Virtual exceptional points in an electromechanical system

TL;DR

This paper demonstrates the creation of virtual exceptional points in a non-Hermitian electromechanical system with highly mismatched modes, enabling exploration of non-Hermitian phenomena in more realistic, diverse physical systems.

Contribution

It introduces a non-Hermitian electromechanical system with vastly different modes and shows how to dynamically couple them to realize virtual exceptional points.

Findings

Virtual EPs can be realized in highly mismatched resonators.

Numerical simulations confirm the coalescence of eigenvalues at the virtual EP.

The system maintains access to non-Hermitian phenomena despite mode disparities.

Abstract

Non-Hermitian Hamiltonians can give rise to exceptional points (EPs) which have been extensively explored with nominally identical coupled resonators. Here a non-Hermitian electromechanical system is developed which hosts vibration modes that differ massively in their spatial profile, frequency and even the sign of their dissipation. An optomechanical-like parametric modulation is employed to dynamically couple 2 of these disparate modes and in the appropriate parameter regime their imaginary eigenvalues coalesce whilst their normal modes split. The presence of this virtual EP is confirmed via numerical simulations of the coupled equations of motions describing the dynamics of this non-degenerate system. These results suggest that virtual EPs can be accessed in systems composed from highly mismatched resonators whilst still maintaining access to the non-trivial phenomenon in their proximity, as recently demonstrated for topological operations, thus enabling non-Hermitian singularities to be more widely exploited with realistic physical systems.