  We introduce a dynamical system that instead of exchanging a single photon as
in the atomic system of the usual Jaynes-Cummings model (JCM), it exchanges
instead a squeezed coherent photon. Accordingly, the creation and annihilation
photon operators in the JCM are replaced by the creation and annihilation
operators of squeezed coherent states, respectively. This transformation
generates a photon Hamiltonian that modifies the JCM that includes terms
usually omitted in the JCM when making the rotating-wave approximation and, in
addition, the transformation introduces atom exchange terms absent in the JCM.
