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Chinese Physics Letters

Decoherence Induced by Spin Chain Environment

Lincheng Wang, Cui Hai-Tao, Yi Xue-Xi

Published Sep 27, 2006• 0 citations
Publisher

Abstract

We study the decoherence process of an exact solvable model that consists of a central spin-1/2 coupling to the surrounding anisotropy spin-1/2 chain in transverse fields. The Loschmidt echo is calculated to study the character of decoherence with different degree of anisotropy. Our results show that the degree of anisotropy γ greatly affects the decoherence process of the central spin-system when the spin chain is in weak transverse fields, but it gives weak effect in the strong transverse field. The decoherence process of the central system changed dramatically along the line of the critical points, and this may be explained as the reflection of quantum phase transitions.

DOI
10.1088/0256-307x/23/10/007

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For a central system uniformly coupled to a XY spin-1/2 bath in a transverse field, we explicitly calculate the Loschmidt echo(LE) to characterize decoherence quantitatively. We find that the anisotropy parameter γγγ affects decoherence of the central system sensitively when γ∈[0,1]γ\in [0,1]γ∈[0,1]% , in particular, the LE becomes unit without varying with time when $γ=0 $, implying that environment-induced decoherence vanishes . Some other cases in which the LE is unit are discussed also.
We study the Loschmidt echo (LE) of a coupled system consisting of a central spin and its surrounding environment described by a general XYXYXY spin-chain model. The quantum dynamics of the LE is shown to be remarkably influenced by the quantum criticality of the spin chain. In particular, the decaying behavior of the LE is found to be controlled by the anisotropy parameter of the spin chain. Furthermore, we show that due to the coupling to the spin chain, the ground-state Berry phase for the central spin becomes nonanalytical and its derivative with respect to the magnetic parameter $\ensuremath{\lambda}$ in spin chain diverges along the critical line $\ensuremath{\lambda}=1$, which suggests an alternative measurement of the quantum criticality of the spin chain.
By introducing the Dzyaloshinsky-Moriya (DM) interaction, the Loschmidt Echo ( LE ) of a quantum system consisting of a central spin and its surrounding environment characterized by an XY spin chain was investigated analytically and numerically. At the critical points of the magnetic field, the LE presents an obvious decay. The decay amplitude can be tuned by the DM interaction. In some specific intervals the DM interaction can remarkably delay the decay of the LE . On the other hand, the DM interaction can change the effects of the anisotropy parameter on the LE.
We study the decoherence process induced by a spin chain environment on a central spin consisting of R spins and we apply it on the dynamics of quantum correlations (QCs) of three interacting qubits. In order to see the impact of the initial prepared state of the spin chain environment on the decoherence process, we assume the spin chain environment prepared in two main ways, namely, either the ground state or the vacuum state in the momentum space. We develop a general heuristic analysis when the spin chain environment in prepared in these states, in order to understand the decoherence process against the physical parameters. We show that the decoherence process is mainly determined by the choice of the initial prepared state, the number of spin of the chain, the coupling strength, the anisotropy parameter and the position from the quantum critical point. In fact, in the strong coupling regime, the decoherence process does not appear for the environment prepared in the vacuum state and it behaves oscillatory in the case of evolution from ground state. On the other hand, in the weak coupling regime and far from the quantum critical point, decoherence induced by the ground state is weaker than that of the vacuum state. Finally, we show that, QCs are completely shielded from decoherence in the case of evolution from the W state and obey the same dynamics as the decoherence factors for the GHZ state.
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