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We introduce a new Hamiltonian model which interpolates between theJaynes-Cummings model and other types of such Hamiltonians. It works with twointerpolating parameters, rather than one as traditional. Taking advantage ofthis greater degree of freedom, we can perform continuous interpolation betweenthe various types of these Hamiltonians. As applications we discuss a paradoxraised in literature and compare the time evolution of photon statisticsobtained in the various interpolating models. The role played by the averageexcitation in these comparisons is also highlighted.

On the paradoxical evolution of the number of photons in a new model of interpolating Hamiltonians