  Extending a previous result on the generation of two-photon generalized
binomial field states, here we propose an efficient scheme to generate with
high-fidelity, in a single-mode high-Q cavity, N-photon generalized binomial
states with a maximum number of photons N>2. Besides their interest for
classical-quantum border investigations, we discuss the applicative usage of
these states in realizing universal quantum computation, describing in
particular a scheme that performs a controlled-NOT gate by dispersive
interaction with a control atom. We finally analyze the feasibility of the
proposed schemes, showing that they appear to be within the current
experimental capabilities.
