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Modern Physics Letters B

QUANTUM DYNAMICS OF DOUBLE QUBIT IN A SPIN STAR LATTICE WITH AN x–y INTERACTION

Jun Jing, Zhiguo Lü, Hongru Ma

Published Mar 20, 2009• 1 citation
Publisher

Abstract

The dynamics of two spins-1/2 interacting with a spin-bath via the quantum Heisenberg x–y coupling is studied. The purity, z-component summation and the concurrence of the central subsystem are determined by the Laguerre polynomial scheme. It is found that (i) at a low temperature, the uncoupled subsystem in a product state can be entangled by the bath, which is tested by the Peres–Horodecki separability; (ii) the resistance of the subsystem in Bell states to the destroy effect from the bath increases with its inner-coupling strength.

DOI
10.1142/s0217984909019144

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The dynamics of two spins-1/2 interacting with a spin-bath via the quantum Heisenberg x–y coupling is studied. The purity, z-component summation and the concurrence of the central subsystem are determined by the Laguerre polynomial scheme. It is found that (i) at a low temperature, the uncoupled subsystem in a product state can be entangled by the bath, which is tested by the Peres–Horodecki separability; (ii) the resistance of the subsystem in Bell states to the destroy effect from the bath increases with its inner-coupling strength.
The dynamics of two coupled spins-1/2 interacting with a spin-bath via the quantum Heisenberg XY coupling is studied. The pair of central spins served as a quantum open subsystem are initially prepared in two types of states: the product states and the Bell states. The bath, which consists of NNN (in the thermodynamic limit N→∞N\to\inftyN→∞) mutually coupled spins-1/2, is in a thermal state at the beginning. By the Holstein-Primakoff transformation, the model can be treated effectively as two spin qubits embedded in a single mode cavity. The time-evolution of the purity, z-component summation and the concurrence of the central spins can be determined by a Laguerre polynomial scheme. It is found that (i) at a low temperature, the uncoupled subsystem in a product state can be entangled due to the interaction with bath, which is tested by the Peres-Horodecki separability; however, at a high temperature, the bath produces a stronger destroy effect on the purity and entanglement of the subsystem; (ii) when the coupling strength between the two central spins is large, they are protected strongly against the bath; (iii) when the interaction between the subsystem and the bath is strong, the collapse of the two spin qubits from their initial entangled state is fast.
The dynamics of two coupled spins of 1/2 coupled to spin-bath of a quantum Heisenberg XY type \\cite{Breuer, Yuan} is studied. The center pair of spins served as an quantum open subsystem were initially prepared in a Bell state or a product state and the bath consisted of NNN (NtoinftyN\\to\\inftyNtoinfty as the thermodynamic limit) spins-1/2 is in a thermal state at different temperatures from the beginning. Transformed by the Holstein-Primakoff operator, the model will be treated effectively as two spin qubits embedded in a single mode cavity. Then the von-Neumann entropy, z-component summation and the concurrence of the center spins can be determined by a novel polynomial scheme for the time-evolution of quantum systems. It is found that (i) with increasing temperature, the bath plays a more strong destroy effect on the coherence or entanglement of the subsystem; (ii) the larger the coupling strength between the subsystem spins, the less the variation of the initial state; (iii) the stronger the interaction between the subsystem and the bath, the faster the variation of the initial state.
The dynamics of two 1∕21∕21∕2-spin qubits under the influence of a quantum Heisenberg XYXYXY-type spin-bath is studied. After the Holstein-Primakoff transformation, numerical polynomial scheme is used to give the time-evolution calculation of the center qubits initially prepared in a product state or a Bell state. Then the concurrence of the two qubits, the zzz-component moment of either of the subsystem spins, and the fidelity of the subsystem are shown; they exhibit sensitive dependence on the anisotropic parameter, the temperature, the coupling strength, and the initial state. It is found that (i) the larger the anisotropic parameter $\ensuremath{\gamma}$, the bigger the probability of maintaining the initial state of the two qubits; (ii) with increasing temperature TTT, the bath plays a stronger destroy effect on the dynamics of the subsystem, so does the interaction g0{g}_{0}g0​ between the subsystem and the bath; and (iii) the time evolution of the subsystem is dependent on the initial state. The revival of the concurrence does not always mean the restoration of the state. Further, the dynamical properties of the subsystem should be judged by the combination of concurrence and fidelity.
The dynamics of entanglement and fidelity for a subsystem of two separate spin-1∕21∕21∕2 qubits prepared in Bell states is investigated. One of the subsystem qubit labeled AAA is under the influence of a Heisenberg XYXYXY spin bath, while another one labeled BBB is uncoupled with that. We discuss two cases: (i) the number of bath spins is infinite, $N\ensuremath{\rightarrow}\ensuremath{\infty}$, and (ii) NNN is finite, N=40N=40N=40. In both cases, the bath is initially prepared in a thermal equilibrium state. It is shown that the time dependence of the concurrence and the fidelity of the two subsystem qubits can be controlled by tuning the parameters of the spin bath, such as the anisotropic parameter, the temperature, and the coupling strength with qubit AAA. It is interesting to find that the dynamics of the concurrence is independent of four different initial Bell states and that of the fidelity is divided into two groups.
We investigate the transient dynamics of quantum coherence for a system of two central spins in a spin-star environment by employing a numerical procedure based on a Laguerre polynomial expansion scheme. The dynamics of the total, local, and global coherence are calculated for different values of the anisotropy parameter, the system-bath interaction strengths, and temperature for different initial bipartite states. Significant dynamical features of quantum coherence are found as follows: (i) an XXX state can only have global coherence; (ii) a state with only initial local coherence gains global coherence during the course of evolution by the induced correlations between the two-qubit system and the common bath; (iii) an incoherent state gains coherence by interacting with an external bath. We find there are two primary ways to gain coherence for an incoherent state: one is by interacting with the external quantum bath and the other is through interconversion of other quantum properties such as purity into coherence. Finally, we demonstrate that our results for the system in an infinite bath also hold qualitatively when the system is in contact with a finite bath.
The decoherence and entanglement dynamics of two interacting qubits coupled through Heisenberg XY interactions to a spin bath in thermal equilibrium are studied. The exact form of the reduced density matrix is derived for finite and infinite numbers of environmental spins. It is shown that decoherence can be minimized at low bath temperatures and strong coupling between the qubits. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The relation between the fidelity and the concurrence is also investigated.