Exotic effects in non-Hermitian quantum optics.

Non-Hermitian photonic reservoirs provide a testbed for intriguing phenomena which cannot be observed in an Hermitian environment. We investigate exotic effects due to the interaction of atoms with such reservoirs. We study the effective interactions between atoms mediated by the photonic modes of a lossy photonic lattice. We show in a paradigmatic case study that when these losses are suitably structured, exotic emission properties can be observed. Photons can mediate dissipative, fully non-reciprocal, interactions between the emitters with range critically dependent on the loss rate. When this loss rate corresponds to specific points in the spectrum of the reservoir, called "exceptional points", the effective couplings are exactly nearest-neighbour, implementing a dissipative, fully non-reciprocal effective interaction between atoms, which is called Hatano-Nelson model. Counterintuitively, this occurs irrespectively of the lattice boundary conditions. Thus, photons can mediate an effective emitters' Hamiltonian which is translationally invariant despite the fact that the field is not. We interpret these effects in terms of metastable atom-photon dressed states, which can be exactly localised.