Engineering the non-Hermitian SSH model with skin effects in Rydberg atom arrays

We propose and systematically analyze a practical scheme for implementing a one-dimensional non-Hermitian Su-Schrieffer-Heeger model using individually addressable Rydberg atom arrays. Our setup consists of an atomic chain with three-atom unit cells, in which a synthetic gauge field is generated by applying multi-color laser fields. By engineering fast dissipative channels for one auxiliary atom in each unit cell, the adiabatic elimination effectively gives rise to a non-Hermitian skin effect. We examine how fluctuations in the experimental parameters influence both the skin effect and the topological invariant under open and periodic boundary conditions in real space and find that both features remain highly robust. This work establishes a versatile, controllable, and programmable open-system quantum simulator with neutral atoms, providing a clear route for exploring rich non-Hermitian topological phenomena.