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arXiv:1109.4341 · Physical Review A

Quantum interference in timed Dicke basis and its effect on bipartite entanglement

Eyob Alebachew Sete, Sumanta Das

Published Apr 4, 2011• 9 citations
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Abstract

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.

DOI
10.1103/physreva.83.042301

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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.
The transmission spectrum of a two-atom timed Dicke state is investigated in an open optical cavity. In the proposed system, two identical atoms are excited by an external single photon field. In this process, the excited atoms grasp different excitation phases for their different spatial positions. For identical coupling strength of atoms and cavity, the excitation phases get coupled via cavity and vacuum fields, and they finally induce cosine-type quantum interference on the two splitting peaks of the spectrum. However, when one of the atoms is decoupled with the cavity, the excitation phases cannot get coupled directly via the cavity but must be mediated by the vacuum fields, which leads to opposite quantum interference effects on the two splitting peaks. In addition, we find that the real and virtual vacuum-mediated excitation phase couplings generate different quantum interferences. The real vacuum-meditated coupling induces sine-type quantum interference, while it becomes cosine-type for the virtual vacuum-mediated coupling. Our study clarifies the mechanism of quantum interference in the two-atom timed Dicke state and provides a feasible scheme for investigating the effect of vacuum-mediated excitation phase coupling.
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 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.
The concept of time delayed creation of entanglement by the dissipative process of spontaneous emission is investigated. A threshold effect for the creation of entanglement is found where the initially unentangled qubits can be entangled after a finite time despite the fact that the coherence between the qubits exists for all times. This delayed creation of entanglement, which we call sudden birth of entanglement, is opposite to the currently extensively discussed sudden death of entanglement and is characteristic for transient dynamics of one-photon entangled states of the system. We determine the threshold time for the creation of entanglement and find it is related to time at which the antisymmetric state remains the only excited state being populated. It is shown that the threshold time can be controlled by the distance between the qubits and the direction of initial excitation relative to the interatomic axis. This effect suggests an alternative for the study of entanglement and provides an interesting resource for creation on demand of entanglement between two qubits.