Jaynes-Cummings model:: Solutions without rotating-wave approximation

The Jaynes-Cummings model in the general nonresonant case without rotating-wave approximation is considered. The analysis is carried out using the resolvent formalism. It is shown that one, given the matrix of Hamiltonian resolvent, can easily find all basic physical quantities corresponding to the given model. The matrix of the resolvent of the total Hamiltonian for the given model is found. Matrix elements of the resolvent are expressed in terms of continued fractions. It is shown that these fractions uniformly converge to meromorphic functions, which corresponds to a purely point spectrum of the total Hamiltonian. The time evolution in the case of exact resonance for different coupling constants is numerically studied. It is shown that the rotating-wave approximation is not satisfactory for large coupling constants even in the case of exact resonance. In this case, probabilities of multiphoton transitions increase with increasing coupling constant. (C) 2000 MAIK Nauka/Interperiodica.