Figure 1

Scheme for nonlinearly coupled QED cavities. (a) An array of QED cavities nonlinearly coupled by N-type atoms. The photon hopping between nearest-neighbor cavities has a strength t. Each effective site is composed of a cavity and an atom (dashed box). (b) Level structure of the N-type atoms. The transition \(\vert 1 \rangle \leftrightarrow \vert 3 \rangle \) is resonantly coupled to the cavity mode of its own site with strength \(g_{1}\), while \(\vert 2 \rangle \leftrightarrow \vert 4 \rangle\) is coupled to the cavity mode of its right nearest-neighbor site with strength \(g_{2}\), and has a detuning Δ. The transition \(\vert 2 \rangle \leftrightarrow \vert 3 \rangle \) is in resonance with an external laser field of strength Ω.