Petermann-factor limited sensing near an exceptional point

TL;DR

This paper investigates the fundamental limits of sensing near exceptional points in non-Hermitian systems, revealing that increased responsivity is offset by fundamental noise increases, thus constraining sensor performance.

Contribution

It provides the first quantitative analysis of the fundamental sensitivity limits of sensors operating near exceptional points, highlighting the role of the Petermann factor in noise enhancement.

Findings

Responsivity increases near EPs are offset by linewidth broadening.

Fundamental noise increases according to the Petermann factor.

Experimental observations confirm biorthogonal mode analysis.

Abstract

Non-Hermitian Hamiltonians describing open systems can feature singularities called exceptional points (EPs). Resonant frequencies become strongly dependent on externally applied perturbations near an EP which has given rise to the concept of EP-enhanced sensing in photonics. However, while increased sensor responsivity has been demonstrated, it is not known if this class of sensor results in improved signal-to-noise performance. Here, enhanced responsivity of a laser gyroscope caused by operation near an EP is shown to be exactly compensated by increasing sensor noise in the form of linewidth broadening. The noise, of fundamental origin, increases according to the Petermann factor, because the mode spectrum loses the oft-assumed property of orthogonality. This occurs as system eigenvectors coalesce near the EP and a biorthogonal analysis confirms experimental observations. Besides its importance to the physics of microcavities and non-Hermitian photonics, this is the first time that fundamental sensitivity limits have been quantified in an EP sensor.