Saturation Dynamics in Non-Hermitian Topological Sensing Systems

TL;DR

This paper investigates the saturation behavior of non-Hermitian topological sensors, revealing how system parameters and terminal couplings influence sensitivity and eigenenergy scaling, with implications for sensor design.

Contribution

It elucidates the dependence of saturation and sensitivity on system parameters and introduces how unidirectional coupling can invert eigenenergy size dependence.

Findings

Eigenenergy saturation depends on a winding number.

Unidirectional coupling flips eigenenergy size dependence.

Saturation behavior is characterized by system parameters.

Abstract

A class of non-Hermitian topological sensors (NTOSs) was recently proposed in which the NTOS comprises a non-Hermitian Su-Schrieffer-Heeger chain with a measurant-dependent coupling between the two ends of the chain. The smallest eigenenergy of the system, which serves as the readout signal, has an exponential dependence on the system size at small system sizes but saturates above a critical size. In this study, we further elucidate the dependence of the sensor sensitivity and saturation behavior on the system parameters. We explain how the behavior of the NTOS is characterized by a winding number, which indicates whether the smallest eigenenergy decreases to zero exponentially with the system size or grows exponentially up to a critical size. Interestingly, we further show that by imposing unidirectionality on the coupling between the two ends of a sensor, we can flip the size dependence of the smallest eigenenergy value from an exponentially increasing trend to an exponentially decreasing one. Our findings provide important insights into the saturation phenomenon and the impact of terminal couplings on the sensing characteristics of NTOSs.