  In this paper we treat a cavity QED quantum computation. Namely, we consider
a model of quantum computation based on n atoms of laser-cooled and trapped
linearly in a cavity and realize it as the n atoms Tavis-Cummings Hamiltonian
interacting with n external (laser) fields.
  We solve the Schr{\" o}dinger equation of the model in the weak coupling
regime to construct the controlled NOT gate in the case of n=2, and to
construct the controlled-controlled NOT gate in the case of n=3 by making use
of several resonance conditions and rotating wave approximation associated to
them. We also present an idea to construct general quantum circuits.
  The approach is more sophisticated than that of the paper [K. Fujii,
Higashida, Kato and Wada, Cavity QED and Quantum Computation in the Weak
Coupling Regime, J. Opt. B : Quantum Semiclass. Opt. {\bf 6} (2004), 502].
  Our method is not heuristic but completely mathematical, and the significant
feature is based on a consistent use of Rabi oscillations.
