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Physical Review A

Sudden death and birth of entanglement in photonic crystals

M. Al-Amri, Gao‐xiang Li, Rong Tan, Muhammad Suhail Zubairy

Published Aug 11, 2009• 28 citations
Publisher

Abstract

We explore the entanglement dynamics of two qubits embedded in one-dimensional (1D) and three-dimensional (3D) photonic crystals. Our 1D results show sudden death and sudden birth of the entanglement, restricted by the initial coherence and the population in the excited state as well as the detuning. The results for the 3D crystal show entanglement death but no birth. We also discuss the entanglement of $N$ qubits in the aforementioned photonic crystals.

DOI
10.1103/physreva.80.022314

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We explore the entanglement dynamics of two qubits embedded in one-dimensional (1D) and three-dimensional (3D) photonic crystals. Our 1D results show sudden death and sudden birth of the entanglement, restricted by the initial coherence and the population in the excited state as well as the detuning. The results for the 3D crystal show entanglement death but no birth. We also discuss the entanglement of NNN qubits in the aforementioned photonic crystals.
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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.
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In this paper, the origin of disentanglement for two specific sub-classes of [Formula: see text]-states namely maximally nonlocal mixed states (MNMSs) and maximally entangled mixed states (MEMSs) is investigated analytically for a physical system consisting of two spatially separated qubits interacting with a common vacuum bath. The phenomena of entanglement sudden death (ESD) and the entanglement sudden birth (ESB) are observed, but the characteristics of ESD and ESB are found to be different for the case of two-photon coherence and single photon coherence states. The role played by initial coherence for the underlying entanglement dynamics is investigated. Further, the entanglement dynamics of MNMSs and MEMSs under different environmental noises namely phase damping, amplitude damping and random telegraph noise (RTN) noise with respect to the decay and revival of entanglement is analyzed. It is observed that the single photon coherence states are more robust against the sudden death of entanglement, indicating the usability of such states in the development of technologies for the practical implementation of quantum information processing tasks.
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