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

TL;DR

This paper demonstrates a linear, time-modulated electronic circuit approach to generate high-order exceptional points using synthetic gauge fields, avoiding non-linear amplification and enabling advanced sensing and energy transfer applications.

Contribution

It introduces a theoretical and numerical framework for designing high-order EPs in linear electronic circuits with synthetic gauge fields, expanding the possibilities beyond non-linear systems.

Findings

High-order EPs can be realized in linear, time-modulated RLC circuits.

Theoretical mapping to non-Hermitian Hamiltonians with PT-symmetry constraints.

Numerical Floquet analysis reveals exceptional contours of arbitrary order.

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, ultra-sensitive opto-electronic devices. However, arguably one of their major drawbacks is that they rely on non-linear 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 $2N$ dynamical variables and time-dependent parameters can be mapped onto an $N$-site, time-dependent, non-Hermitian Hamiltonian, and obtain constraints for $\mathcal{PT}$-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.