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Spontaneous excitation of a uniformly accelerated atom coupled with vacuum Dirac field fluctuations

We study the spontaneous excitation of a uniformly accelerated two-level atom non-linearly coupled with vacuum Dirac field fluctuations using the formalism proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji (DDC) and generalized to the present case in the current paper. We find that a cross term involving both vacuum fluctuations and radiation reaction appears, which is absent in the linear coupling cases such as an atom interacting with vacuum scalar or electromagnetic fluctuations. Furthermore, the contribution of this term actually dominates over that of radiation reaction. Thus, the mean rate of change of the atomic energy can no longer be distinctively separated into only the contributions of vacuum fluctuations and radiation reaction as in the scalar and electromagnetic cases where the coupling is linear. Our result shows that a uniformly accelerated atom interacting with vacuum Dirac fluctuations would spontaneously excite and a unique feature in sharp contrast to the scalar and electromagnetic cases is the appearance of a term in the excitation rate which is proportional to the quartic acceleration.