  In this paper we generalize the Jaynes--Cummings Hamiltonian by making use of
some operators based on Lie algebras su(1,1) and su(2), and study a
mathematical structure of Rabi floppings of these models in the strong coupling
regime. We show that Rabi frequencies are given by matrix elements of
generalized coherent operators (quant--ph/0202081) under the rotating--wave
approximation.
  In the first half we make a general review of coherent operators and
generalized coherent ones based on Lie algebras su(1,1) and su(2). In the
latter half we carry out a detailed examination of Frasca (quant--ph/0111134)
and generalize his method, and moreover present some related problems.
  We also apply our results to the construction of controlled unitary gates in
Quantum Computation. Lastly we make a brief comment on application to Holonomic
Quantum Computation.
