Theoretical Study On The Dynamics Of Two-level Systems In Special Environments

The progresses in quantum information theory bring us not only the exciting future of science and technology, but also new methods to analyze the traditional quantum phenomenon. In this thesis, the dynamic properties of two-level systems under the influence of many-body quantum systems, such as one-dimensional spin chains, coupled fermion systems, etc, have been studied. The relation between the dynamics and the property of the environment have been established, which will benefit for the study of quantum measurements and many-body systems. The thesis has been divided into seven chapters, and our works are included in the chapters from 2 to 6.In Chapter 1, the background of the study is introduced, such as quantum information theory, decoherence, entanglement, as well as the new approaches to quantum many-body systems.In chapter 2, the model of one dimension XY spin-chain in transverse fields is introduced firstly, then the decoherence in a central spin-1/2 coupled to the chain is studied. The results show that the anisotropy degreeγsignificantly affect the decoherence of the central spin when the spin-chain is in weak transverse fields, while it gives weak effect in the strong transverse field. The decoherence of the central spin changes dramatically near the critical points of the spin chain, which may be understood as the reflection of quantum phase transitions. The same problem in the case of finite temperature has also been studied, showing that the information reflected in the decoherence is completely washed out in high temperature. On the other hand, the quantum Zeno and anti-Zeno effects of the center two-level system under the influence of the spin chain environment has also been discussed. The effective decay rate affected by the environment has been calculated and analyzed. The results show that the Zeno-anti-Zeno transitions can occur in such system, which also reflect the quantum phase transition in the environment.In chapter 3, A relation between entanglement and criticality of spin chains is established. The entanglement is shared between auxiliary particles, which are isolated from each other, but are coupled to the same critical spin-1/2 chain. The reduced density matrix is analytically evaluated, and numerically show the entanglement of the auxiliary particles in the proximity of the critical points of the spin chain. It is shown that the entanglement induced by the spin-chain can signal very well the critical points of the chain.In chapter 4, the decoherence process in a two-level system dephasingly coupled to a fermion environment with phase transitions is studied. The fermion environment is considered from zero temperature to the critical temperature. It is show that the decoherence of the two-level system may also act as the witness of the environment's phase transitions, which is similar to the relation between quantum phase transitions and decoherence in the former study.In chapter 5, the Landau-Zener(LZ) transition of a two-level system coupling to a surrounding spin chain in a transverse field is studied. The effects of system-chain coupling on the LZ transition is analyzed, and a relation to the critical points of the spin chain is established. These results suggest that the LZ transition may also serve as a witness of criti-cality of spin chain. This may provide a new way to study the phenomena of quantum phase transition as well as LZ transition.In chapter 6, Beyond the quantum Markov approximation and the weak coupling limit, a general theory to calculate the geometric phase for open systems with and without conserved energy has been presented. As an example, the geometric phase for a two-level system coupling both dephasingly and dissipatively to its environment is calculated. Comparison with the results from quantum trajectory analysis is presented and discussed.Finally, the results are summarized in chapter 7.