  We develop a systematic method of solving two non-interacting Jaynes-Cummings
models by using the dressed state formalism in Hilbert space
$\mathcal{H}_{AB}^{(2\otimes2)}$. It is shown that such model, called Double
Jaynes-Cummings model (D-JCM), can be exactly solved if we take the initial
bare state as the linear superposition of two Bell states. The collapse and
revival oscillation, which is the standard trait of typical Jaynes-Cummings
model, can be recovered if we make measurement at each local sites. Some
consequence of the entanglement-induced dressing is discussed.
