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arXiv:0805.3785 · Optics Communications

Entanglement in Weisskopf–Wigner theory of atomic decay in free space

J.F. Leandro, F. L. Semião

Published Sep 12, 2009• 8 citations
arXivHTMLPDF
DOI
10.1016/j.optcom.2009.08.059

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In this work we review the Weisskopf-Wigner formalism for spontaneous emission considering the spatial modes of light as well as external atomic degrees of freedom, which we introduce in the theory by modeling the atom as a wave packet in momentum space with a given initial uncertainty. We perform a purity calculation in order to quantify the entanglement encoded in the momentum variables of the atom-photon system. Our purity calculations reveal two high-entanglement regimes depending on the initial atomic momentum uncertainty: (1) the Recoil entanglement regime (which arises in the small momentum uncertainty region) where recoil effects dominate the mechanisms that originate entanglement, and (2) the Doppler entanglement regime (in the large momentum uncertainty region) where homogeneous Doppler shifts in the emitted photon's frequency play the fundamental part in the build up of quantum correlations in the system. Physical considerations are made to explain the nature of each entanglement regime as well as provide their respective thresholds.
The authors study the regeneration contribution to the decay law in Wigner-Weisskopf theory for times less than and up to the golden rule time. A power series expansion for the regeneration term and the part of the product of the amplitudes which has the semigroup property is carried out in second-order perturbation theory, the same order to which the Wigner-Weisskopf calculation is carried out in their estimate of the line widths in atomic decay. They show that the regeneration contribution as a smaller leading behaviour in t than the amplitudes at times of the order of the golden rule time, thus accounting for an approximate semigroup behaviour, on this scale, within the framework of the Wigner-Weisskopf theory. For very short times, the estimates of Misra and Sinha (1977) are obtained.