Geometric Phase in a Two Energy Level k-Photon Jaynes-Cummings Model with Imaginary Photon Process

By using the Lewis-Riesenfeld invariant theory, we have studied the dynamical phase and the geometric phase in a two energy level k-photon Jaynes-Cummings model with imaginary photon process. We find that the geometric phase in a cycle case is independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. We predict the physical effect of the geometric phase in the imaginary photon process may be measured.