Research On Vacuum Inducted The Berry Phase

Berry showed that the state of a quantum system can acquire a purely geometric phase (called now as Berry phase), in addition to the usual dynamical phase, after slowly changed and eventually returned to its initial form. Basically, Berry phase does not depend on the dynamical properties of the system, but just depends on the topological feature of the parameter space. Up to now, Berry phase has been found in various systems, such as spins, polarized lights, atoms and so on. Recent researches also show that the geometric method can be used to implement quantum computation.Orginally, the Berry phase has been studied in the semiclassical contexts, e. g., the drivings of the system are classical. However, a complete description of the interaction between the system and its driving field should be full quantization, i.e., the quantization of the field is necessary. Recent work done by I. Fuentes-Guridi et al [Phys. Rev. Lett.89, 220404 (2002)] indicates that the vacuum of a quantized optical field could also induce an observable Berry phase. In order to observe the related vacuum-induced geometric effects, two field modes were introduced to interact with a two-level atom. As a consequence, the experimental tests of the vaccum-induced Berry phases are relatively complicated.In this work, we show that only one field mode interacting with a two-level atom could be utilized to detect the vacuum induced Berry phase. Beginning with a generic model, that is, the m-quantum JCM, we show how the desirable Berry phase can be acquired by an evolved quantum state in a parameter-dependent single-mode JCM. Furthermore, we design a Ramsey interference system involved with only one field mode to detect the geometric effect related to the quantization of field.