Entanglement extracted from vacuum into accelerated Unruh-DeWitt detectors and energy conservation

Abstract

We consider a pair of two-level Unruh-DeWitt detectors accelerated uniformly in the Minkowski vacuum of a massless neutral scalar field, and analyze, within the perturbation theory, the entanglement extracted from the vacuum into the Unruh-DeWitt detectors when the switching of the detectors are performed adiabatically enough at the asymptotic past and future. We consider the cases where the detectors are accelerated parallelly, anti-parallelly, and in differently orientated directions. We show that entanglement is extracted if they are accelerated anti-parallelly and the ratios of the excitation energy to the magnitude of the acceleration coincide between the two detectors. On the other hand, we find the detectors are not entangled when the detectors are accelerated parallelly or in orientated directions. We discuss these results from the viewpoint of the energy conservation associated with the timelike boost Killing vector fields tangent to the worldlines of the detectors.

Role of thermal field in entanglement harvesting between two accelerated Unruh-DeWitt detectors

“…Having said our motivation in the introduction, let us now talk about the model which will be dealt with in this article. The model on which we will concentrate here was originally introduced in [38][39][40]. Therefore, without going into the details of this and the derivation of the required formulas, the final expressions which are needed in this paper will be summarised here.…”

“…It should be noted that in initial works [4,9] the authors found these eigenvalues to be dependent on quantities estimated from positive frequency Wightman functions connecting different spacetime events of the same or different detectors. However, recent rigorous investigations [38][39][40] have suggested proper time ordering into the picture, which results in the inception of Feynman propagator rather than Wightman function in the estimation of the eigenvalues. These recent methods provide a meticulous and more general formulation for the understanding of entanglement harvesting.…”

“…Then it will be pretty fascinating to study the situation of entanglement harvesting for accelerated observers interacting with thermal fields, which is not there in the literature up JHEP07(2021)124 to our knowledge. In this regard, in literature [38,40] the Feynman propagators and the positive frequency Wightman functions, necessary to understand entanglement extraction, are estimated in the Minkowski position space. Then for the calculations relating to accelerated observers, the relevant transformations to Rindler coordinates are made to those Green's functions, and this method does not encounter any particular issue.…”

“…In this work, we are going to investigate the condition for entanglement harvesting and study the concurrence [38,40,49], a measure of the harvested entanglement, for two accelerated Unruh-DeWitt detectors interacting with a massless thermal scalar field in (1 + 1) and (1 + 3) dimensions. In particular, we consider the interaction between the two-level point-like detectors and the scalar field to be of monopole type.…”

“…We observe that the specific form of this monopole moment operator is not needed to understand the role of the spacetime trajectories and the thermal bath in entanglement extraction. We use the prescription as provided in [47] for the construction of the Green's functions and follow the formulation of articles [38,40] for entanglement harvesting. We arrive at the same assertions that entanglement extraction is possible only for the anti-parallelly accelerated detectors and not for the parallelly accelerated ones, and also encounter the phenomena of degrading entanglement extraction with increasing temperature of the thermal bath [41,42].…”