Fig. 2: Hermitian topological preservation.
From: Hermitian and non-Hermitian topology from photon-mediated interactions
A Scheme of the photonic Su–Schrieffer–Heeger (SSH) lattice with staggered \(v\) and \(w\) \({{{{{\rm{couplings}}}}}}\). The coupling strength between each quantum emitter and each resonator is \(g\). B A sketch of the mediated emitters’ Hamiltonian \({\hat{H}}_{a}\) is shown in purple (where the multiple links highlight its high connectivity). Open boundary conditions for the atomic system are obtained by removing quantum emitters, but leaving the photonic lattice unaffected (hence it remains translationally invariant). C Modulus of the wave function of the photonic edge states with \(N=60\) resonators (top), and atomic edge states with \({N}_{e}=44\) emitters (bottom) coupled to a periodic SSH lattice with \(N\) resonators (top) and \(d=8\) sites. The resonators are numbered in increasing order including both types (1 and 2, cf. Equation 4) of resonators. Atomic open boundary conditions are obtained by removing 2\(d\) quantum emitters (outer violet stripes) while maintaining the periodic photonic structure. Atomic edge states are mostly localized on the first and last sites (notice the logarithmic scale). The nonzero amplitude on the remaining sites is a finite-size effect. The insets show the photonic and atomic energy spectra under open boundary conditions in units of \(v\). Parameters: \(w=1.5v,g=0.1v\), and \({\omega }_{e}=0\).
