The role of nonlinearity on topology has been investigated extensively in Hermitian systems, while nonlinearity has only been used as a tuning knob in a PT-symmetric non-Hermitian system. Here, we show that nonlinearity plays a crucial role in forming a new type of exceptional point, which is dubbed as nonlinear exceptional points (NEPs). We start with a simple and intuitive example by constructing a NEP within two coupled resonators with a nonlinear saturable gain. Such a NEP is a higher-order exceptional point with a hybrid topological invariant (HTI). We show that unstable solutions, which were generally considered irrelevant to dynamics, can play a crucial role in NEP. With the introduction of one more resonator, we are able to realize a 5th-order NEP (NEP₅) within only three coupled resonators. In contrast to the conventional wisdom that the coalescence of eigenvectors inevitably leads to the loss of completeness of the eigenbasis, we show such a NEP₅ exhibits a complete basis in dynamics. Consequently, the noise that diverges at conventional EPs converges at this NEP₅.

Prof. Meng Xiao received his BSc degree from Wuhan University in 2010 and his Ph.D. from the Hong Kong University of Science and Technology (HKUST) in 2014 under the supervision of Prof. C. T. Chan. After that, he worked as a postdoc fellow with Prof. C. T. Chan (at HKUST) and Prof. Shanhui Fan (at Stanford). He joined Wuhan University in 2018.

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