Probing the non-Hermitian skin effect via the cavity transmission spectrum

In recent years, the study of non-Hermitian systems has attracted significant attention, particularly for their unique topological phenomena such as the non-Hermitian skin effect (NHSE). Here we investigate the NHSE in a non-Hermitian Su-Schrieffer-Heeger atomic chain and its coupling with a cavity mode, focusing on how NHSE modifies the cavity's transmission spectrum. We theoretically model the atomic chain which possesses a specific symmetry under open boundary conditions. Our results show that the eigenstates localize at the chain edges for certain parameters, indicating the existence of the NHSE. This effect produces distinct peaks in the cavity transmission spectrum at frequencies corresponding to eigenstates in the nontrivial phase; these peaks vanish in the trivial phase. By tuning atomic gain and loss, we identify sharp spectral minima at the topological phase transition point, which enables precise detection of the transition. These results demonstrate that the cavity transmission spectrum serves as a sensitive probe for non-Hermitian topological effects, offering a scalable experimental framework to explore the NHSE without calculating topological invariants.