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Exceptional points (EPs) with their intriguing spectral topology haveattracted considerable attention in a broad range of physical systems, withpotential sensing applications driving much of the present research in thisfield. Here we theoretically demonstrate the realization of EPs in a systemwith significant nonlinearity, a non-equilibrium exciton-polariton condensate.With the possibility to control loss and gain and nonlinearity by opticalmeans, this system allows for a comprehensive analysis of the interplay ofnonlinearities (Kerr-type and saturable gain) and non-Hermiticity. Not only dowe find that EPs can be intentionally shifted in parameter space by thesaturable gain, we also observe intriguing rotations and intersections ofRiemann surfaces, and find nonlinearity-enhanced sensing capabilities. Ourresults are quite general in nature and illustrate the potential of tailoringspectral topology and related phenomena in non-Hermitian systems bynonlinearity.

Tweaking Spectral Topology and Exceptional Points by Nonlinearity in Non-Hermitian Polariton Systems