Imaginary photon effect in a generalized k-Photon Λ-type Jaynes–Cummings model with inverse field operators

By using the Lewis-Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent k-photon Λ-type Jaynes–Cummings model with inverse field operators. We find that the geometric phases in a cycle case are independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. It is apparent that the geometric phases have the pure geometric and topological characteristics, which means that the geometric phases represent the holonomy in the Hermitian linear bundles.