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 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 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).
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.
We study the properties of the transition probability and entanglement harvesting phenomenon for circularly accelerated detectors locally interacting with massless scalar fields. The dependence of the transition probability on the parameters associated with the circular motion is first analyzed in detail. By a cross-comparison with the situation of the uniformly accelerated motion, we obtain that the transition probability and the possible thermalization behavior for detectors rotating with an extremely large circular radius are analogous to that for uniformly accelerated detectors, but for a very small linear speed and a large acceleration, the effective temperature which characterizes the detectors' thermalization in a finite duration is much lower than that for uniformly accelerated detectors. We then focus on the phenomenon of entanglement harvesting in two special situations of circular trajectories, i.e., the coaxial rotation and the mutually perpendicular axial rotation by examining the concurrence as the entanglement measure in detail. We find that when two circularly accelerated detectors have equivalent acceleration and size of circular trajectory, the harvested entanglement rapidly decays with increasing acceleration or separation between two detectors. In contrast with the situation of uniform acceleration, the angular velocity would have significant impacts on entanglement harvesting. Especially for those detectors circularly moving in different directions, both the acceleration and trajectory radius play an important inhibiting role in entanglement harvesting. When two circularly accelerated detectors have different values of acceleration or angular velocity, we find that the entanglement can still be extracted by such detectors, even in the situation that one detector is at rest and the other is in a circular motion.
Abstract We study the radiative process of two entangled two-level atoms uniformly accelerated in a thermal bath, coupled to a massless scalar field. First, by using the positive frequency Wightman function from the Minkowski modes with a Rindler transformation we provide the transition probabilities for the transitions from maximally entangled symmetric and anti-symmetric Bell states to the collective excited or ground state in (1 + 1) and (1 + 3) dimensions. We observe a possible case of anti-Unruh-like event in these transition probabilities, though the (1+1) and (1+3) dimensional results are not completely equivalent. We infer that thermal bath plays a major role in the occurrence of the anti-Unruh-like effect, as it is also present in the transition probabilities corresponding to a single detector in this case. Second, we have considered the Green’s functions in terms of the Rindler modes with the vacuum of Unruh modes for estimating the same. Here the anti-Unruh effect appears only for the transition from the anti-symmetric state to the collective excited or ground state. It is noticed that here the (1 + 1) and (1 + 3) dimensional results are equivalent, and for a single detector, we do not observe any anti-Unruh effect. This suggests that the entanglement between the states of the atoms is the main cause for the observed anti-Unruh effect in this case. In going through the investigation, we find that the transition probability for a single detector case is symmetric under the interchange between the thermal bath’s temperature and the Unruh temperature for Rindler mode analysis; whereas this is not the case for Minkowski mode. We further comment on whether this observation may shed light on the analogy between an accelerated observer and a real thermal bath. An elaborate investigation for the classifications of our observed anti-Unruh effects, i.e., either weak or strong anti-Unruh effect, is also thoroughly demonstrated.
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 We explore the entanglement dynamics of two detectors undergoing uniform acceleration and circular motion within a massive scalar field, while also investigating the influence of the anti-Unruh effect on entanglement harvesting. Contrary to the conventional understanding of the weak anti-Unruh effect, where entanglement typically increases, we observe that the maximum entanglement between detectors does not exhibit a strict monotonic dependence on detector acceleration. Particularly at low accelerations, fluctuations in the entanglement maxima show a strong correlation with fluctuations in detector transition rates. We also find that the maximum entanglement of detectors tends to increase with smaller field mass. Novelly, our findings indicate the absence of a strong anti-Unruh effect in (3+1)-dimensional massive scalar fields. Instead, thermal effects arising from acceleration contribute to a decrease in the detector entanglement maximum.