  A hybrid quantum system combines two or more distinct quantum components,
exhibiting features not seen in these individual systems. In this work, we
study the one-dimensional Jaynes-Cummings- Hubbard model in the two-excitation
subspace. We find that the center momentum of two-excitation induces a magnetic
ux piercing the 4-leg ladder in the auxiliary space. Furthermore, it is shown
that the system in {\pi}-center-momentum subspace is equivalent to a chain
system for spin-1 particle with spin-orbit coupling. As a simple application,
based on this concise description, a series of bound-pair eigenstates is
presented, which displays long-range correlation.
