Anomalous point-gap interactions unveil the mirage bath

Non-Hermitian topology has revolutionized our understanding of energy gaps and band topology, unveiling phases that do not exist within the Hermitian framework. Nonetheless, its fundamental implications for quantum interactions in open quantum systems remain largely unexplored. Here, we uncover an interaction mechanism by examining a quantum-optical system where quantum emitters interact through the photonic band gap of a dissipative photon bath with periodic boundaries, described by a nonreciprocal Su-Schrieffer-Heeger model. Although localized photons within the gap should inhibit interactions between emitters in certain regimes, we find that interactions emerge even over long distances, defying conventional expectations. These anomalous interactions are mediated by a “mirage bath”—a virtual bath that unfolds onto a distinct layer of the Riemann surface. This mirage bath generates emitter dynamics identical to those produced by the physical bath but possesses distinct band topology. Crucially, the interactions inherit the topology of the mirage bath, not the physical one. This bath duality is universal to any dissipative bath with point gaps, leading to a mechanism for interactions and correlations across the multilayered Riemann surface, unseen in traditional settings. We demonstrate that the topological mismatch between the dual baths arises necessarily from their equivalent observable dynamics. We further show how such dynamical equivalence enforces the unification of non-Hermitian topologies with different boundaries. Our findings open avenues in quantum optics, many-body quantum simulations, and offer fresh insights into non-Hermitian topology.