Abstract
The two-photon non-degenerate Jaynes-Cummings models are investigated. By solving the Heisenberg equations of motion, the exact solutions are obtained. The dynamical behavior of the photon annihilation operator a( t), of the atomic dipole-moment operator σ −( t), and of the population difference operator σ z ( t) are analyzed and demonstrated as a function of the interaction time. It will be shown that the cross-correlation functions between two different field modes with different times can be easily derived from our solutions. By varying the parameter of the time differences, the several field correlation functions will be plotted as a function of the interaction time. The equation for the dipole-dipole correlation functions of the atom are presented also. The comparisons of our computer simulations with the results obtained by the density operator method will be presented.
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