Abstract
A theoretical analysis of Berry's phases, which is based on the Cartan subalgebra, is given for three-level atomic systems. The analysis is developed under the adiabatic approximation and is related to topological fibre bundle theories. The topological Berry's phases derived in the present study, are related to phase shifts and can be applied, also, for partial cycles. Some possible applications of the present theory are discussed, for three-level and two-level atomic systems, interacting with nearly resonant monochromatic fields, under the semiclassical and rotating-wave approximations.
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