Giant emitters in a structured bath with non-Hermitian skin effect

Giant emitters derive their name from nonlocal field-emitter interactions and feature diverse self-interference effects. Authors of most of the existing works on giant emitters have considered Hermitian waveguides or photonic lattices. In this letter, we unveil how giant emitters behave if they are coupled to a non-Hermitian bath, i.e., a Hatano-Nelson (HN) model which features the non-Hermitian skin effect due to the asymmetric intersite tunneling rates. We show that the behaviors of the giant emitters are closely related to the stability of the bath. In the convectively unstable regime, where the HN model can be mapped to a pseudo-Hermitian lattice, a giant emitter can either behave as in a Hermitian bath or undergo excitation amplification, depending on the relative strength of different emitter-bath coupling paths. Based on this mechanism, we can realize protected nonreciprocal interactions between giant emitters, with nonreciprocity opposite to that of the bath. Such giant-emitter effects are not allowed, however, if the HN model enters the absolutely unstable regime, where the coupled emitters always show secular energy growth. Our proposal provides a paradigm of non-Hermitian quantum optics, which may be useful for, e.g., engineering interactions between quantum emitters and performing many-body simulations in the non-Hermitian framework.