Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields

Abstract

Exceptional points (EPs) are degeneracies of non-Hermitian systems, where both eigenvalues and eigenvectors coalesce. Classical and quantum systems exhibiting high-order EPs have recently been identified as fundamental building blocks for the development of novel, ultrasensitive optoelectronic devices. However, arguably one of their major drawbacks is that they rely on nonlinear amplification processes that could limit their potential applications, particularly in the quantum realm. In this work, we show that high-order EPs can be designed by means of linear, time-modulated, chain of inductively coupled RLC (where R stands for resistance, L for inductance, and C for capacitance) electronic circuits. With a general theory, we show that 𝑁 coupled circuits with 2⁢𝑁 dynamical variables and time-dependent parameters can be mapped onto an 𝑁-site, time-dependent, non-Hermitian Hamiltonian, and obtain constraints for 𝒫𝒯 symmetry in such models. With numerical calculations, we obtain the Floquet exceptional contours of order 𝑁 by studying the energy dynamics in the circuit. Our results pave the way toward realizing robust, arbitrary-order EPs by means of synthetic gauge fields, with important implications for sensing, energy transfer, and topology.