Arunn Suntharalingam,¹ Lucas Fernández-Alcázar,^2,3 Pablo Fabián Wagner-Boián,³ Mattis Resiner,¹ Ulrich Kuhl,^1,4 Tsampikos Kottos¹

¹Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, CT 06459, United States
²Institute for Modeling and Innovative Technology, IMIT (CONICET – UNNE), W3404AAS, Corrientes, Argentina
³Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina, W3404AAS, Corrientes, Argentina
⁴Université Côte d’Azur, CNRS, Institut de Physique de Nice (INPHYNI), 06200, Nice, France

Exceptional point degeneracies (EPDs) occur in the parameter space of non-Hermitian systems where resonances and their corresponding eigenvectors coalesce. Their presence molds the topology of the eigenmode Riemann surfaces (RS) leading to many novel phenomena with technological applications. Here, using an experimental platform of two coupled nonlinear RLC tanks with balanced amplification and attenuation mechanisms [1], we demonstrate a nonlinearity-induced metamorphosis of the (linear) RS that involves the emergence of unstable branches accompanied by the formation of higher order nonlinear EPDs (occurring between nonlinear eigenmodes – fixed points) and bistable domains. Their width scales with a parameter variation from the EPD in a power law fashion that is engineered by the form of the nonlinearities. We design nonlinearities that enforce square-root scaling and demonstrate a prototypical sensor with diverging sensitivity and noise suppression near the nonlinear EPD due to the broad basins of stability. This unconventional behavior opens opportunities for precise avionic sensing, biosensing, but also for memories and triggers.

References:
[1] A. Suntharalingam, L. J. Fernández-Alcázar, R. Kononchuk, T. Kottos, Nat. Commun. 14, 5515 (2023).