Synthetic dimension with light-mater coupling

We propose that light-matter coupling can be used to realize a synthetic dimension. In particular, we consider a one-dimensional chain of exciton-polariton sites to create a ladder model that exhibits a transition from a Lieb lattice 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 dimension, one can explore various phases in the polariton lasing regime. Our proposal paves the way for studying non-Hermitian systems in higher dimensions.