Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system

TL;DR

This paper investigates the potential for enhanced parameter estimation sensitivity near exceptional points in non-Hermitian systems, revealing that eigenstate coalescence counteracts the expected divergence, resulting in no dramatic sensitivity enhancement.

Contribution

The study applies quantum Fisher information to analyze parameter sensitivity near exceptional points, showing that coalescence prevents divergence in sensitivity.

Findings

Eigenstate coalescence counteracts susceptibility divergence.

No dramatic sensitivity enhancement at exceptional points.

Sensitivity remains a smooth function of the perturbation.

Abstract

The exceptional points of non-Hermitian systems, where $n$ different energy eigenstates merge into an identical one, have many intriguing properties that have no counterparts in Hermitian systems. In particular, the $\epsilon^{1/n}$ dependence of the energy level splitting on a perturbative parameter $\epsilon$ near an $n$-th order exceptional point stimulates the idea of metrology with arbitrarily high sensitivity, since the susceptibility $d\epsilon^{1/n}/d\epsilon$ diverges at the exceptional point. Here we theoretically study the sensitivity of parameter estimation near the exceptional points, using the exact formalism of quantum Fisher information. The quantum Fisher information formalism allows the highest sensitivity to be determined without specifying a specific measurement approach. We find that the exceptional point bears no dramatic enhancement of the sensitivity. Instead, the coalescence of the eigenstates exactly counteracts the eigenvalue susceptibility divergence and makes the sensitivity a smooth function of the perturbative parameter.