A general theoretical framework for decoherence is proposed, which encompasses formalisms originally devised to deal just with open or with closed systems. The conditions for decoherence are clearly stated and the relaxation and decoherence times are compared. Finally, the spin-bath model is developed in detail from the new perspective.
One of the challenges of the Environment-Induced Decoherence (EID) approach is to provide a simple general definition of the moving pointer basis or moving preferred basis. In this letter we prove that the study of the poles that produce the decaying modes in non-unitary evolution, could yield a general definition of the relaxation, the decoherence times, and the moving preferred basis. These probably are the most important concepts in the theory of decoherence, one of the most relevant chapters of theoretical (and also practical) quantum mechanics. As an example we solved the Omnès (or Lee-Friedrich) model using our theory.
The works on decoherence due to spin baths usually agree in studying a one-spin system in interaction with a large spin bath. In this paper we generalize those models by analyzing a manyspin system and by studying decoherence or its suppression in function of the relation between the numbers of spins of the system and the bath. This model may help to identify clusters of particles unaffected by decoherence, which, as a consequence, can be used to store quantum information. I. INTRODUCTIONDecoherence refers to the quantum process that turns a coherent pure state into a decohered mixed state. It is essential in the account of the emergence of classicality from quantum behavior, since it explains how interference vanishes in an extremely short decoherence time. The orthodox explanation of the phenomenon is given by the environment-induced decoherence approach (see Refs.[1], [2], [3], [4]), according to which decoherence is a process resulting from the interaction of an open quantum system and its environment. By studying different physical models, it is proved that the reduced state ρ S (t) = T r E ρ SE (t) of the open system rapidly diagonalizes in a well defined pointer basis, which identifies the candidates for classical states.The environment-induced approach has been extensively applied to many areas of physics −such as atomic physics, quantum optics and condensed matter−, and has acquired a great importance in quantum computation, where the loss of coherence represents a major difficulty for the implementation of information processing hardware that takes advantage of superpositions. In particular, decoherence resulting from the interaction with nuclear spins is the main obstacle to quantum computations in magnetic systems. This fact has lead to a growing interest in the study of decoherence due to spin baths (see Refs.[5] to [14]). By beginning from the seminal paper of Zurek ([1]), many works have studied the decoherence due to a collection of independent spins. More recently, some papers have directed the attention to the interactions between modes within the bath. For instance, by studying a central spin coupled to a spin-bath, Tessieri and Wilkie ([6]) showed that, whereas in the absence of intra-environmental coupling the decoherence of the central spin is fast and irreversible, strong intra-environmental coupling leads to decoherence suppression. The same model was further analyzed by Dawson et al. ([7]), with the purpose of relating decoherence with the pairwise entanglement between individual bath spins. In turn, Rossini et al. ([10]) left behind the assumption that the central spin is coupled isotropically to all the spins of the bath, and considered the case where the spin system interacts with only few spins of the bath.Our analysis can be framed in the context of the above works; it aims at generalizing the paradigmatic spin-bath model. In fact, most of the works done so far agree in studying a one-spin system in interaction with a large spin bath. The crucial feature of our work is the analysis o...
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