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arXiv:quant-ph/0604053 · Physical Review A

Dark periods and revivals of entanglement in a two-qubit system

Z. Ficek, R. Tanaś

Published Aug 30, 2006• 379 citations
arXivHTMLPDF

Abstract

In a recent paper Yu and Eberly [Phys. Rev. Lett. 93, 140404 (2004)] have shown that two initially entangled and afterward not interacting qubits can become completely disentangled in a finite time. We study transient entanglement between two qubits coupled collectively to a multimode vacuum field, assuming that the two-qubit system is initially prepared in an entangled state produced by the two-photon coherences, and find the unusual feature that the irreversible spontaneous decay can lead to a revival of the entanglement that has already been destroyed. The results show that this feature is independent of the coherent dipole-dipole interaction between the atoms but it depends critically on whether or not collective damping is present.

DOI
10.1103/physreva.74.024304

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Abstract Bipartite entanglement is a necessary resource in most processes in quantum information science. Decoherence resulting from the interaction of the bipartite system with environment not only degrades the entanglement, but can result in abrupt disentanglement, known as entanglement sudden death (ESD). In some cases, a subsequent revival of entanglement is also possible. ESD is an undesirable feature for the state to be used as a resource in applications. In order to delay or avoid ESD, it is necessary to understand its origin. In this work we investigate the role of initial coherence on entanglement dynamics of a spatially separated two qubit system in a common vacuum reservoir with dipolar interaction. We construct two classes of X states, namely, states with one photon coherence ( X 1 ) and states with two photon coherence ( X 2 ). Considering them as initial states, we study entanglement dynamics under Markov approximation. We find for states in X 1 , ESD time, revival time and time over which the state remains disentangled increase with increase in coherence. On the other hand for states in X 2 , with increase in coherence ESD time increases, revival time remains same and time of disentanglement decreases. Thus, states with two photon coherence are better resources for applications since their entanglement is robust against decoherence compared to states with one photon coherence.
The decoherence of two initially entangled qubits in a squeezed vacuum cavity has been investigated exactly. The results show that, first, in principle, the disentanglement time decreases with the increasing of squeeze parameter r, due to the augmenting of average photon number of every mode in squeezed vacuum cavity. Second, there are entanglement revivals after complete disentanglement for the case of even parity initial Bell state, while there are entanglement decrease and revival before complete disentanglement for the case of odd parity initial Bell state. The results are quite different from that of the case for qubits in a vacuum cavity.
The decoherence of two initially entangled qubits coupled with a squeezed vacuum cavity separately is investigated exactly. The results show that, first, in principle, the disentanglement time decreases with the increase of squeeze parameter r, due to the augmenting of average photon number of every mode in the squeezed vacuum cavity. Second, there appear entanglement revivals after the complete disentanglement for the case of even parity initial Bell state, while there occur the entanglement decrease and the entanglement revival before the complete disentanglement for the case of odd parity initial Bell state. The results are quite different from those for the case of qubits in a vacuum cavity.
Abstract The intrinsic decoherence effect for two qubits interacting with a coherent field, under the dipole-dipole interaction and two-photon resonance, is analytically described. We investigate numerically the population inversion and the quantum coherence. The results show that the generated mixture entropy and the entanglement negativity, can be enhanced and protected by the dipole-dipole interaction and by reducing the initial coherent field intensity. In particular, we find that, the collapses and revivals of the population inversion present high sensitivity to these physical parameters. The nonlinearity of the two-photon processes leads to a generation of a strong two-qubit entanglement. This generated entanglement depends on the initial coherent field intensity, the dipole-dipole interaction and the intrinsic decoherence.