Exact Solutions for Jaynes-Cummings Models with Non-degenerate Two-Photon Transitions in the Ladder Configuration

摘要

In the present paper, the eigenfunctions and eigenvalues of the Hamiltonian of the interacting system have been obtained in two generalized Jaynes Cummings models separately, one in which the transition are mediated by two different modes of photon in the ladder configuration and the other involving two mode multi-photon interaction between the field and the atom. Effect of intensity dependent coupling between the field and the atom in both the above-mentioned cases have been investigated. Graphical features of the time dependence of population inversion have been analyzed when one of the field modes is prepared initially in a coherent state while the other one in a vacuum state. The unitary transformation method presented here for the special case of exact resonance not only solves the time-dependent problem but also provides the eigensolutions of the interacting Hamiltonian at the same time.