Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. The bath dynamics can start either from a pure state or, more generally, from a statistical ensemble. In the preceding article [W. Yang and R. B. Liu, Phys. Rev. B 78, 085315 (2008)], we developed the cluster-correlation expansion (CCE) theory for the so-called single-sample bath dynamics initiated from a factorizable pure state. Here we present the ensemble CCE theory, which is based on similar ideas of the single-sample CCE. The bath evolution is factorized into the product of all possible cluster correlations, each of which accounts for the authentic (nonfactorizable) collective excitation of a group of bath spins and for the finite-time evolution in the qubit decoherence problem. Convergent results can be obtained by truncating the ensemble CCE by keeping cluster correlations up to a certain size. A difference between the ensemble CCE and single-sample CCE is that the mean-field treatment in the latter formalism of the diagonal part of the spin-spin interaction in the bath is not possible in the former case. The ensemble CCE can be applied to nonfactorizable initial states. The ensemble CCE is checked against the exact solution of an $XY$ spin bath model. For small spin baths, it is shown that single-sample dynamics is sensitive to the sampling of the initial state from a thermal ensemble and hence very different from the ensemble average.Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. The bath dynamics can start either from a pure state or, more generally, from a statistical ensemble. In the preceding article [W. Yang and R. B. Liu, Phys. Rev. B 78, 085315 (2008)], we developed the cluster-correlation expansion (CCE) theory for the so-called single-sample bath dynamics initiated from a factorizable pure state. Here we present the ensemble CCE theory, which is based on similar ideas of the single-sample CCE. The bath evolution is factorized into the product of all possible cluster correlations, each of which accounts for the authentic (nonfactorizable) collective excitation of a group of bath spins and for the finite-time evolution in the qubit decoherence problem. Convergent results can be obtained by truncating the ensemble CCE by keeping cluster correlations up to a certain size. A difference between the ensemble CCE and single-sample CCE is that the mean-field treatment in the latter formalism of the diagonal part of the spin-spin interaction in the bath is not possible in the former case. The ensemble CCE can be applied to nonfactorizable initial states. The ensemble CCE is checked against the exact solution of an $XY$ spin bath model. For small spin baths, it is shown that single-sample dynamics is sensitive to the sampling of the initial state from a thermal ensemble and hence very different from the ensemble average.

arXiv:0902.3055Physical Review BMar 26, 2009103 citations

Quantum many-body theory for qubit decoherence in a finite-size spin bath

Wen Yang, Ren‐Bao Liu, Hsi‐Sheng Goan +1 more

We develop a cluster‐correlation expansion theory for the many‐body dynamics of a finite‐size spin bath in a time scale relevant to the decoherence of a center spin or qubit embedded in the bath. By introducing the cluster correlation as the evolution of a group of bath spins divided by the correlations of all the subgroups, the propagator of the whole bath is factorized into the product of all possible cluster correlations. Each cluster‐correlation term accounts for the authentic (non‐factorizable) collective excitations within that group. Convergent results can be obtained by truncating the cluster‐correlation expansion up to a certain cluster size, as verified in an exactly solvable spin‐chain model.We develop a cluster‐correlation expansion theory for the many‐body dynamics of a finite‐size spin bath in a time scale relevant to the decoherence of a center spin or qubit embedded in the bath. By introducing the cluster correlation as the evolution of a group of bath spins divided by the correlations of all the subgroups, the propagator of the whole bath is factorized into the product of all possible cluster correlations. Each cluster‐correlation term accounts for the authentic (non‐factorizable) collective excitations within that group. Convergent results can be obtained by truncating the cluster‐correlation expansion up to a certain cluster size, as verified in an exactly solvable spin‐chain model.

AIP conference proceedingsJan 1, 200853 citations

Suppression of spin-bath dynamics for improved coherence of multi-spin-qubit systems

Nir Bar‐Gill, Linh Pham, Chinmay Belthangady +6 more

Nature CommunicationsMay 22, 2012243 citations

Spin bath decoherence of quantum entanglement

Z. Gedik

arXiv:quant-ph/0505176Solid State CommunicationsMar 4, 200619 citations

Quantum many-body theory of qubit decoherence in a finite-size spin bath

Wen Yang, Ren‐Bao Liu

Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. We develop a cluster-correlation expansion (CCE) theory for the spin-bath dynamics relevant to the qubit decoherence problem. A cluster-correlation term is recursively defined as the evolution of a group of bath spins divided by the cluster correlations of all the subgroups. This correlation accounts for the authentic (nonfactorizable) collective excitations within a given group. The bath propagator is the product of all possible cluster correlation terms. For a finite-time evolution as in the qubit decoherence problem, a convergent result can be obtained by truncating the expansion up to a certain cluster size. The two-spin cluster truncation of the CCE corresponds to the pair-correlation approximation developed previously [W. Yao et al., Phys. Rev. B 74, 195301 (2006)]. In terms of the standard linked cluster expansion, a cluster-correlation term is the infinite summation of all the connected diagrams with all and only the spins in the group flip-flopped, and thus the expansion is exact whenever convergence occurs. When the individual contribution of each higher-order correlation term to the decoherence is small (while all the terms combined in product could still contribute substantially), as the usual case for relatively large baths, where the decoherence could complete well within the bath spin flip-flop time, the CCE coincides with the cluster expansion [W. M. Witzel and S. Das Sarma, Phys. Rev. B 74, 035322 (2006)]. For small baths, however, the qubit decoherence may not complete within the bath spin flip-flop time scale and thus individual higher-order cluster correlations could become significant. In such cases, only the CCE converges to the exact coherent dynamics of multispin clusters. We check the accuracy of the CCE in an exactly solvable spin-chain model.Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. We develop a cluster-correlation expansion (CCE) theory for the spin-bath dynamics relevant to the qubit decoherence problem. A cluster-correlation term is recursively defined as the evolution of a group of bath spins divided by the cluster correlations of all the subgroups. This correlation accounts for the authentic (nonfactorizable) collective excitations within a given group. The bath propagator is the product of all possible cluster correlation terms. For a finite-time evolution as in the qubit decoherence problem, a convergent result can be obtained by truncating the expansion up to a certain cluster size. The two-spin cluster truncation of the CCE corresponds to the pair-correlation approximation developed previously [W. Yao et al., Phys. Rev. B 74, 195301 (2006)]. In terms of the standard linked cluster expansion, a cluster-correlation term is the infinite summation of all the connected diagrams with all and only the spins in the group flip-flopped, and thus the expansion is exact whenever convergence occurs. When the individual contribution of each higher-order correlation term to the decoherence is small (while all the terms combined in product could still contribute substantially), as the usual case for relatively large baths, where the decoherence could complete well within the bath spin flip-flop time, the CCE coincides with the cluster expansion [W. M. Witzel and S. Das Sarma, Phys. Rev. B 74, 035322 (2006)]. For small baths, however, the qubit decoherence may not complete within the bath spin flip-flop time scale and thus individual higher-order cluster correlations could become significant. In such cases, only the CCE converges to the exact coherent dynamics of multispin clusters. We check the accuracy of the CCE in an exactly solvable spin-chain model.

arXiv:0806.0098Physical Review BAug 21, 2008209 citations

XY

spin bath model. For small spin baths, it is shown that single-sample dynamics is sensitive to the sampling of the initial state from a thermal ensemble and hence very different from the ensemble average.