependence of the energy renormalization of the lower and upper polariton resonances with cavity detuning for different polariton densities. We use the exciton-photon based Gross-Pitaevskii equation to model the experiment for both lower and upper polariton modes. The theoretical results reproduce qualitatively the experimental observations revealing the magnitude and sign of the parallel and antiparallel spin interaction strength. We evidence the strong influence of the biexciton resonance on the antiparallel spin polariton energy shift and provide the exciton-biexciton coupling constant. We derive our results in the lower polariton basis using the Gross-Pitaevskii equation, from which we express analytically the spinor polariton interactions and identify the clear role of the biexciton resonance.