Effect of pure dephasing on the Jaynes-Cummings nonlinearities.

We study the effect of pure dephasing on a two-level system in strong coupling in the nonlinear regime with the single mode of a cavity. The photoluminescence spectrum of the cavity has a robust tendency to display triplet structures, instead of the expected Jaynes-Cummings pairs of doublets at the incommensurate frequencies +/- (square root n +/- square root (n-1)) for integer n. We discuss recent experimental works that may already manifest signatures of single photon nonlinearities.