Abstract
By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a two energy level Jaynes-Cummings model with imaginary photon process. We find that the geometric phases in a cycle case have nothing to do with the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. If we use the more accuracy device, the geometric phases in the imaginary photon process may be observed, and the geometric phases in this process have the observable physical effect.
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