Geometric phases and the Rabi Hamiltonian

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Calderon, J
De Zela, F
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American Physical Society
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We address Berry phases that have been predicted to appear when a two-level system interacts with a quantized field, including the vacuum state. The issue became controversial after it was argued that the appearance of such Berry phases is an artifact of the rotating-wave approximation (RWA). As is widely believed, whenever the RWA applies, one may replace the Rabi model of a two-level system interacting with a quantized field by the analytically solvable Jaynes-Cummings model. Conflicting predictions of these two models under conditions that validate the RWA would signal a serious inconsistency of this approximation. We show that this is not the case and that claims to the contrary are inconsistent with analytical results concerning the Rabi model. We provide also numerical evidence supporting our analytical approach. Furthermore, we argue that the appearance of Berry phases in the addressed cases does not depend on adiabatic conditions nor on any particular Hamiltonian, but on the underlying vector space. Thus, the appropriate framework is given by the kinematic approach to geometric phases, which contains Berry's phase as a special case.
This work was partially financed by DGI-PUCP (Grant No. 2015-224). J.C. received financial support from CONCYTEC/FONDECYT (Peru).
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RWA applies, Jaynes-Cummings model, Rabi model