Spontaneous Excitation Of A Circularly Accelerated Atom Coupled With Vacuum Dirac Field Fluctuations

Spontaneous emission is an important atomic radiative property, and its phys-ical interpretation can be attributed to vacuum fluctuations, radiation reaction or a linear combination of them. The ambiguity arises from different choices of order-ing of commuting operators of atom and field in the interaction Hamiltonian. In the 1980s, Dalibard, Dupont-Roc and Cohen-Tannoudji (DDC) solved this prob-lem in their studies of the interaction between an atom and the radiation fields, by choosing a symmetric ordering between the operators of the atom and the fields, which renders the contribution of vacuum fluctuations and radiation reaction sep-arately physically meaningful, and they also established a new method to study the interaction between atoms and fields, which can be called DDC formalism. Then this formalism was widely used in the studies of the evolution of the atom coupled with the field.Audretsch and Miiller used DDC formalism to study the evolution of the atom coupled with vacuum scalar field fluctuations firstly, and they studied the average rate of change of atomic energy and the atomic lamb shift of the static atom and uniformly accelerated atom coupled with vacuum scalar field fluctuations. Late, Passante generalized DDC formalism to the cases of the atom coupled with vacuum electromagnetic fluctuations. As the coupling between the atom and vacuum scalar field fluctuations or vacuum electromagnetic fluctuations are both linear coupling, thus the atomic evolution is attributed to the contributions of vacuum fluctuations and radiation reaction. For a static ground-state atom. the contribution of vacuum fluctuations and radiation reaction to the average rate of change of its energy cancel completely, which ensures the stability of the static ground-state atom. For a uniformly accelerated ground-state atom, the contribution of vacuum fluctuations and radiation reaction to the average rate of change of its energy can not cancel, which means that the spontaneous excitation of the atom would happen.When the DDC formalism is generalized to the case of the atom coupled with vacuum Dirac field fluctuations, the coupling between the atom and vacuum Dirac field is nonlinear coupling, then some new features of the evolution of the atom appear. As the coupling between the atom and Dirac field is nonlinear, the evolution of the atom is attributed to the contributions of vacuum fluctuations, atomic radiation reaction and the cross term of vacuum fluctuations and radiation reaction, and the contributions of vacuum fluctuations and the cross term are of the same order, while the contribution of radiation reaction is of higher order than other two parts. Like the case of the uniformly accelerated atom coupled with vacuum scalar field fluctuations and vacuum electromagnetic fluctuations, the average rate of change of atomic energy in the case of the atom coupled with Dirac field is also related to atomic acceleration and frequency. While the difference is the average rate of change of atomic energy in the case of the atom coupled with Dirac field has one more term proportional to quadruplicate acceleration, for a ground-state atom, the contribution of vacuum fluctuations and the contribution of the cross term can not cancel, which means that the ground-state atom would spontaneously excite.We study the spontaneous excitation of a circularly accelerated atom coupled with vacuum Dirac field fluctuations by separately calculating the contribution to the excitation rate of vacuum fluctuations and a cross term which involves both vacuum fluctuations and radiation reaction, and demonstrate that although the spontaneous excitation for the atom in its ground state would occur in vacuum, such atoms in circular motion do not perceive a pure thermal radiation as their counterparts in linear acceleration do since the transition rates of the atom do not contain the Planckian factor characterizing a thermal bath. We also find that the contribution of the cross term including both vacuum fluctuations and radiation reaction in the Dirac fields that plays the same role as that of radiation reaction in the scalar and electromagnetic fields cases, and they always diminish the atomic energy. The noteworthy difference is the contribution to the mean rate of change of atomic energy of the cross term including both vacuum fluctuations and radiation reaction in the cases of Dirac fields differs for atoms in circular motion from those in linear acceleration, while the contribution to the mean rate of change of atomic energy of the radiation reaction in the scalar or electromagnetic fields cases are the same for the atoms in circular motion and those in linear acceleration. This suggests that the conclusion drawn for atoms coupled with the scalar and electromagnetic fields that the contribution of radiation reaction to the mean rate of change of atomic energy does not vary as the trajectory of the atom changes from linear acceleration to circular motion is not a general trait that applies to the Dirac field where the role of radiation reaction is played by the cross term.