JAYNES-CUMMINGS MODEL FOR MANY M-PHOTON LASERS

We extend the Jaynes-Cummings model for double m-photon lasers of our recent result to a more general situation, and show that the Hamiltonian of an n-level atom with n - 1 lower levels being almost degenerate interacting with a field through n - 1 m-photon processes, can also be reduced to a standard Jaynes-Cummings model. The time evolution operator for the system and the density operator for this many m-photon laser field are also given. Based on the results we show that the phase squeezing and the brightness of the squeezed light of many two-photon lasers are increased with the addition of more coherently prepared lower atomic levels.