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

Exceptional points (EPs) with their intriguing spectral topology have attracted considerable attention in a broad range of physical systems, with potential sensing applications driving much of the present research in this field. Here we theoretically demonstrate the realization of EPs in a system with significant nonlinearity, a non-equilibrium exciton-polariton condensate. With the possibility to control loss and gain and nonlinearity by optical means, this system allows for a comprehensive analysis of the interplay of nonlinearities (Kerr-type and saturable gain) and non-Hermiticity. Not only do we find that EPs can be intentionally shifted in parameter space by the saturable gain, we also observe intriguing rotations and intersections of Riemann surfaces, and find nonlinearity-enhanced sensing capabilities. Our results are quite general in nature and illustrate the potential of tailoring spectral topology and related phenomena in non-Hermitian systems by nonlinearity.