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arXiv:quant-ph/0404161 · Physical Review Letters

Finite-Time Disentanglement Via Spontaneous Emission

Ting Yu, Joseph H. Eberly

Published Sep 29, 2004• 1,643 citations
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Abstract

We show that under the influence of pure vacuum noise two entangled qubits become completely disentangled in a finite-time, and in a specific example we find the time to be given by ln((2+sqrt[2] / 2) times the usual spontaneous lifetime.
DOI
10.1103/physrevlett.93.140404

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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.
Abstract Ever since the seminal work by Yu and Eberly [Phys. Rev. Lett. 93 , 140404 (2004)], it has become widely accepted that nonlocal entanglement is more fragile than local coherence, in the sense that even under the influence of pure vacuum noise, the two‐qubit entanglement may end within a finite time, while the single‐qubit coherence always decays exponentially. By contrast, in this paper, it is shown that, for a pair of rotating qubits under pure vacuum noise with appropriate orbital radius and angular velocity, nonlocal entanglement as compared to local coherence is not only more resilient against vacuum noise to be preserved in the steady‐state for initially entangled states, but more importantly is also predestined to be created and be preserved for initially separable states. The generation of predestined entanglement here is essentially different from the dissipative steady‐state entanglement generation in existing schemes insofar as it is inevitably generated in pure vacuum instead of an elaborately designed environment.
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.
We consider the decay of quantum entanglement quantified by the concurrence of a pair of two-level systems, each of which is interacting with a reservoir at finite temperature TTT. For a broad class of initially entangled states, we demonstrate that the system always becomes disentangled in a finite time, i.e., ``entanglement sudden death'' occurs. This class includes all states which previously had been found to have long-lived entanglement in zero-temperature reservoirs. Our general result is illustrated by an example.