Figure 1

(a) Schematic diagram of a compressed 2D hexagonal photonic crystal with a square supperlattice of band gap cavities. The photonic crystal can be fabricated by drilling through a thin membrane. Each cavity is defined by four enlarged holes surrounding the red sphere ($C_{2v}$ symmetry point). Photons hop between the nearest cavities with a hopping rate $\kappa$. To explore spin-dependent photon-photon interactions, we insert a single $V$-type three-level atom into each cavity. (b) Brillouin zone of the compressed 2D hexagonal lattice. This configuration has $A_2$ symmetry modes centered about the $C_{2v}$ symmetry points (red spheres), with dominant Fourier components situated at $\{\pm {\mathbf{k}}_{x1},\pm {\mathbf{k}}_{j2}\}$. The electrical fields of these components are perpendicular to the wave vectors, so each cavity supports only $\sigma$ polarized light. (c) Schematic diagram showing the pertinent $V$-type energy level within each atom-cavity system.Reuse & Permissions

Figure 2

Eigenspectrum for a $V$-type atom in a cavity as a function of zero field atom-cavity detuning $\Delta$. (a) Eigenspectrum of one-photon ground state and two-photon excited state $E_{|-,1⟩}$ and $E_{|-,2⟩}$ without the Zeeman field, ${\Delta }_B=0$. (b) The Eigenspectrum splits into two branches for one-photon ground state, and to three branches for the two-photon excited state with ${\Delta }_B=0.5\Delta$.Reuse & Permissions