We describe a mathematical solution for the generation of entangled N-photon
states in two field modes. A simple and compact solution is presented for a
two-mode Jaynes-Cummings model by combining the two field modes in a way that
only one of the two resulting quasi-modes enters in the interaction term. The
formalism developed is then applied to calculate various generation
probabilities analytically. We show that entanglement, starting from an initial
field and an atom in one defined state may be obtained in a single step. We
also show that entanglement may be built up in the case of an empty cavity and
excited atoms whose final states are detected, as well as in the case when the
final states of the initially excited atoms are not detected.Comment: v2: 5 pages, RevTeX4, minor text changes + 1 figure added, revised
version to be published in PRA, May 200