  By jointly using quantum Zeno dynamics and the approach of "transitionless
quantum driving (TQD)" proposed by Berry to construct shortcuts to adiabatic
passage (STAP), we propose an efficient scheme to fast generate multiatom
Greenberger-Horne-Zeilinger (GHZ) states in separate cavities connected by
opitical fibers only by one-step manipulation. We first detail the generation
of the three-atom GHZ states via TQD, then, we compare the proposed TQD scheme
with the traditional ones with adiabatic passage. At last, the influence of
various decoherence factors, such as spontaneous emission, cavity decay and
fiber photon leakage, is discussed by numerical simulations. All the results
show that the present TQD scheme is fast and insensitive to atomic spontaneous
emission and fiber photon leakage. Furthermore, the scheme can be directly
generalized to realize N-atom GHZ states generation by the same principle in
theory.
