Scattering properties of anti-parity-time symmetric non-Hermitian system

TL;DR

This paper explores the unique scattering behaviors of an anti-parity-time symmetric non-Hermitian system, revealing reciprocal reflection and transmission, size-dependent probability relations, and parity-dependent scattering matrix properties.

Contribution

It provides the first detailed analysis of scattering properties in anti-parity-time symmetric non-Hermitian systems, including experimental realization and theoretical characterization.

Findings

Reflection and transmission are reciprocal.

R+T=1 or R-T=1 depending on system size parity.

Scattering matrix properties depend on the parity of the scattering center.

Abstract

We investigate the scattering properties of an anti-parity-symmetric non-Hermitian system. The anti-parity-symmetric scattering center possesses imaginary nearest-neighbor hoppings and real onsite potentials, it has been experimentally realized through dissipative coupling and frequency detuning between atomic spin waves. We find that such anti-parity-symmetric system displays three salient features: Firstly, the reflection and transmission are both reciprocal. Secondly, the reflection and transmission probabilities satisfy R+T=1 or R-T=1, which depends on the parity of the scattering center size. Thirdly, the scattering matrix satisfies (S_z)(S_z)*=I for scattering center with even-site; for scattering center with odd-site, the dynamics exhibits Hermitian scattering behavior, possessing unitary scattering matrix SS{\dag}=I.