Fig. 1. Schematic configuration of the two-site coupled-cavity system. The system is composed of two harmonic resonators and two Λ-type three-level atoms. For the atom, |e⟩ represents the excitation state, and |H⟩ and |V⟩ are the degenerate ground states of the atom.

Fig. 2. Entropies in the ground states as a function of detuning and hopping strength. Parameter values are gV=0.5gH, where gH=1 is set as the basic unit throughout this paper.

Fig. 3. Probabilities for the purely atomic states in the ground states.

Fig. 4. Probabilities for the intersect states, one atom being in the excited state in one cavity, while a photon is in its eigenstate in the other cavity, in the ground states.

Fig. 5. Probabilities for the intersect states, two excitations being in the same cavity, in the ground states.

Fig. 6. Probabilities for the all-photon states.

Fig. 7. Probabilities of the intersect states: (a) one atom excited in one cavity and one H-polarized photon excited in the other cavity, (b) one atom excited in one cavity and one V-polarized photon excited in the other cavity, (c) one atom and one H-polarized photon excited in the same cavity, and (d) one atom and one V-polarized photon excited in the same cavity.

Fig. 8. Probability distribution of the H-polarized photons under the small hopping limit. Parameter values are gH=2gV and A=0.01gH.

Fig. 9. Bipartite entanglement under the small hopping limit. Parameter values are gH=2gV and A=0.01gH.

Fig. 10. Probability distribution of the eigenstates in the one-site subsystem. The inset shows the total probability for the three eigenstates. Parameter values are gH=2gV and A=0.01gH.

Fig. 11. Bipartite entanglement under the large hopping limit. Parameter values are gH=2gV and A=10gH.

Fig. 12. Dependence of S=⟨MxNα⟩+⟨MxNβ⟩+⟨MyNα⟩−⟨MyNβ⟩ on the detuning Δ. The solid curves show the results calculated in the classical manner, while the dashed curves are the results calculated in the quantum manner. From top to bottom, and from left to right, panels (a)–(i) correspond to the results calculated for directions α=0,π/4,π/2,3π/4,π,5π/4,3π/2,7π/4, and 2π, respectively. The gray lines are the gridlines of ±2,±22. Parameters are gH=2gV and A=0.01gH.