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Harvesting correlations from complex scalar and fermionic fields with linearly coupled particle detectors

Tales Rick Perche, Caroline Lima, Eduardo Martín-Martínez

Published Nov 24, 2021• 0 citations
OpenAlex

Abstract

We explore entanglement harvesting with particle detectors that couple linearly to non-Hermitian fields. Specifically, we analyze the case of particle detectors coupled to a complex scalar quantum field and to a spin 1/2 fermionic field. We then compare these models with the well-known case of a real scalar field and previous results using quadratic models. Unlike quadratic models, the linear models are able to distinguish the particle from the anti-particle sector of the field. This leads to striking differences between quadratic couplings -- which cannot be related to physically observable processes -- and linear couplings -- that can be related to high-energy physics. Finally, we use this analysis to comment on the role that the field statistics plays on the protocol.

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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.

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We explore entanglement harvesting with particle detectors that couple linearly to non-Hermitian fields. Specifically, we analyze the case of particle detectors coupled to a complex scalar quantum field and to a spin 1/2 fermionic field. We then compare these models with the well-known case of a real scalar field and previous results using quadratic models. Unlike quadratic models, the linear models are able to distinguish the particle from the anti-particle sector of the field. This leads to striking differences between quadratic couplings -- which cannot be related to physically observable processes -- and linear couplings -- that can be related to high-energy physics. Finally, we use this analysis to comment on the role that the field statistics plays on the protocol.
We explore entanglement harvesting with particle detectors that couple linearly to non-Hermitian fields. Specifically, we analyze the case of particle detectors coupled to a complex scalar quantum field and to a spin 1/21/21/2 fermionic field. We find that the complex scalar model can be a good approximation for the fermionic model in the protocol of entanglement harvesting when the mass of the field is sufficiently large compared to the inverse interaction time. Moreover, we show that taking advantage of the U(1)U(1)U(1) degree of freedom of a complex detector it is possible to increase the harvested negativity by up to two orders of magnitude when compared to the case of a real detector.
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.
We analyze correlations between pairs of particle detectors quadratically coupled to a real scalar field. We find that, while a single quadratically coupled detector presents no divergences, when one considers pairs of detectors, there emerge unanticipated persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire from the field. We have characterized such divergences, discussed whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally found a UV-safe quantifier of harvested correlations. Our results are relevant to future studies of the entanglement structure of the fermionic vacuum.
Abstract Many states of linear real scalar quantum fields (in particular Reeh–Schlieder states) on flat as well as curved spacetime are entangled on spacelike separated local algebras of observables. It has been argued that this entanglement can be ‘harvested’ by a pair of so-called particle detectors, for example singularly or non-locally coupled quantum mechanical harmonic oscillator Unruh detectors. In an attempt to avoid such imperfect coupling, we analyse a model-independent local and covariant entanglement harvesting protocol based on the local probes of a recently proposed measurement theory of quantum fields. We then introduce the notion of a local particle detector concretely given by a local mode of a linear real scalar probe field on possibly curved spacetime and possibly under the influence of external fields. In a non-perturbative analysis we find that local particle detectors cannot harvest entanglement below a critical coupling strength when the corresponding probe fields are initially prepared in quasi-free Reeh–Schlieder states and are coupled to a system field prepared in a quasi-free state. This is a consequence of the fact that Reeh–Schlieder states restrict to truly mixed states on any local mode.
We investigate the protocol of entanglement harvesting, where two spacelike separated particle detectors extract quantum correlations from a quantum field. Specifically, we analyze the role of the mass of the field and the energy gap of the detectors in the protocol. Perhaps surprisingly, we find that there are regimes in which the entanglement harvested can increase with the mass of the field by decreasing the noise experienced by the detectors. Finally, we study the optimal relationship between the gap of the detectors and the other parameters of the setting that maximizes the entanglement harvested, showing that a small mass can improve the protocol even in this case.
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.