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

The exceptional points (EPs) 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 ${ϵ}^{1/n}$ dependence of the energy level splitting on a perturbative parameter ϵ near an nth order EP stimulates the idea of metrology with arbitrarily high sensitivity, since the susceptibility dϵ ^1/n/dϵ diverges at the EP. Here we theoretically study the sensitivity of parameter estimation near the EPs, using the exact formalism of quantum Fisher information (QFI). The QFI formalism allows the highest sensitivity to be determined without specifying a specific measurement approach. We find that the EP 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. (paper)