  We study two-photon scattering in a one-dimensional coupled resonator arrays
(CRA) by a two-level system (TLS), which is localized as a quantum controller.
The $S$-matrix is analytically calculated for various two-photon scattering
processes by TLS, e.g., one photon is confined by TLS to form a bound state
while the other is in the scattering state. It is discovered from the poles of
the $S$-matrix that there exist two kinds of three-body bound states for
describing two bound photons localized around TLS.
