Study On Quantum Entanglement Of Atom-systems Under Different Conditions

The preparation of quantum entangled states and quantum decoherence are two im-portant subjects in quantum information and are fundamental to quantum communicationand quantum computers. The development of quantum information both in theory and inexperiment indicates that quantum entangled states are indispensable resources in quan-tum information processes such as quantum teleportation, quantum information storage, etc.Therefore, quantum information demonstrates its significance only when entangled qubits,convenient for integration, storage and manipulation, are realized in experimentally-accessiblephysical systems. On the other hand, if the effects of the environment are taken into account,the interaction of the system in question and the environment will inevitably cause decoher-ence. Thus, the study of the process of the decoherence is very important for the theory andpractice of quantum information. Environment is often treated as noise in quantum informa-tion. Accordingly, study on the issue of the decoherence and quantum noise is fundamentalto applications of the quantum information theory.The motivation of this dissertation arose from the above-stated important role of quan-tum entanglement in quantum information. In this dissertation, the question on quantumentanglement of atom-system under several different conditions is discussed. In the first threechapters, quantum information is briefly reviewed. Some basic quantum theories on quantumentanglement and master equation are discussed, including the definition, measurement andrealization of quantum entangled states and the derivation and solution of the master equa-tions. The above discussions consist of the background for this dissertation. From Chapter4 to Chapter 6, several possible schemes on the generation and application of atom-systementangled states are put forward and discussed under several different conditions. In detail,the influence of quantum noise on quantum entangled states is studied in Chapter 4. Gener-ally speaking, noise is negative for quantum information processes. However, noise-assistedentanglement preparation is investigated and it is found that noise may play a positive rolein entanglement generation. The dependence of the entanglement on the noise intensity aswell as on other parameters in the model is studied both analytically and numerically: theamount of entanglement behaves as monotonic function of the atom decay rate, and reachesits maximum value for an intermediate noise intensity. The results show that the interaction of system with noise is the important factor for entanglement generation. In Chapter 5, aspin-1/2 approximation method to study the quantum entanglement of two-component Bose-Einstein condensates trapped in double wells is proposed. The contours of entanglement withrespect to tunneling rate and time are found to be hyperbolic-like and non-monotonic. Inthis chapter, a new method to deal with multiple-body problem and to transform an ex-act many-body problem to a bipartite two-state problem under the spin-1/2 approximationis proposed. The new method greatly reduces the difficulty of the problem. In addition, thecomparison of classical and quantum physics is also discussed. As an application in quantumcommunication of quantum entangled states, a new fundamental quantum gate based on auniversal intrinsic interaction Hamiltonian is constructed in Chapter 6. New operators, thegeneralized pseudo-spin operators, are introduced and a universal intrinsic Hamiltonian witha two-qubit interaction is studied in terms of these operators. A fundamental quantum gateis constructed based on the universal Hamiltonian and it is shown that the role of the newquantum gate is functionally equivalent to the joint operation of Hadamard and C-Not gates.In summary, the quantum entanglement, the core of the quantum information theory,is a potential mechanism for the quantum measurement and decoherence, and is criticallyimportant to the understanding of the boundary between quantum physics and classicalphysics. Therefore, the study of both quantum entanglement and its applications in quantuminformation are significant and necessary not only to the further understanding of the specialproperties of the quantum mechanics but also to the providing of practical physical resourcesfor information transmission and information processing. Some theoretical investigations onquantum entanglement are pursued in this dissertation. Quantum information theory is arapidly-developing research field. Further investigations of quantum entanglement will beundertaken in future.