Probing photon correlations in the dark sites of geometrically frustrated cavity lattices

We explore theoretically the driven-dissipative physics of geometrically frustrated lattices of cavity resonators with relatively weak nonlinearities, i.e., a photon-photon interaction smaller than the loss rate. In such systems, photon modes with zero probability at dark sites are present at the single-particle level due to interference effects. In particular, we study the behavior of a cell with three coupled resonators as well as extended Lieb lattices in one and two dimensions. By considering a partial pumping scheme, with the driving field not applied to the dark sites, we predict that even in the presence of relatively weak photon-photon interactions the nominally dark sites achieve a finite photonic population with strong correlations. We show that this is a consequence of biphoton and multiphoton states that in the absence of frustration would not be visible in the observables.