We propose a scheme for entanglement distribution among different single atoms trapped in separated cavities. In our scheme, by reflecting an input coherent optical pulse from a cavity with a single trapped atom, a controlled phase-shift gate between the atom and the coherent optical pulse is achieved. Based on this gate and homodyne detection, we construct an $n$-qubit parity gate and show its use for distribution of a large class of entangled states in one shot, including the GHZ state $leftvert GHZ_{n}rightrangle $, W state $leftvert W_{n}rightrangle $, Dicke state $leftvert D_{n,k}rightrangle $ and certain sums of Dicke states $% leftvert G_{n,k}rightrangle $. We also show such distribution could be performed with high success probability and high fidelity even in the presence of channel loss.
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