Approach to a generalized Jaynes-Cummings model and the geometric phase.

Abstract

Adopting the recently introduced inverses of boson creation and annihilation operators, we construct a nonunitary transformation to solve exactly a generalized Jaynes-Cummings (JC) model. The method reveals that the JC model in a new frame can be viewed simply as a system of a spin-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 ${\ensuremath{\gamma}}_{\mathit{g}}$. We discuss the properties of ${\ensuremath{\gamma}}_{\mathit{g}}$ in the large l limit.