Abstract
By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Λ-type Jaynes–Cummings model. We find that, compared with the dynamical phases, 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 pointed out that the geometric phases in a cycle case can be measured under the case of a stronger time-dependent photon field and a stronger coupling photon-atom system. On the other hand, the geometric phases of the model may be measured in the composition of cold atoms.
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