Geometric Phase Of An Accelerated Atom In The Presence Of Boundary

An uniformly accelerated observer in Minkowski vacuum will feel as if it was immersed in a bath of thermal radiation, whose temperature is proportional to the acceleration. This is the so-called Unruh effect. Theoretically the acceleration required to achieve a temperature of ～ 1 K, is as large as ～ 1021m/s2. This quite challenges current laboratory technology. Therefore, a lot of efforts have been directed to exploring alternative means to relax the extreme conditions.As we all know, for a quantum system whose Hamilton has cyclic evolution,after one period of adiabatic process, the final state will obtain an additional phase difference compared to the initial state. This phase difference is called geometric phase, distinguished from the dynamical phase. People find the geometric phase owning the property of being accumulative with the evolution of system. Thus, it is considered as a sensitive quantity to reflect the Unruh effect recently. Moreover,an accelerated detector is supposed to be coupled with the fluctuating vacuum field, and the geometric phase of the detector in the frame of itself is dependent on its acceleration. The geometric phase difference between an inertial detector and an accelerated one will evidence the Unruh effect. According to the coupled types,people investigate two models. The first one is studied by E. Mart′?nez, I. Fuentes and R. B. Mann. They restricted the detector in a resonator cavity coupled with the bounded vacuum massless scalar field, and discussed the geometric phase of the whole system. H. W. Yu and J. W. Hu proposed another model, in which a two-level atom is treated as the detector coupled with all vacuum modes of electromagnetic field in free space. In addition, they computed the geometricphase of the atom using the open quantum system theory. Based on current phase observation accuracy, the two models together gave a similar lower limit of acceleration of the order of 1017～ 1018m/s2.This paper follows the second model’s mechanism, i.e. a two-level atom coupled with the vacuum electromagnetic field. Differently, we discuss the geometric phase of a two-level atom coupled with the vacuum electromagnetic field in the presence of an infinite perfectly reflecting plane. Due to the reflection of the boundary, the fluctuation of the vacuum field will inevitably be affected, thus the electric Wightman function must be corrected from its free space form. After a few detailed calculation, we find the geometric phase in presence of a boundary, is not only determined by the energy level spacing, the spontaneous emission rate and the acceleration of the atom like the free space value, but also by the atomic polarization and the distance to the boundary. We discuss the geometric phase difference between an inertial atom and an accelerated one in two distance limit situations.In the long distance limit, the phase difference appears very close to the free space value. While in near distance limit, the phase difference shows multi-styles variations with the orientation of the atomic polarization compared to the free space value. Especially when the atom is polarized perpendicular to the boundary, the phase difference is twice of the free space value in the near distance limit. Our result suggests that the detectability of the Unruh effects using an atom interferometer which registers the interference pattern caused by the geometric phase difference of the accelerated and inertial atoms can be significantly increased by the presence of a boundary using atoms with anisotropic polarizability.