Harvesting correlations from the quantum vacuum

Alejandro Pozas-Kerstjens and Eduardo Martín-Martínez

Phys. Rev. D 92, 064042 – Published 24 September 2015

Abstract

We analyze the harvesting of entanglement and classical correlations from the quantum vacuum to particle detectors. We assess the impact on the detectors’ harvesting ability of the spacetime dimensionality, the suddenness of the detectors’ switching, their physical size and their internal energy structure. Our study reveals several interesting dependences on these parameters that can be used to optimize the harvesting of classical and quantum correlations. Furthermore, we find that, contrary to previous belief, smooth switching is much more efficient than sudden switching in order to harvest vacuum entanglement, especially when the detectors remain spacelike separated. Additionally, we show that the reported phenomenology of spacelike entanglement harvesting is not altered by subleading-order perturbative corrections.

Received 10 June 2015

DOI:https://doi.org/10.1103/PhysRevD.92.064042

Authors & Affiliations

Alejandro Pozas-Kerstjens¹ and Eduardo Martín-Martínez^1,2,3,*

¹Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada
²Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
³Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

^*Corresponding author. emartinmartinez@uwaterloo.ca

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Vol. 92, Iss. 6 — 15 September 2015

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Images

Figure 1
Negativity for all the cases described in Secs. 2a and 2b, in the following order: (a) three-dimensional (3D) Gaussian switching and Gaussian spatial profile; (b) 3D Gaussian switching and pointlike detectors; (c) 3D sudden switching and Gaussian spatial profile; (d) 3D sudden switching and near-pointlike detectors ( $σ / T ≪ 1$ ); (e) one-dimensional (1D) Gaussian switching and Gaussian spatial profile; (f) 1D Gaussian switching and pointlike detectors; (g) 1D sudden switching and Gaussian spatial profile; (h) 1D sudden switching and pointlike detectors. The plots a.1), b.1), …, h.1) (first and third columns) show in (dark) red the values of $d / T$ and $Ω T$ for which entanglement harvesting is possible, and in (light) grey the values for which there is no entanglement harvesting. The plots denoted by a.2), b.2), …, h.2) (second and fourth columns) show the specific value of the negativity estimator $N^{(2)}$ as a function of the spatial separation of the detectors and the time delay between their switching functions for a given value of $Ω T$ (recall that there is entanglement harvesting when $N^{(2)} > 0$ ). In all plots the dashed lines represent the boundaries of the light cone. In the second and fourth columns, the points to the right of the rightmost dark line represent spacelike separation. These boundaries are placed at $Δ = d \pm T$ in the cases of pointlike detectors which are switched suddenly, and at $Δ = d \pm 7 T / \sqrt{2}$ in the rest, which is a reasonable estimation given the discussion in Sec. 2, subsection A1. All cases of Gaussian spatial profile have $σ / T = 1$ except for the near-pointlike detectors (plots d.1 and d.2), for which $σ / T = 0.01$ . We see that Gaussian switching always allows for spacelike entanglement harvesting for sufficiently large values of $Ω T$ , while this is not the case for sudden switching. For the $1 + 1$ -dimensional scenarios the IR cutoff was taken $Λ T = 0.001$ , much smaller than all the relevant frequency scales in the setup.
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Figure 2
Dependence of entanglement harvesting on the size of the detectors for various values of the internal energy gap. The detectors are located in a $3 + 1$ -dimensional flat spacetime, and are switched on using the Gaussian profile (22). We see that the larger the detectors, the less efficient they are for entanglement harvesting.
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Figure 3
$Ξ_{3}$ and ${| L_{A B} |}^{2}$ for the cases of spatially smeared detectors in $3 + 1$ dimensions and a) Gaussian and b) sudden switching functions, for a time delay of $Δ = 10 T$ between their switchings. The vertical dashed lines represent the boundaries of the light cone. Recall that there is a fourth-order contribution to entanglement harvesting only if $| L_{A B} |^{2} > Ξ_{3}$ , which never happens in these cases. Notice the use of different $y$ -axis scales for $| L_{A B} |^{2}$ and $Ξ_{3}$ .
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Figure 4
Mutual Information for all the cases described in Secs. 2a and 2b, in the following order: (a) 3D Gaussian switching and Gaussian spatial profile; (b) 3D Gaussian switching and pointlike detectors; (c) 3D sudden switching and Gaussian spatial profile; (d) 3D sudden switching and near-pointlike detectors ( $σ / T ≪ 1$ ); (e) 1D Gaussian switching and Gaussian spatial profile; (f) 1D Gaussian switching and pointlike detectors; (g) 1D sudden switching and Gaussian spatial profile; (h) 1D sudden switching and pointlike detectors. The graphs show the harvested mutual information as a function of the spatial separation of the detectors and the time delay between their switching functions for $Ω T = 1$ . In all plots the dashed lines represent the boundaries of the light cone. These boundaries are placed at $Δ = d \pm T$ in the cases of pointlike detectors which are switched suddenly, and at $Δ = d \pm 7 T / \sqrt{2}$ in the rest, which is a reasonable estimation given the discussion in Sec. 2, subsection A1. All cases of a Gaussian spatial profile have $σ / T = 1$ except for the near-pointlike detectors (plot d), for which $σ / T = 0.01$ .
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Figure 5
Mutual information (dashed red) and negativity (solid blue) to $O (λ_{ν}^{2})$ for $1 + 1$ -dimensional detectors with Gaussian spatial smearing and Gaussian switching. The black, dashed line represents the usual estimation of the effective end of the lightcone $β = γ + 7 / \sqrt{2}$ .
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