Berry phases and Rabi oscillations

Abstract

The Berry phases for a spherically symmetric atom in a circularly polarized semiclassical radiation field are calculated using an operator decomposition scheme. The author then takes the two-level atomic limit and recovers the Berry phases already calculated by other means. His attention is then focused on the two-level atom. He shows that in the semiclassical problem the Rabi oscillations do not arise from cyclic wavefunctions. Hence any comparison of the phases of the initial and final states must use the Pancharatnam connection. In the quantum model he no longer gets perfect Rabi oscillations as there are partial collapses and revivals. These collapses and revivals are exploited in alternative quantum optical models, the Raman coupling model and intensity-dependent coupling model, for which they are exactly cyclic. Again he finds that he must invoke the Pancharatnam connection.