On the time evolution at a fluctuating exceptional point

Abstract

We theoretically evaluate the impact of drift-free noise on the dynamics of $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as promising templates for sensing applications, because of their intrinsically extremely sensitive response to external perturbations. However, this applies equally to the impact of fabrication imperfections and fluctuations in the system parameters. Here we focus on the influence of such fluctuations caused by inevitable (thermal) noise and show that the exceptional-point eigenstate is not stable in its presence. To this end, we derive an effective differential equation for the mean time evolution operator averaged over all realizations of the noise field and via numerical analysis we find that the presence of noise leads to exponential divergence of any initial state after some characteristic period of time. We therefore show that it is rather demanding to design sensor systems based on continuous operation at an exceptional point.

arXiv comment7 pages, 2 figures

References in corpus (10)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• The physics of exceptional points
• Topological Band Theory for Non-Hermitian Hamiltonians
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• No exceptional precision of exceptional point sensors
• Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals
• Fluctuations and noise-limited sensing near the exceptional point of $\mathcal{P}\mathcal{T}$-symmetric resonator systems
• Topological Wave-Guiding Near an Exceptional Point: Defect-Immune, Slow-Light, Loss-Immune Propagation
• Time behaviour near to spectral singularities

Cited by in corpus (11)

• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Non-Hermitian Photonic Lattices: tutorial
• Detection sensitivity enhancement of magnon Kerr nonlinearity in cavity magnonics induced by coherent perfect absorption
• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities
• Signature of exceptional point phase transition in Hermitian systems
• Enhanced quantum sensing with hybrid exceptional-diabolic singularities
• Fundamental issues with light propagation through $\mathcal{P}\mathcal{T}$-symmetric systems
• Dynamical transition in non-Hermitian Chern insulator
• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology