  Rephasing and non-rephasing two-dimensional coherent spectra map the
anti-crossing associated with normal-mode splitting in a semiconductor
microcavity. For a 12-meV detuning range near zero detuning, it is observed
that there are two diagonal features related to the intra-action of
exciton-polariton branches and two off-diagonal features related to coherent
interaction between the polaritons. At negative detuning, the lineshape
properties of the diagonal intra-action features are distinguishable and can be
associated with cavity-like and exciton-like modes. A biexcitonic companion
feature is observed, shifted from the exciton feature by the biexciton binding
energy. Closer to zero detuning, all features are enhanced and the diagonal
intra-action features become nearly equal in amplitude and linewidth. At
positive detuning the exciton- and cavity-like characteristics return to the
diagonal intra-action features. Off-diagonal interaction features exhibit
asymmetry in their amplitudes throughout the detuning range. The amplitudes are
strongly modulated (and invert) at small positive detuning, as the lower
polariton branch crosses the bound biexciton energy determined from negative
detuning spectra.
