Abstract
We investigate the effects of field temperature T(f) on the entanglement harvesting between two uniformly accelerated detectors. For their parallel motion, the thermal nature of fields does not produce any entanglement, and therefore, the outcome is the same as the non-thermal situation. On the contrary, T(f) affects entanglement harvesting when the detectors are in anti-parallel motion, i.e., when detectors A and B are in the right and left Rindler wedges, respectively. While for T(f) = 0 entanglement harvesting is possible for all values of A’s acceleration aA, in the presence of temperature, it is possible only within a narrow range of aA. In (1 + 1) dimensions, the range starts from specific values and extends to infinity, and as we increase T(f), the minimum required value of aA for entanglement harvesting increases. Moreover, above a critical value aA = ac harvesting increases as we increase T(f), which is just opposite to the accelerations below it. There are several critical values in (1 + 3) dimensions when they are in different accelerations. Contrary to the single range in (1 + 1) dimensions, here harvesting is possible within several discrete ranges of aA. Interestingly, for equal accelerations, one has a single critical point, with nature quite similar to (1 + 1) dimensional results. We also discuss the dependence of mutual information among these detectors on aA and T(f).
Highlights
This phenomenon is better known as entanglement harvesting [4, 9, 17,18,19,20,21], which states that from quantum fields, one can harvest entanglement among atoms or other suitable systems interacting with the field
T (f) affects entanglement harvesting when the detectors are in anti-parallel motion, i.e., when detectors A and B are in the right and left Rindler wedges, respectively
One can notice that η, −η denote the proper times in Rindler wedge (RRW) and left Rindler wedge (LRW) respectively while a is the proper acceleration of the observer when ξ = 0 = ξ
Summary
Having said our motivation in the introduction, let us talk about the model which will be dealt with in this article. These states are non degenerate so that E1j = E0j, and it is assumed that ∆Ej = E1j − E0j > 0 We consider these detectors to be interacting through monopole interactions mj(τj) with a massless, minimally coupled scalar field Φ(X). In these expressions the switching functions have not appeared as we have considered them κj(τj) = 1; i.e. the detectors are interacting with fields all the time. Where, an equal magnitude of the coupling constant cA = cB = c between different detectors and the scalar field is assumed. Using the expression of the density matrix from eq (2.2), and considering the equal couplings between the field and the two detectors, one can express the mutual information of (2.11) as [42]. It is necessary to investigate both of these measures to understand the correlation between the two detectors
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