  We investigate polariton-polariton interactions in a semiconductor
microcavity through two-dimensional Fourier transform (2DFT) spectroscopy. We
observe, in addition to the lower-lower and the upper-upper polariton
self-interaction, a lower-upper cross-interaction. This appears as separated
peaks in the on-diagonal and off-diagonal part of 2DFT spectra. Moreover, we
elucidate the role of the polariton dispersion through a fine structure in the
2DFT spectrum. Simulations, based on lower-upper polariton basis
Gross-Pitaevskii equations including both self and cross-interactions, result
in a 2DFT spectra in qualitative agreement with experiments.

Mesoscale and Nanoscale Physics