  We examine the eigenstates of the one-dimensional Jaynes-Cummings-Hubbard
(JCH) 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 ratio
as a function of the quasi-momentum quantum number, and indicate that the bound
states carry a strong correlation in which the two polaritons appear to be
spatially confined together.
