Noise Constraints for Nonlinear Exceptional Point Sensing

Abstract

Exceptional points (EPs) are singularities in the parameter space of a non-Hermitian system where eigenenergies and eigenstates coincide. They hold promise for enhancing sensing applications, but this is limited by the divergence of shot noise near EPs. According to recent studies, EP sensors operating in the nonlinear regime may avoid these limitations. By analyzing an exemplary nonlinear system, we show that the interplay of noise and nonlinearity introduces previously-unidentified obstacles to enhanced sensing. The noise effectively displaces the EP in parameter space and reduces its order, thereby eliminating the sought-for divergence in the signal-to-noise ratio. Moreover, the noise near the nonlinear EP experiences a stronger divergence than predicted by standard calculations of the Petermann noise factor, due to the properties of the Bogoliubov-de Gennes Hamiltonian governing the fluctuations. Our semi-analytical estimates for the noise level agree quantitatively with the results of stochastic numerical simulations.

References in corpus (8)

• The physics of exceptional points
• Loss-induced suppression and revival of lasing
• Observation of coherent perfect absorption at an exceptional point
• Light stops at exceptional points
• Quantum synchronization of two Van der Pol oscillators
• Exceptional-point Sensors Offer No Fundamental Signal-to-Noise Ratio Enhancement
• Exceptional precision of a nonlinear optical sensor at a square-root singularity
• Petermann factors and phase rigidities near exceptional points

Cited by in corpus (7)

• Enhancement of signal-to-noise ratio at a high-order exceptional point of coherent perfect absorption
• Theory for the spectral splitting exponent of exceptional points
• Achieving the Quantum Fisher Information Bound in Pseudo-Hermitian Sensors
• Recent advances in the combination of nonlinearity and exceptional points
• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology
• The Role of Exceptional Points and Transmission Peak Degeneracies in Non-Hermitian Sensing
• Impact of noise on nonlinear-exceptional-point-based sensors