An　approach　for　realizing　conditional　phase　gate　for　two　atoms　separately　trapped　in　two　distant　cavities　mediated　by　an　optical　fiber　is　proposed.　Utilizing　the　adiabatic　passage,　the　atomic　spontaneous　emission,　and　the　decays　of　the　fiber　and　cavities　are　avoided　under　certain　condition.　The　effects　of　the　losses　in　the　fiber　and　cavities　on　the　fidelity　are　analyzed.　Moreover,　our　scheme　is　not　restricted　to　Lamb-Dicke　limit.　We　also　generalize　the　approach　to　generate　one-dimensional　cluster　state　and　entangled　state　for　two　collections　of　atoms.　(C)　2007　Elsevier　B.V.　All　rights　reserved.