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

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.

25 pages, 4 figures

References in corpus (33)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Quantum sensing
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Topological Band Theory for Non-Hermitian Hamiltonians
• Coherent Perfect Absorbers: Time-reversed Lasers
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Topological energy transfer in an optomechanical system with exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• PT-Symmetric Phonon Laser
• Exceptional Points of Non-hermitian Operators
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Observation of the exceptional point in cavity magnon-polaritons
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• $\mathcal{P}\mathcal{T}$-Symmetry-Breaking Chaos in Optomechanics
• Dynamically encircling exceptional points: Exact evolution and polarization state conversion
• Waves in Open Systems: Eigenfunction Expansions
• A review of progress in the physics of open quantum systems: theory and experiment
• Quantum parameter estimation using general single-mode Gaussian states
• Quantum parameter estimation using general single-mode Gaussian states
• No exceptional precision of exceptional point sensors
• Signatures of three coalescing eigenfunctions
• Light stops at exceptional points
• Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point
• Fidelity for displaced squeezed states and the oscillator semigroup
• Experimental demonstration of an anisotropic exceptional point
• Incident Direction Independent Wave Propagation and Unidirectional Lasing
• Chirality of wave functions for three coalescing levels
• Exceptional Point Engineered Glass Slide for Microscopic Thermal Mapping
• Jordan blocks and generalized bi-orthogonal bases: realizations in open wave systems
• Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators
• Hamiltonian and Linear-Space Structure for Damped Oscillators: II. Critical Points

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• Signatures of Liouvillian exceptional points in a quantum thermal machine
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• Non-Hermitian Topological Phases: Principles and Prospects
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• Non-Dissipative Non-Hermitian Dynamics and Exceptional Points in Coupled Optical Parametric Oscillators
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• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• Theory for the spectral splitting exponent of exceptional points
• Resonant-amplified and invisible Bragg scattering based on spin coalescing modes
• Achieving the Quantum Fisher Information Bound in Pseudo-Hermitian Sensors
• Recognizing critical lines via entanglement in non-Hermitian systems
• Enhanced quantum sensing with hybrid exceptional-diabolic singularities
• Quantum Enhanced Sensitivity through Many-Body Bloch Oscillations
• Controlling quasi-parametric amplifications: From multiple PT-symmetry phase transitions to non-Hermitian sensing
• Recent advances in the combination of nonlinearity and exceptional points
• Non-Hermitian physics and engineering in silicon photonics
• Simulation of exceptional-point systems on quantum computers for quantum sensing
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• An interferometric method to estimate the eigenvalues of a Non-Hermitian two-level optical system
• Anti-parity-time topologically undefined state
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Robustness of tripartite entangled states in passive PT-symmetric qubits
• Impact of noise on nonlinear-exceptional-point-based sensors
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: II. Nonconventional PT-symmetric dynamics and unidirectional coupling
• Stability via symmetry breaking in interacting driven systems
• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology
• Real critical exponents from the $\epsilon$-expansion in an interacting $U(1)$ model with non-Hermitian $Z_4$ anisotropy