Dynamics, Geometric Phase And Quantum Entanglement Of An Elementary Quantum System In Curved Spacetime

With the rapid development of quantum information science, physical systems which can be applied in quantum information processing have been extensively studied. However, any real quantum system has to be an open system because of its inevitable coupling to the external environment. Different types of environment may lead to distinct dynamical behaviors of quantum systems. Therefore, one may draw information on the nature of the environment from the dynamics of the open quantum system. In this dissertation, we study the dynamical behaviors, the geometric phase, and the quantum entanglement of an elementary quantum system. The main conclusions come as follows:1. We investigate the dynamics of a radially polarizable two-level atom in multipolar coupling to fluctuating electromagnetic fields in the Unruh vacuum which is placed at a fixed radial distance outside a Schwarzschild black hole. With the help of the master equation, we analyze the transition rates between atomic energy levels and the steady state the atom is driven to. It is shown that, regardless of its initial state, the atom always thermalizes towards a steady thermal state at an effective temperature which depends on the transition frequency of the atom. This counterintuitive behavior is, however, in close analogy to what happens for a two-level atom in a stationary environment out of thermal equilibrium near a dielectric body of certain geometry and dielectric permittivity. On one hand, our result is a reflection of the fact that the Unruh vacuum exhibits a nonequilibrium nature. On the other hand, it suggests, in principle, a possibility to verify the peculiar features of the Hawking radiation by observing the dynamical behaviors for a two-level atom in tabletop experiments using engineered metamaterials with desired dielectric properties and superconducting circuits for an experimental implementation of two-level atoms.2. Based on the dynamics of open quantum systems, we study the geometric phase of an open two-level atom. We consider a uniformly accelerated one in the Minkowski vacuum, an inertial one near an infinite ideal reflecting boundary, and a static one outside a Schwarzschild black hole. For a uniformly accelerated atom, it is found that there is a correction to the geometric phase due to the acceleration, and this phase variation can in principle be observed via atomic interferometry between the accelerated atom and an inertial one, thus providing an evidence of the Unruh effect. For an inertial atom whose trajectory is parallel to a reflecting boundary, we find that the geometric phase is position dependent as a result of the presence of the boundary which modifies the quantum fluctuations, hence a possible way is proposed to detect vacuum fluctuations in experiments involving geometric phase. For a static atom outside a Schwarzschild black hole, we consider the atom coupled to a bath of fluctuating scalar fields in the Boulware, Unruh and Hartle-Hawking vacua respectively. We find the geometric phase is corrected by the presence of the backscattering of spacetime curvature and the Hawking radiation. So, a measurement of the change of the geometric phase as opposed to that in a flat spacetime can in principle demonstrate the existence of the Hawking radiation.3. Further, we have investigated the dynamics of open two-atom systems and the entanglement generation. First, we discuss the asymptotic entanglement of two mutually independent two-level atoms placed at a fixed radial distance outside a Schwarzschild black hole, and demonstrate the Hawking effect from a new perspective. Then, we study the entanglement generation between two mu-tually independent static two-level atoms in de Sitter spacetime. It is shown that, although a single atom behaves as if there were a thermal bath, the conditions for entanglement generation are different for the two situations. So, in principle, one can tell whether he is in a thermal bath or in de Sitter space by checking the entanglement creation between two initially separable static atoms in certain circumstances.