We have studied the entanglement dynamics for a two-qubit system coupled to a spin environment of different configurations by a z–x-type interaction. Quantum dynamics of the models considered in this paper is solved analytically. Moreover, we show that simple and concise results may be obtained when certain approximations are properly made. Our purpose is to find out how the entanglement of a central spin system is affected by the pre-designed factors of the system and its environment, such as their initial states and the coupling constants between the system and its environment. Clearly, how the system is coupled to its environment will inevitably change the feature of entanglement evolution of the central spin system. Our major findings include the following: (i) the entanglement of the system of interest is sensitive to the number of spins in the environment, (ii) the initial states of the environment can profoundly affect the dynamics of the entanglement of the central spin system and (iii) the entangled environment can speed up the decay and revival of the entanglement of the central spin system. Our results exhibit some interesting features that have not been found for a bosonic environment.We have studied the entanglement dynamics for a two-qubit system coupled to a spin environment of different configurations by a z–x-type interaction. Quantum dynamics of the models considered in this paper is solved analytically. Moreover, we show that simple and concise results may be obtained when certain approximations are properly made. Our purpose is to find out how the entanglement of a central spin system is affected by the pre-designed factors of the system and its environment, such as their initial states and the coupling constants between the system and its environment. Clearly, how the system is coupled to its environment will inevitably change the feature of entanglement evolution of the central spin system. Our major findings include the following: (i) the entanglement of the system of interest is sensitive to the number of spins in the environment, (ii) the initial states of the environment can profoundly affect the dynamics of the entanglement of the central spin system and (iii) the entangled environment can speed up the decay and revival of the entanglement of the central spin system. Our results exhibit some interesting features that have not been found for a bosonic environment.

arXiv:1009.2128Journal of Physics A Mathematical and TheoreticalApr 5, 201113 citations

Exact dynamics in the central-spin model

Michael Bortz

We study the dynamics of a single spin-1/2 coupled to a bath of spins-1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. This formula is evaluated explicitly for initial conditions such that the bath spins are completely polarized at the beginning. For this case we find, after an initial decay, a persistent oscillatory behaviour of the central spin. For a large number of bath spins $N_b$ , the oscillation frequency is proportional to $N_b$ , whereas the amplitude behaves like $1/N_b$ , to leading order. No asymptotic decay due to the non-uniform couplings is observed, in contrast to some recent studies.We study the dynamics of a single spin-1/2 coupled to a bath of spins-1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. This formula is evaluated explicitly for initial conditions such that the bath spins are completely polarized at the beginning. For this case we find, after an initial decay, a persistent oscillatory behaviour of the central spin. For a large number of bath spins $N_b$, the oscillation frequency is proportional to $N_b$, whereas the amplitude behaves like $1/N_b$, to leading order. No asymptotic decay due to the non-uniform couplings is observed, in contrast to some recent studies.

Dec 15, 20060 citations

Dynamics of Two-Dimensional Quantum Spin Systems

M. S. Makivić, Mark Jarrell

Springer proceedings in physicsJan 1, 19930 citations

Correlations in strongly coupled spin systems

C.J.M. Schoutens, Jean-Sébastien Caux, Rob Hagemans

Jan 1, 20030 citations

Central spin dynamics and relaxation of antiferromagnetic order in a central-spin $-$ XXZ-chain system.Central spin dynamics and relaxation of antiferromagnetic order in a central-spin$-$XXZ-chain system.

Jiaxiu Li, Ye Cao, Ning Wu

Using an equations-of-motion method based on analytical representations of spin-operator matrix elements in the XX chain, we obtain exact long-time dynamics of a composite system consisting of a spin- $S$ central spin and an XXZ chain, with the two interacting via inhomogeneous XXZ-type hyperfine coupling. Three types of initial bath states, namely, the Neel state, the ground state, and the spin coherent state are considered. We study the reduced dynamics of both the central spin and the XXZ bath. For the Neel state, we find that strong hyperfine couplings slow down the initial decay but facilitate the long-time relaxation of the antiferromagnetic order. Moreover, for fixed hyperfine coupling a larger $S$ leads to a faster initial decay of the antiferromagnetic order. We then study the purity dynamics of an $S=1$ central spin coupled to an XXZ chain prepared in the ground state. The time-dependent purity is found to reach the highest values at the critical point. We finally study the polarization dynamics of the central spin homogeneously coupled to a bath prepared in the spin coherent state. Under the resonant condition, the polarization dynamics for $S>\frac{1}{2}$ exhibits collapse-revival behaviors with fine structures. However, the collapse-revival phenomena is found to be fragile with respect to the anisotropic intrabath coupling.Using an equations-of-motion method based on analytical representations of spin-operator matrix elements in the XX chain, we obtain exact long-time dynamics of a composite system consisting of a spin-$S$ central spin and an XXZ chain, with the two interacting via inhomogeneous XXZ-type hyperfine coupling. Three types of initial bath states, namely, the Neel state, the ground state, and the spin coherent state are considered. We study the reduced dynamics of both the central spin and the XXZ bath. For the Neel state, we find that strong hyperfine couplings slow down the initial decay but facilitate the long-time relaxation of the antiferromagnetic order. Moreover, for fixed hyperfine coupling a larger $S$ leads to a faster initial decay of the antiferromagnetic order. We then study the purity dynamics of an $S=1$ central spin coupled to an XXZ chain prepared in the ground state. The time-dependent purity is found to reach the highest values at the critical point. We finally study the polarization dynamics of the central spin homogeneously coupled to a bath prepared in the spin coherent state. Under the resonant condition, the polarization dynamics for $S>\frac{1}{2}$ exhibits collapse-revival behaviors with fine structures. However, the collapse-revival phenomena is found to be fragile with respect to the anisotropic intrabath coupling.

Aug 16, 20210 citations

N_b

, the oscillation frequency is proportional to

N_b

, whereas the amplitude behaves like

1/N_b

, to leading order. No asymptotic decay due to the non-uniform couplings is observed, in contrast to some recent studies.

Central spin dynamics and relaxation of antiferromagnetic order in a central-spin

-

XXZ-chain system.

S

central spin and an XXZ chain, with the two interacting via inhomogeneous XXZ-type hyperfine coupling. Three types of initial bath states, namely, the Neel state, the ground state, and the spin coherent state are considered. We study the reduced dynamics of both the central spin and the XXZ bath. For the Neel state, we find that strong hyperfine couplings slow down the initial decay but facilitate the long-time relaxation of the antiferromagnetic order. Moreover, for fixed hyperfine coupling a larger

S

leads to a faster initial decay of the antiferromagnetic order. We then study the purity dynamics of an

S=1

central spin coupled to an XXZ chain prepared in the ground state. The time-dependent purity is found to reach the highest values at the critical point. We finally study the polarization dynamics of the central spin homogeneously coupled to a bath prepared in the spin coherent state. Under the resonant condition, the polarization dynamics for

S>\frac{1}{2}

exhibits collapse-revival behaviors with fine structures. However, the collapse-revival phenomena is found to be fragile with respect to the anisotropic intrabath coupling.