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arXiv:1808.05980

Entanglement harvesting from multiple massless scalar fields and divergences in Unruh-DeWitt detector models

Allison Sachs, Robert B. Mann, Eduardo Martín-Martínez

Published Aug 17, 2018• 2 citations
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Abstract

We analyze scenarios in which pairs of Unruh-DeWitt-like detectors interact with scalar field(s) with bi-linear and quadratic coupling. For all cases -- real scalar fields, charged scalar fields, and even for couplings mixing two different scalar fields -- we find that the detectors' dynamics depends on the Wightman function of a real scalar field with the same functional form up to a constant multiple. Consequently, entanglement harvesting exhibits low sensitivity to either the kind of scalar field or their charged nature. Furthermore, we show on general grounds that pairs of Unruh-DeWitt-like detectors exhibit persistent divergences when they interact with scalar field(s) with a quadratic or bi-linear coupling and discuss possible avenues to improve the models through the regularization of such divergences.

DOI
10.48550/arxiv.1808.05980

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We analyze correlations between pairs of detectors quadratically coupled to real and complex scalar bosonic fields in 3+1 dimensions. This is a first step toward studying the entanglement structure of the fermionic vacuum through the entanglement harvesting protocol. We find that, while a single quadratically coupled Unruh-DeWitt presents no divergences, when one considers pairs of detectors there emerge persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire \nfrom the field. These divergences were not anticipated in previous studies. We characterize the divergences, discuss whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally find a UV-safe quantifier of harvested correlations.
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We study entanglement harvesting with particle detectors coupled to the renormalized energy density of a massless scalar field. Our analysis identifies the distributional mechanism underlying the persistent ultraviolet divergences previously observed for quadratic detector couplings and discusses that the energy density coupling exhibits the same underlying structure. We show that these divergences are entirely controlled by the switching correlation at coincident interaction times. Consequently, pointlike detectors are UV finite whenever the switchings do not overlap. For Gaussian-smeared detectors, the harvesting correlations are automatically finite in 1+1 and 2+1 dimensions, while in higher dimensions the remaining divergences are removed by non-overlapping switchings. Finally, we derive general expressions for arbitrary zero-mean Gaussian states and illustrate the formalism with a thermal field state.
A bstract We study two accelerating Unruh-DeWitt detectors coupled linearly or quadratically with a scalar field, by using an approach different from previous ones. We use Rindler frame, and integrate over the spacetime coordinates before over the momenta. In this way, the divergent problem previously encountered is avoided. We show that entanglement between the detectors can be created by coupling with the field, and is divergent only in the limit that the two detectors coincide in spacetime. For linear coupling, entanglement increases monotonically with the decrease of acceleration, as previously found, while for quadratic coupling, entanglement behaves non-monotonically, as noted for the first time.
We study bipartite entanglement harvesting from the quantum vacuum of a massless scalar field between two subsystems, each composed of a finite number of Unruh-DeWitt detectors. Using perturbation theory, we show that the leading-order negativity is fully determined by a submatrix of the reduced density matrix, with the submatrix dimension scaling only linearly with the number of detectors. Within this framework, we analyze how the detectors' spatial arrangement influences harvesting. For all three-detector configurations and several symmetric four-detector configurations, we derive analytic expressions for the negativity and identify the configurations that maximize it. For a linear chain, we find that the harvested entanglement scales linearly with the number of detectors. These results clarify how to arrange multiple detectors to optimize harvesting and show that increasing their number broadens the ranges of energy gaps and separations over which entanglement can be extracted from the field.