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Decoherence by a spin thermal bath: Role of spin-spin interactions and initial state of the bath

We study the decoherence of two coupled spins that interact with a spin-bath environment. It is shown that the connectivity and the coupling strength between the spins in the environment are of crucial importance for the decoherence of the central system. For the anisotropic spin bath, changing the connectivity or coupling strength changes the decoherence of the central system from Gaussian to exponential decay law. The initial state of the environment is shown to affect the decoherence process in a qualitatively significant manner. I. INTRODUCTION Understanding the decoherence in quantum spin systems is a subject of numerous works for reviews, see Refs. 1 and 2. The issue seems to be very complicated and despite many efforts, even some basic questions about the character of the decoherence process are yet unsolved. Due to the interactions with and between the spin of the bath, an analytical treatment can be carried out in exceptional cases, even if the central systems contain one spin only. Recent work suggests that the internal dynamics of the environment can be crucial to the decoherence of the central system. 3‐15 In this paper, we present results of extensive simulation work of a two-spin system interacting with a spin-bath environment and show that the decoherence of the two-spin system can exhibit different behaviors, depending on the characteristics of the coupling with the environment, the internal dynamics, and the initial state of the latter. We also provide a simple physical picture to understand this behavior. In general, the behavior of an open quantum system crucially depends on the ratio of typical energy differences of the central system Ec and the energy Ece, which characterizes the interaction of the central system with the environment. The EcEce case has been extensively studied in relation to the “Schrodinger cat” problem and the physics is quite clear: 16,17 As a result of time evolution, the central system passes to one of the “pointer states” 17 that, in this case, are the eigenstates of the interaction Hamiltonian Hce .I n the opposite case, E c E ce is less well understood. There is a conjecture that, in this case, the pointer states should be the eigenstates of the Hamiltonian H c of the central system, but this has been proven for a very simple model only. 18 On the other hand, this case is of primary interest if, say, the central system consists of electron spins whereas the environment is nuclear spins, for instance, if one considers the possibility of quantum computation by using molecular magnets. 19,20