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arXiv:1004.0564 · Physical Review A

Protecting bipartite entanglement by quantum interferences

Sumanta Das, G. S. Agarwal

Published May 28, 2010• 37 citations
arXivHTMLPDF

Abstract

We show that vacuum-induced coherence in three-level atomic systems can lead to preservation of bipartite entanglement when two such atoms are prepared as two initially entangled qubits, each independently interacting with their respective vacuum reservoirs. We explicitly calculate the time evolution of concurrence for two different Bell states and show that a large amount of entanglement can survive in the long time limit. The amount of entanglement left between the two qubits depends strongly on the ratio of the nonorthogonal transitions in each qubit and can be more than $50%$. Moreover, we find that as a consequence of vacuum-induced coherence, sudden death of entanglement is prevented for an initial mixed entangled state of the qubits.

DOI
10.1103/physreva.81.052341

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Comment on “Protecting bipartite entanglement by quantum interferences”

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In an interesting article [Phys. Rev. A 81, 052341 (2010)], Das and Agarwal have discussed the preservation of bipartite entanglement in three-level atoms employing the coherences induced by spontaneous emission. The authors considered various initially entangled qubits prepared from two $\mathsf{V}$-type three-level atoms and showed that more than $50%$ of the initial (bipartite) entanglement can be preserved in steady state due to vacuum-induced coherence. In this Comment, we point out that their analytical formulas for the entanglement measure contain errors affecting all the numerical results of that article. We substantiate our claim by giving correct analytical results for the time evolution of the two-atom system.

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We show that vacuum-induced coherence in three-level atomic systems can lead to preservation of bipartite entanglement when two such atoms are prepared as two initially entangled qubits, each independently interacting with their respective vacuum reservoirs. We explicitly calculate the time evolution of concurrence for two different Bell states and show that a large amount of entanglement can survive in the long time limit. The amount of entanglement left between the two qubits depends strongly on the ratio of the nonorthogonal transitions in each qubit and can be more than 5050%50. Moreover, we find that as a consequence of vacuum-induced coherence, sudden death of entanglement is prevented for an initial mixed entangled state of the qubits.
In an interesting article [Phys. Rev. A 81, 052341 (2010)], Das and Agarwal have discussed the preservation of bipartite entanglement in three-level atoms employing the coherences induced by spontaneous emission. The authors considered various initially entangled qubits prepared from two V\mathsf{V}V-type three-level atoms and showed that more than 5050%50 of the initial (bipartite) entanglement can be preserved in steady state due to vacuum-induced coherence. In this Comment, we point out that their analytical formulas for the entanglement measure contain errors affecting all the numerical results of that article. We substantiate our claim by giving correct analytical results for the time evolution of the two-atom system.
Abstract We investigate the entanglement dynamics in a 2 ⨂ 3 quantum system consisting of a two-level atom and a three-level V-type atom interacting independently with their environments. Pure and mixed initial states, including one-parameter and two-parameter states of the atoms are analyzed. It is observed that the entanglement in the qubit-qutrit system disappears in a finite time, commonly referred to as ESD (entanglement sudden death). We analytically calculate the ESD time using the negativity as an entanglement measure. Remarkably, the presence of vacuum-induced coherence in the three-level atom (qutrit) delays the occurrence of ESD and effectively protects the entanglement from decoherence.
We investigate the phenomenon of sudden death of entanglement in a bipartite system subjected to dissipative environments with arbitrary initial pure entangled state between two atoms. We find that in a vacuum reservoir the presence of the state where both atoms are in excited states is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for an infinite time and decays asymptotically with the decay of individual qubits. For pure 2-qubit entangled states in a thermal environment, we observe that the sudden death of entanglement always happens. The sudden death time of the entangled states is related to the temperature of the reservoir and the initial preparation of the entangled states.
Abstract The entanglement dynamics of a pair of three-level V-type atoms decaying spontaneously in a common vacuum reservoir is investigated. Under the condition that the decaying transitions in the atoms have parallel dipole moments, the effect of coherences induced by spontaneous emission is considered in the atomic dynamics. We show that vacuum-induced coherence (VIC) and collective effects in atomic decay play a significant role in the creation of entanglement. By using negativity as a measure of entanglement, we study the time evolution of entanglement for initial separable and generalized Dicke states as well as maximally entangled qutrit states. We show that the effects of VIC enhance the production of entanglement from initial separable states of the atoms. We also show that the entanglement can be protected in steady-state for atoms evolving from initial entangled states. The amount of entanglement that can be preserved is more in the presence of VIC than in its absence.
Entanglement plays a crucial role in quantum information protocols; thus the dynamical behavior of entangled states is of great importance. In this paper, we suggest a useful scheme that permits a direct measure of entanglement in a two-qubit cavity system. It is realized through cavity-QED technology utilizing atoms as flying qubits. To quantify entanglement we use the concurrence. We derive the conditions that ensure that the state remains entangled in spite of the interaction with the reservoir. The phenomenon of entanglement sudden death in a bipartite system subjected to a squeezed vacuum reservoir is examined. We show that the sudden death time of the entangled states depends on the initial preparation of the entangled state and the parameters of the squeezed vacuum reservoir.
We analyze the effect of the position-dependent excitation phase on the properties of entanglement between two qubits formed in atomic systems. We show that the excitation phase induces a vacuum-mediated quantum interference in the system that affects the dynamical behavior of entanglement between the qubits. It is also found that the quantum interference leads to a coherent population transfer between the symmetric and antisymmetric states that can considerably modify the dynamics of two-qubit entanglement and can even prevent finite-time disentanglement (sudden death) under certain conditions.