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Chinese Physics B

On entanglement invariant for a double Jaynes–Cummings model

Man Zhong-Xiao, Yun‐Jie Xia

Published Dec 1, 2008• 2 citations
Publisher

Abstract

In a recent paper [ Phys. Rev. A 76 042313 (2007)], Sainz and Bjork introduced an entanglement invariant E under evolution for a system of four qubits interacting through two isolated Jaynes–Cummings Hamiltonians. This paper proves that this entanglement invariant E is closely connected with the linear entropy between two independent subsystems.

DOI
10.1088/1674-1056/17/12/007

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In a recent paper [ Phys. Rev. A 76 042313 (2007)], Sainz and Bjork introduced an entanglement invariant E under evolution for a system of four qubits interacting through two isolated Jaynes–Cummings Hamiltonians. This paper proves that this entanglement invariant E is closely connected with the linear entropy between two independent subsystems.
We study entanglement dynamics between four qubits interacting through two isolated Jaynes-Cummings Hamiltonians, via an entanglement measure based on the wedge product. We compare the results with similar results obtained using bipartite concurrence resulting in what is referred to as ``entanglement sudden death.'' We find a natural entanglement invariant under evolution, demonstrating that entanglement spreads out over all of the system's degrees of freedom that become entangled through the interaction. We also provide an analysis of why certain initial states lose all their entanglement in a finite time, although their excitation and coherence vanish only asymptotically with time.
A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes–Cummings model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom–cavity couplings and off-resonant interactions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin-correlated and anti-correlated Bell states Φ and Ψ, a full, periodic and directed transfer of entanglement into a specific qubit pair is possible, for resonant interactions, depending on the choice of relative couplings. Furthermore, entanglement transfer and sudden death (ESD) can be prevented using off-resonant interactions, although for some initial states, detunings will trigger an otherwise frozen entanglement, to allow a full entanglement transfer.
The linear entropy, the von Neumann entropy and the atomic Wehrl entropy are frequently used to quantify entanglement in the quantum systems. These relations provide typical information on the entanglement in the Jaynes-Cummings model (JCM). In this Letter, we explain the origin of this analytically and derive a closed form for the atomic Wehrl entropy. Moreover, we show that it is more convenient to use the Bloch sphere radius for quantifying entanglement in the JCM instead of these entropic relations.
Abstract The entanglement between two stationary qubits is a kind of valuable quantum resources in quantum information or quantum network. This paper investigates the time evolution of the entanglement between two atoms, which are initially prepared in the Bell states and each of which interacts with its own cavity field in the identical and non-identical double damping Jaynes-Cummings (J-C) system. It mainly considers the effect of the atomic spontaneous decay Γ and the decay of cavity field κ on the two-qubit entanglement in such system. While causing the decay of entanglement, Γ and κ can also play a positive role in the entanglement evolution, which may imply a way to better control and maintain the entanglement. What is more, the rules governing the transfer of entanglement between two-qubit subsystems in strong coupling regime are finally studied by taking Γ and κ into consideration .