Quantum Entanglement Of Atoms, Hawking Radiation Of A Black Hole And The Theory Of Open Quantum Systems

Quantum mechanics is one of the most fundamental theories of modern physics. It not only plays an important role in every branches of physics, but also has been applied in other subjects, such as chemistry, biology, information science, etc. In the process of advancing the development of other subjects, the theory of quantum mechanics has also been enriched more and more. Quantum information theory, which is a result of a combination of quantum mechanics and classical information theory, has become a hot topic in modern science. The development of quantum information theory will have a surprising effect on finance, national defence, communication and so on, and it may, therefore, change the living style of modern human being, and introduce the society to a new "quantum knowledge age". Entanglement, as one of the correlations of quantum systems, inherently exists in quantum systems. It is considered to be the key resource in quantum information science, which can be used to accomplish the task and protocol in quantum information. Therefore, the discussion and research on entanglement is of key importance in quantum information science.On the other hand, if quantum mechanics is one of the two pillars in modern physics, the other is general relativity. Black hole, as a hot topic in quantum gravity and quantum cosmology, is recognized as a bridge that connects quantum mechanics and general relativity. The research on black hole not only advances the development of quantum mechanics and general relativity, but also helps us understand some physical concepts more deeply. In quantum theory, the dynamics of ensembles of isolated systems is usually described by Schrodinger equation, and the corresponding evolution of states is unitary. However, quantum mechanical systems must be regarded as open systems. This is due to the fact that any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a non-negligible way. Therefore, the corresponding (?)volution of the reduced density should be obtained in the framework of open systems.In this thesis, with the help of the theory of open quantum systems, we will consider dynamical evolution and entanglement generation of two independent atoms in two special cases. The first one is assuming two static atoms to be immersed in a thermal bath with the presence of a perfectly reflecting plane boundary, and the other is that two atoms are uniformly accelerated in the Minkowski spacetime with a perfectly reflecting plane boundary. Besides these, we also study the Hawking radiation in the framework of open systems by examining the time evolution of a detector interacting with vacuum massless scalar fields. The main results can be summarized as follows.(1) We examine the entanglement creation between two independent two-level atoms immersed in a thermal bath with the presence of a perfectly reflecting plane boundary. With the help of the master equation, in the weak-coupling, we find that the presence of the boundary may play a significant role in the entanglement creation in some circumstances and the new parameter, besides the bath temperature and the separation between the atoms, gives us more freedom in manipulating entanglement generation. Remarkably, the final remaining entanglement in the equilibrium state is independent of the presence of the boundary.(2) We then study the entanglement generation of two independent uniformly accelerated atoms in interaction with the vacuum fluctuations of massless scalar fields subjected to a reflecting plane boundary. We demonstrate that, with the presence of the boundary, the accelerated atoms exhibit distinct features from static ones in a thermal bath at the corresponding Unruh temperature in terms of the entanglement creation at the neighborhood of the initial time. In this sense, accelerated atoms in vacuum do not necessarily have to behave as if they were static in a thermal bath at the Unruh temperature.(3) When an ideal two-level atom detector is placed outside a Schwarzschild black hole, we calculate the probability of spontaneous excitation for the detector outside two-dimensional black hole in detail. Our results show that the Hawking effect can be understood as a manifestation of thermalization phenomena in the framework of open quantum systems. Moreover, for the case of a four-dimensional black hole, we calculate the probability of spontaneous excitation of the detector in the three vacua in the background of the black hole. We find that the probability of spontaneous excitation of the detector behalves differently in the three vacua. In other words, the detector in both the Unruh and Hartle-Hawking vacua would spontaneously excite with a nonvanishing probability the same as what one would obtain if there is thermal radiation at the Hawking temperature from the black hole. However, in the Boulware vacuum, the detector will not be excited just as if it is in the vacuum which we usually refers to in the Minkowski spacetime.