Photon conversion among multichromatic waves in two-level atom systems

In this paper, we shall discuss a generalized version of the Jaynes-Cummings model in which a two-level atom is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that this two-level atom system can be mapped into an effective model in which a quantum particle moves in a lattice whose sites specify the number of photons in the multichromatic waves. In general, when the number L of modes is greater than two, large energy exchanges among different monochromatic waves are possible (L = 2 is a special case; exchanges of a large number of photons are possible only for degenerate modes). Depending on the frequencies of the elecromagnetic modes, we can classify the two-level systems in two categories. In one case, the eigenfunctions of the quantum particle are extended and thus exchange of a large number of photons is possible. In the other case, the eigenfunctions of the quantum particle are localized and exchange of a large number of photons is greatly suppressed.