Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system
By Chong Chen, Liang Jin, Renbao Liu. New Journal of Physics, 2018
162 citations recorded by the source corpus.
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 dϵ1/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.
Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f6039f970616e98d0fc0d76cc138aea12c90d28d
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Citations in the corpus
- Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps (2019, background): “However, more detailed analyses of noise showed some fundamental limits of HEP-enhanced sensors [73–78].”
- Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories (2020, background): “The advantages of EPs for applications remain a very active topic of research [16, 61–74] and correctly modeling noise and quantum jumps is fundamental to correctly address the question of, e.”