Non-Hermitian synthetic lattices with light-matter coupling

We propose that light-matter coupling can be used to realize synthetic lattices. In particular, we consider a one-dimensional chain of exciton-photon sites to create a comb lattice that exhibits a transition from a flat band to a finite mass dispersion by tuning site-dependent light-matter coupling. Moreover, in a non-Hermitian system with gain and loss, the flat-band phase is much more robust, and the transition is accompanied by the appearance of exceptional points in the complex energy spectrum. We demonstrate that by engineering the light-matter coupling in the synthetic lattice, one can explore various phases in the lasing regime. Our proposal paves the way for studying non-Hermitian systems in higher dimensions.