APPROACH TO A GENERALIZED JAYNES-CUMMINGS MODEL AND THE GEOMETRIC PHASE

Adopting the recently introduced inverses of boson creation and annihi lation operators, we construct a nonunitary transformation to solve ex actly a generalized Jaynes-Cummings (JC) model. The method reveals tha t the JC model in a new frame can be viewed simply as a system of a sp in-1/2 atom interacting with a magnetic field dependent on the photon number. For the initial state with fixed photon number l, the JC model becomes a cyclic evolution, and exhibits a geometric phase gamma(g). We discuss the properties of gamma(g) in the large l limit.