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Chinese Physics B

Spin-star environment assisted entanglement generation in weakly coupled bipartite systems

Gen-Fang Wang, Jian-Mei Lü, Lincheng Wang

Published May 1, 2014• 2 citations
Publisher

Abstract

We study the entanglement evolution in a weakly coupled bipartite system with a large energy level difference under the influence of spin-star environments. The subsystems can be coupled to a pure state or a thermal equilibrium state spin-star environment. Our results show that, in the case of the coupling strength being less than the energy level difference of the subsystems (weakly coupled), the spin-star environment can always be used to assist the entanglement generation of the bipartite system.

DOI
10.1088/1674-1056/23/5/050311

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We study the entanglement evolution in a weakly coupled bipartite system with a large energy level difference under the influence of spin-star environments. The subsystems can be coupled to a pure state or a thermal equilibrium state spin-star environment. Our results show that, in the case of the coupling strength being less than the energy level difference of the subsystems (weakly coupled), the spin-star environment can always be used to assist the entanglement generation of the bipartite system.
The exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XYXYXY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using an operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming-like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment, and the interaction between the constituents of the spin environment. We also investigate the effect of detuning, which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two-spin qubits.
We discuss two central spin models coupled, respectively, to a quantum Heisenberg XY spin star environment [1] and to an antiferromagnetic environment [2]. In the first model [1], the exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using a novel operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment and the interaction between the constituents of the spin environment. We also investigate the effect of detuning which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two spin qubits.
We derive the exact reduced dynamics of a central two-qubit system in a spin star configuration. The exact evolution of the reduced system density matrix is obtained and we compute the limit of an infinite number of environment spins. Initially pure states of the central system evolve into mixed ones and we determine the decoherence-free states of the model. The long-time behavior is studied, partial decoherence is shown to be a result of the coupling of the qubits to the environment, and entanglement evolution of the central system is investigated.
We investigate the entanglement dynamics of a two-qubit system which interacts with a Heisenberg XYXYXY spin chain constrained to carry an energy current. We show an explicit connection between the decoherence factor and entanglement, and numerically and analytically study the dynamical process of entanglement in both weak- and strong-coupling cases for two initial states, the general pure state and the mixed Werner state. We provide results that the entanglement evolution depends not only on the energy current, the anisotropy parameter and the system-environment couplings but also on the size of degrees of freedom of environment. In particular, our results imply that entanglement will be strongly suppressed by the introduction of energy current on the environmental spin chain in the weak-coupling region while it is not sensitive to the energy current in the strong-coupling region. We also observe the sudden death of entanglement in the system and show how the energy current affects the phenomenon.
We investigate the decoherence of a spin- 1/2 subsystem weakly coupled to an environment of many spins- 1/2 with and without mutual coupling. The total system is closed, its state is pure, and evolves under Schrödinger dynamics. Nevertheless, the considered spin typically reaches a quasistationary equilibrium state. Here we show that this state depends strongly on the coupling to the environment on the one hand and on the coupling within the environmental spins on the other. In particular we focus on spin star and spin ring-star geometries to investigate the effect of intra-environmental coupling on the central spin. By changing the spectrum of the environment, its effect as a bath on the central spin is also changed and may even be adjustable to some degree. We find that the relaxation behavior is related to the distribution of the energy eigenstates of the total system. For each of these relaxation modes, there is a dual mode for which the resulting subsystem approaches an inverted state occupation probability (negative temperature).
Abstract We investigate the time evolution of a general two-qubit pure entangled state in different structured environments. A general expression is obtained to evaluate the entanglement dynamics of two-qubit systems for two different dissipative environments in the non-Markovian regime. In one case it is single Lorentzian and is detuned from the system while in the other case two Lorentzians form a photonic band gap and is resonant with the system. In the first case, we show that entanglement can be generated from the initial separable state in the non-Markovian regime. Compared to our earlier work under Markov approximation (Tahira et al 2008 J. Phys. B: At. Mol. Opt. Phys . 41 205501), we show that disentanglement rates as well as sudden death times are modified in structured environments. Therefore, we can retain the entanglement for a longer time by controlling the system–environment coupling parameters.