| Qubits, the carrier of quantum information, can not be an isolated system. The interaction of the qubit with its environment will induce the qubit dissipation or dephasing, and weaken its quantum coherence. As a result, it will cause the qubit collapse from a coherent superposition state to a mixed or single pure state, and quantum information lost. This process is known as quantum decoherence. So quantum decoherence is one of the main barriers which hold back the storage and processing of quantum information, and has become a research hotspot. When the decoherent properties of several qubit models are studied, this thesis also searches for the external driving fields to eliminate the qubits' decoherence which is induced by their environments. These results will provide some theory guidance for the realization of the storage and processing of quantum information.Indeterminacy principle has been regarded as a source of quantum decoherence. But the most prime source of inducing the decoherence of quantum information system is the entanglement between measure apparatus and quantum systems. A qubit model which transition and decay coexist has been described by using the decoherent formal theory in this thesis. By using the Kraus operator, the density matrix of the qubit has been worked out. The analysis to the diminishment of the matrix off-diagonal elements denotes that the interaction between a qubit and its environment weakens the qubit's coherence and evolves it from a coherent superposition state into a single pure state.The environment can be treated as a thermal reservoir when the interaction of the quantum system with its environment is very weak (otherwise they are not distinguishable). This thesis lays its emphasis on calculating the off-diagonal elements of the reduced density matrix of the qubit in the nonresonant model, the intensity dependent coupling J-C model and the degenerate two-photon J-C model with Stark effect by using perturbation theory and tracing over thermal reservoir. The properties of their decoherence are obtained by analyzing the decay of the off-diagonal elements. At the same time, the thesis gets the external driving fields which are used to eliminate the qubits' decoherence. This makes it possible for these qubits to be using in quantum information systems. The decoherence of the nonresonant model is independent of the transition frequency of the qubit because the nonresonant interaction doesn't induce the transition between the two linear independent states of the qubit. The qubit's decoherence is determined by the frequencies of the oscillators of the thermal reservoir and the average photon numbers of the optical field. For the intensity dependent coupling J-C model and the degenerate two-photon J-C model with Stark effect, the interactions directly induce the transition between the two linear independent states, so the decoherence of these models are dependent on the transition frequency of the qubit yet. The qubit's decoherent properties are dependent on the coupling intensity in the intensity dependent coupling J-C model, and the Stark shift have great effect on the qubit's decoherence in the degenerate two-photon J-C model with Stark effect. With the discussing of the qubit's decoherence, we also search for external driving fields to eliminate their decoherence and get the external driving fields' restriction equations. The studies indicate that not only the decoherence of the qubits but also the external driving fields which are used to eliminate the decoherence both tie up with the interaction types of the qubit with the thermal reservoir, the frequencies of the oscillators of the thermal reservoir and the average photo numbers of the optical field.This thesis is organized as following: In the part of introduction, we simply describe the background of quantum information and the significances of the study to quantum decoherence. In chapter 1, the quantum states, qubits and thermal reservoir have been introduced. In chapter 2, classical coherenc...
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