Exceptional-point-like Sensing near Hermitian Critical Points

TL;DR

This paper demonstrates that Hermitian systems at critical points can achieve exceptional-point-like sensitivity, surpassing non-Hermitian limits, by exploiting eigenvector orthogonality at critical points without phase transitions.

Contribution

It introduces a Hermitian cavity at a critical point that mimics exceptional point sensitivity, overcoming Petermann factor limitations inherent in non-Hermitian systems.

Findings

Hermitian cavity exhibits square-root response to refractive index changes.

Enhanced sensitivity surpassing non-Hermitian exceptional point sensors.

Sensor operates without phase transitions, simplifying practical implementation.

Abstract

A non-Hermitian system at an exceptional point (EP), a specific critical point (CP) associated with the parity-time symmetric phase transition, exhibits a sublinear response to perturbation and promise unprecedented sensitivity beyond the linear-response Hermitian sensors, so far operating at the diabolic points (DP). Despite great advancements, its sensitivity enhancement is fundamentally limited by the divergent Petermann factor, intrinsically rooted in the non-Hermitian eigenvector degeneracy, and practically by the system complexity. Here, we report the CP-resulting square-root response to the refractive index change and enhanced sensitivity in a simple chiral Hermitian cavity without phase transitions. Because of the inherent eigenvector orthogonality, this CP-based Hermitian sensor exhibits an EP-like response and enhanced sensitivity, breaking the Petermann-factor limit of sensitivity in non-Hermitian counterparts. This work paves the way towards exploring the Hermitian CPs for ultrasensitive sensing outperforming both the EP- and DP-based sensors.