We present a practical scheme of preparing a temporally stationary single-p
hoton-trapped state. A special dynamics at two-photon resonance in the coup
led atom-cavity system, where a two-level atom is driven by a classical fie
ld, is investigated for this purpose. It is found that significant atomic d
amping is required, rather than avoided, to establish the one-photon Fock s
tate. We analytically derive the optimal conditions in the large detuning l
imit.