Both cavity quantum electrodynamics and photons are promising candidates for quantum information processing. We consider a combination of both candidates with a single photon going through spatially separate cavities to entangle the atomic qubits, based on the input-output process of the cavities. We present a general expression for the input-output process regarding the low- cavity confining a single atom, which works in a wide range of parameters. Focusing on low- cavity case, we propose some schemes for quantum information processing with Faraday rotation using single photons, which is much different from the high- cavity and strong-coupling cases.