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Acta Physica Sinica

Entanglement evolution of two three-level atoms in a fermionic environment

Xiao-San Ma, Wang An-Min, (1)中国科学技术大学近代物理系，合肥 230026; (2)中国科学技术大学近代物理系，合肥 230026；安徽工业大学电气信息学院，马鞍山 243002

Published Jan 1, 2008• 5 citations
Publisher

Abstract

We study the entanglement evolution of two three-level atoms in a fermionic environment. Our results show that the entanglement evolution depends not only on the strength of the interaction between the system and environment， but also on the structure of states. For the cases of concern， we find that the stronger the interaction between the system and environment is， the faster the entanglement of the system decreases. The entanglement of pure quantum states vanishes completely when the time goes to infinity; while for the mixed state，the entanglement will be completely destroyed by decoherence in finite time. The decoherence-free subspace SDF has been identified by using linear entropy to measure decoherence. A density matrix that only can be expanded by the elements of SDF does not perceive the presence of the environment and the entanglement and its linear entropy remain unchangeable. Our analysis will shed some light on the effect of a fermionic environment on the entanglement of bosonic systems.

DOI
10.7498/aps.57.2026

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We study the entanglement evolution of two three-level atoms in a fermionic environment. Our results show that the entanglement evolution depends not only on the strength of the interaction between the system and environment， but also on the structure of states. For the cases of concern， we find that the stronger the interaction between the system and environment is， the faster the entanglement of the system decreases. The entanglement of pure quantum states vanishes completely when the time goes to infinity; while for the mixed state，the entanglement will be completely destroyed by decoherence in finite time. The decoherence-free subspace SDF has been identified by using linear entropy to measure decoherence. A density matrix that only can be expanded by the elements of SDF does not perceive the presence of the environment and the entanglement and its linear entropy remain unchangeable. Our analysis will shed some light on the effect of a fermionic environment on the entanglement of bosonic systems.
Abstract We analyze the dynamics of entanglement due to decoherence in a system of two identical fermions with spin 3/2 interacting with a global bosonic environment. We make use of an appropriate measure of the so-called fermionic entanglement to quantify the fermionic correlations, and compare the dynamical effects due to decoherence with those that arise in a pair of distinguishable qubits immersed in the same environment. According to the system’s initial state, three types of qualitatively different dynamics are identified: i) invariant regime , corresponding to initial states that belong to a decoherence free subspace (DFS), which maintain invariant their entanglement and coherence throughout the evolution; ii) exponential decay , corresponding to initial states orthogonal to the DFS, and evolve towards states whose entanglement and coherence decrease exponentially; iii) entanglement sudden death , corresponding to initial states that have some overlap with the DFS and exhibit a richer dynamics leading, in particular, to the sudden death of the fermionic entanglement, while the coherence decays exponentially. Our analysis offers insights into the dynamics of entanglement in open systems of identical particles and into the existence of decoherence free subspaces and entanglement sudden death in indistinguishable-fermion systems.
We study the entanglement dynamics of three two-level atoms interacting with a structured reservoir. The atoms are initially prepared in a mixed W state while the reservoir is in the vacuum. We show the dependence of entanglement dynamics on the purity of initial atomic state and on the amount of non-Markovianity. When the initial state of atoms is in a W pure state, the entanglement will decay asymptotically, while it vanishes in a finite time if the initial state is in a mixed W state. In addition, as the memory effect of the environment, entanglement can partially revive after it vanishes, and the revival degree is dependent on the strength of non-Markovian effect. In the end, we consider the entanglement generation and its evolution when the initial state of the atoms system is completely separable.
We investigate the entanglement dynamics of three-qubit states in a quantum-critical environment, which is an Ising model in a transverse field. By using negativity as entanglement measure, we find that the entanglement evolution depends not only on the system-environment couplings and the size of degrees of freedom of environment but also on the strength of transverse field and the symmetry of quantum states of concern. In particular, for the cases under study, our results imply that the entanglement decay can be enhanced by the quantum phase transition of the environment under weak coupling. Our analysis implies that the entanglement of any three-qubit quantum state will be completely destroyed by the decoherence under certain conditions, that we detail below.