Nonlinear optics at excited states of exciton polaritons in two-dimensional atomic crystals.

Exciton polaritons (EPs) are partial light partialmatter quasiparticles in semiconductors demonstrating striking quantum phenomena such as Bose-Einstein condensation and single-photon nonlinearity. In these phenomena, the governing process is the EP relaxation into the ground states upon excitation, where various mechanisms are extensively investigated with thermodynamic limits. However, the relaxation process becomes drastically different and could significantly advance the understanding of EP dynamics for these quantum phenomena, when excited states of EPs are involved. Here, for the first time, we observe nonlinear optical responses at the EP excited states in a monolayer tungsten disulfide (WS2) microcavity, including dark excited states and dynamically metastable upper polariton bands. The nonlinear optics leads to unique emissions of ground states with prominent valley degree of freedom (DOF) via an anomalous relaxation process, which is applicable to a wide range of semiconductors from monolayer transition metal dichalcogenides (TMDs) to emerging halide perovskites. This work promises possible approaches to challenging experiments such as valley polariton condensation. Moreover, it also constructs a valleydependent solid-state three-level system for terahertz photonics and stimulated Raman adiabatic passage.