Abstract
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. It is found that, different from the dynamical phases, the geometric phases in a cycle case are independent of the photon numbers, the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency.
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