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The Journal of Atomic and Molecular Sciences

Decoherence Induced by the Environment for Dimerized Anisotropic XY Spin Chain

Zhongjie Wang, Xu Fang, Ren-Gui Zhu

Published Jun 1, 2014• 0 citations
Publisher

Abstract

The Loschmidt echo of single qubit coupling to the environment for dimerized anisotropic XY spin chain in transverse field have been analyzed.We have obtained analytical expression for the Loschmidt echo.By numerically computing the Loschmidt echo, we find that the decay of coherence will be enhanced with the increasing of the staggered parameter.

DOI
10.4208/jams.070514.091614a

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The Loschmidt echo of single qubit coupling to the environment for dimerized anisotropic XY spin chain in transverse field have been analyzed.We have obtained analytical expression for the Loschmidt echo.By numerically computing the Loschmidt echo, we find that the decay of coherence will be enhanced with the increasing of the staggered parameter.
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.
The Loschmidt echo (LE) of a central two-level qubit coupled to nonuniform anisotropic XYXYXY chains in a transverse field is studied. A general formula for LE is derived, which we use to discuss the influence of the criticality of the environment on LE. It is found that for the periodic XYXYXY chain the behaviors of LE in the vicinity of the critical points are similar to those of the uniform case. It is different for the disordered transverse Ising chains. For the aperiodic chains, if the surrounding systems are bounded chains, the behaviors of LE are similar to those of the uniform case, while if the surrounding systems are unbounded chains, they are similar to those of the disordered case.
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. The analytical expression of the LE was obtained. The effects of magnetic field, DM interaction, spin chain size, and anisotropy parameter on the evolution behavior of the LE were discussed numerically. At the critical points of magnetic field, the LE presents an obvious decay following with local oscillation. The decaying and oscillation behavior of the LE can be tuned by the intensity of the DM interaction. With increasing the spin chain size, the decaying amplitude is increased and the following oscillation behavior vanishes for the spin chain with larger size. The effect of the anisotropy parameter on the LE presents different properties at both sides of the knee point. The effect of the DM interaction on the decay of the LE is also related to the value of anisotropy parameter.
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 revisit the problem of decoherence of a qubit centrally coupled to an interacting spin environment, here modeled by a quantum compass chain or an extended XY model in a staggered magnetic field. These two models both support distinct spin-liquid phases, adding a new element to the problem. By analyzing their Loschmidt echoes when perturbed by the qubit we find that a fast decoherence of the qubit is conditioned on the presence of propagating quasiparticles which couple to it. Differently from expectations based on earlier works on central spin models, our result implies that the closeness of an environment to a quantum phase transition is neither a sufficient nor a necessary condition for an accelerated decoherence rate of a qubit.
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.