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Dynamical behavior and geometric phase for a circularly accelerated two-level atom

We study, in the framework of open quantum systems, the time evolution of a circularly accelerated two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields. We find that both the spontaneous transition rates and the geometric phase for a circularly accelerated atom do not exhibit a clear sign of thermal radiation characterized by the Planckian factor in contrast to the linear acceleration case. The spontaneous transition rates and effective temperature of the atom are examined in detail in the ultrarelativistic limit and are shown to be always larger than those in the linear acceleration case with the same proper acceleration. Unlike the effective temperature, the geometric phase is dependent on the initial atomic states. We show that when the polar angle in Bloch sphere, $θ$, that characterizes the initial state of the atom equals $π/{2}$, the geometric phases acquired due to circular and linear acceleration are the same. However, for a generic state with an arbitrary $θ$, the phase will be in general different, and then we demonstrate in the ultrarelativistic limit that the geometric phase acquired for the atom in circular motion is always larger than that in linear acceleration with same proper acceleration for $θ\in(0,\fracπ{2})\cup(\fracπ{2},π)$.