Abstract We consider two Unruh-DeWitt detectors interacting with a massless, minimally coupled scalar field in a (1+1) dimensional Reissner-Nordstrom black hole spacetime. In particular, one of the detectors, corresponding to Alice, is moving along an outgoing null trajectory. While the other detector carried by Bob is static. With this set-up, we investigate the entangling condition and the measure of the entanglement, concurrence, in the nonextremal and extremal scenarios. Our observations suggest, as expected, a qualitative similarity in characteristics of the entanglement between these two scenarios. However, we find a distinct and consistent quantitative feature between the nonextremal and extremal concurrences for a broad range of black hole charges. With moderately large detector transition energy, the extremal background always accounts for the larger entanglement than the nonextremal one. In contrast, with low detector transition energy, entanglement on the nonextremal background can be greater. Therefore, by adjusting the detector transition energy, one can perceive optimum entanglement from either the extremal or the nonextremal background.
We study entanglement degradation near the horizons of regular, Reissner-Nordström, and Schwarzschild-de Sitter black holes, considering the Bardeen, Hayward, and generalized Hayward metrics as regular black holes. To this end, we compute the entanglement negativity,
N, for two Unruh-like modes of a scalar field shared by Alice, who is inertial, and Rob, who hovers at a fractional offset
ρ outside the horizon of the backgrounds under consideration. For each geometry, we locally approximate the metric by a Rindler patch characterized by Rob's proper acceleration
a0. Because this Rindler approximation breaks down near the extremal limit, we also compute a near-extremal cutoff. Tracing over the inaccessible Rindler wedge yields a mixed Alice-Rob state, from which we evaluate
N as a function of the mode frequency
ω and the acceleration
a0. In all geometries considered, except for one,
N increases monotonically with the parameter distinguishing that geometry form the Schwarzschild one. The exception is the Reissner-Nordström metric, for which
N exhibits a shallow local minimum at a particular value of the charge. We also find that the Reissner-Nordström metric is the only background for which the negativity falls below that of the Schwarzschild case. Among all cases studied, the Schwarzschild-de Sitter spacetime provides the strongest protection of entanglement. Finally, across all backgrounds, high-frequency modes undergo less degradation than low-frequency modes. These results suggest that entanglement may serve as a useful probe for distinguishing Schwarzschild spacetime from other geometries.
Abstract We investigate the fate of initial entanglement between two accelerated detectors with respect to an observer attached to one of the detectors. Both (1 + 1) and (1 + 3) spacetime dimensions are being considered here, with the detectors interacting with real massless scalar fields through monopole terms. The investigation is being performed for both non-thermal as well as thermal fields. In general, irrespective of the detectors moving in the same Rindler wedge or opposite wedges, increase of the field temperature reduces the initial entanglement. In all situations, degradation of entanglement is high for high acceleration aA of our observer. Interestingly, the degradation depends on the measure of initial entanglement. For (1 + 1) dimensions, the degradation saturates for small values of aA, whereas the same fluctuates in (1 + 3) dimensions with the decrease of aA. For motions in opposite Rindler wedges, a noticeable feature we observe in (1 + 1) dimensions is that, depending on the strength of initial entanglement, there is a possibility of entanglement harvesting in the system for certain values of the observers’ acceleration. However the same is absent in (1 + 3) dimensions. The whole analysis is operationally different from earlier similar investigations. The thermal equilibrium is satisfied throughout the calculations here, by considering the Wightman functions with respect to the Rindler modes evaluated in the vacuum of Unruh modes, contrary to the use of Minkowski modes.
Abstract It is well-known that the (1 + 1) dimensional Schwarzschild and spatially flat FLRW spacetimes are conformally flat. This work examines entanglement harvesting from the conformal field vacuums in these spacetimes between two Unruh-DeWitt detectors, moving along outgoing null trajectories. In (1 + 1) dimensional Schwarzschild spacetime, we considered the Boulware and Unruh vacuums for our investigations. In this analysis, one observes that while entanglement harvesting is possible in (1+1) dimensional Schwarzschild and (1 + 3) dimensional de Sitter spacetimes, it is not possible in the (1 + 1) dimensional de Sitter background for the same set of parameters when the detectors move along the same outgoing null trajectory. The qualitative results from the Boulware and the Unruh vacuums are alike. Furthermore, we observed that the concurrence depends on the distance d between the two null paths of the detectors periodically, and depending on the parameter values, there could be entanglement harvesting shadow points or regions. We also observe that the mutual information does not depend on d in (1 + 1) dimensional Schwarzschild and de Sitter spacetimes but periodically depends on it in (1 + 3) dimensional de Sitter background. We also provide elucidation on the origin of the harvested entanglement.
We investigate the effects of relative motion on entanglement harvesting by considering a pair of Unruh-Dewitt detectors moving at arbitrary but independent and constant velocities, both linearly interacting with a massless scalar field vacuum in four-dimensional Minkowski spacetime. Working within the weak coupling approximation, we find that the negativity is a (nonelementary) function of the relative velocity of the detectors, as well as their energy gaps and minimal separation. We find parameter regions where negativity increases with velocity up to a maximum and then decreases, reaching zero at some sublight velocity. At any given relative velocity, the harvested entanglement is inversely correlated with the detector energy gap (at sufficiently high values) and the distance of closest approach of two detectors.
Abstract We study, in the framework of open quantum systems, the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-Dewitt detectors interacting with a bath of massive scalar fields in the Minkowski vacuum. We find that the entanglement evolution for the quantum system coupled with massive fields is always slower compared with that of the one coupled with massless fields, and this time-delay effect brought about by the field being massive can however be counteracted by a large enough acceleration, in contrast to the case of a static quantum system in a thermal bath, where this time delay is not affected by the temperature. Remarkably, the maximal concurrence of the quantum system generated during evolution may increase with acceleration for any inter-detector separation while that for static ones in a thermal bath decreases monotonically with temperature, and this can be considered as an anti-Unruh effect in terms of the entanglement generated.
Abstract The quantum vacuum has long been known to be characterized by field correlations between spacetime points. We show that such correlations—vacuum entanglement—in the environment of near-extremal black holes is significantly amplified (up to ten-fold) relative to their slowly rotating counterparts. We demonstrate this effect for rotating Banados–Teitelboim–Zanelli black holes by measuring the entanglement through the concurrence extracted from the vacuum via two-level quantum systems (Unruh–DeWitt detectors). The effect is manifest at intermediate distances from the horizon, and is most pronounced for near-extremal small mass black holes. The effect is also robust, holding for all boundary conditions of the field and at large spacelike detector separations. Smaller amplification occurs near the horizon, where we find that the entanglement shadow—a region near the black hole from which entanglement cannot be extracted—is diminished in size as the black hole’s angular momentum increases.