Two-polariton bound states in the Jaynes-Cummings-Hubbard model

We examine the eigenstates of the one-dimensional Jaynes-Cummings-Hubbard model in the two-excitation subspace. We discover that two-excitation bound states emerge when the ratio of vacuum Rabi frequency to the tunneling rate between cavities exceeds a critical value. We determine the critical value as a function of the quasimomentum quantum number, and indicate that the bound states carry a strong correlation in which the two polaritons appear to be spatially confined together.

Figure 1

Eigenvalues of the $H$ for $N=50$, odd $P$, and $\Delta =0$ for (a) $g/J=0.1$, (b) $g/J=1.7$, (c) $g/J=2$, and (d) $g/J=5$. The eigenvalues are joined by lines for ease of visualization.

Figure 2

Joint probability distributions associated with bound states for the system with $\Delta =0$, $P=1$, and $N=50$ at various coupling strengths. The right column corresponds to $g$ slightly above the critical value.

Figure 3

Illustration of the function $G$ for the system with $\Delta =0$, $N=50$, $P=15$, and $g/J=2$. Nonzero eigenvalues of the Hamiltonian are roots of $G(\lambda )=0$. The red dots inside the gaps are roots corresponding to bound states.

Figure 4

Critical ratio $g_c/J$ as a function of $P$ for $\Delta =0$ systems.