Spectroscopic probes of quantum many-body correlations in polariton microcavities

We investigate the many-body states of exciton-polaritons that can be observed by pump-probe spectroscopy. Here, a weak-probe `spin-down' polariton is introduced into a coherent state of `spin-up' polaritons created by a strong pump. We show that the $\downarrow$ impurities become dressed by excitations of the $\uparrow$ medium, and form new polaronic quasiparticles that feature two-point and three-point many-body quantum correlations, which, in the low density regime, arise from coupling to the vacuum biexciton and triexciton states respectively. In particular, we find that these correlations generate additional branches and avoided crossings in the $\downarrow$ optical transmission spectrum that have a characteristic dependence on the $\uparrow$-polariton density. Our results thus demonstrate a way to directly observe correlated many-body states in an exciton-polariton system that go beyond classical mean-field theories.