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arXiv:2206.13681 · Journal of High Energy Physics

Effect of spacetime dimensions on quantum entanglement between two uniformly accelerated atoms

Jiatong Yan, Baocheng Zhang

Published Oct 7, 2022• 14 citations
arXivHTMLPDF

Abstract

Abstract We investigate the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-DeWitt detectors in different spacetime dimensions. It is found that the range of parameters in which entanglement can be generated is shrunk and the amount of generated entanglement is also decreased with the increasing spacetime dimension, by calculating the evolution of two-atom states using the method for open quantum systems. We study the entanglement evolution between two accelerated atoms for different initial two-atom states, and the influence of corresponding spacetime dimensions for every initial state is discussed. When the spacetime dimensions increase, the change of entanglement becomes slower with time. The influence of spacetime dimensions on the change of entanglement also expands to the case of the massive field. The time delay for entanglement generation is shown in different spacetime dimensions. In particular, entanglement decreases more quickly with the increasing spacetime dimensions compared with that in the case of the massless field. The recently found anti-Unruh effect is discussed, and a novel and interesting phenomenon is found that the Unruh effect in small spacetime dimensions can become the anti-Unruh effect in large spacetime dimensions with the same parameters.

DOI
10.1007/jhep10(2022)051

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Abstract We investigate the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-DeWitt detectors in different spacetime dimensions. It is found that the range of parameters in which entanglement can be generated is shrunk and the amount of generated entanglement is also decreased with the increasing spacetime dimension, by calculating the evolution of two-atom states using the method for open quantum systems. We study the entanglement evolution between two accelerated atoms for different initial two-atom states, and the influence of corresponding spacetime dimensions for every initial state is discussed. When the spacetime dimensions increase, the change of entanglement becomes slower with time. The influence of spacetime dimensions on the change of entanglement also expands to the case of the massive field. The time delay for entanglement generation is shown in different spacetime dimensions. In particular, entanglement decreases more quickly with the increasing spacetime dimensions compared with that in the case of the massless field. The recently found anti-Unruh effect is discussed, and a novel and interesting phenomenon is found that the Unruh effect in small spacetime dimensions can become the anti-Unruh effect in large spacetime dimensions with the same parameters.
We study the influence of the environment-induced interatomic interaction, which is usually neglected, on the entanglement dynamics of two uniformly accelerated atoms coupled with fluctuating massless scalar fields in the Minkowski vacuum. When the two-atom system is initially prepared in a separable state such that the two atoms are in the ground and excited states respectively, the environment-induced interatomic interaction assists entanglement generation, in the sense that the parameter space of acceleration and interatomic separation that allows entanglement generation is enlarged, the rate of entanglement generation at the initial time is enhanced, and the maximum of concurrence generated during evolution is increased compared with when the environment-induced interaction is neglected. Remarkably, the rate of entanglement generation at the initial time and the maximal concurrence generated during evolution decrease monotonically with the acceleration, in contrast to that they exhibit a nonmonotonic behavior as the acceleration varies when the environment-induced interatomic interaction is neglected. In other words, the anti-Unruh phenomenon in terms of the entanglement generation is deprived of by the consideration of the environment-induced interatomic interaction.
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.
We study the influence of the environment-induced interatomic interaction, which is usually neglected, on the entanglement dynamics of two uniformly accelerated atoms coupled with fluctuating massless scalar fields in the Minkowski vacuum. When the two-atom system is initially prepared in a separable state such that the two atoms are in the ground and excited states respectively, the environment-induced interatomic interaction assists entanglement generation, in the sense that the parameter space of acceleration and interatomic separation that allows entanglement generation is enlarged, the rate of entanglement generation at the initial time is enhanced, and the maximum of concurrence generated during evolution is increased compared with when the environment-induced interaction is neglected. Remarkably, the rate of entanglement generation at the initial time and the maximal concurrence generated during evolution decrease monotonically with the acceleration, in contrast to that they exhibit a non-monotonic behavior as the acceleration varies when the environment-induced interatomic interaction is neglected. In other words, the anti-Unruh phenomenon in terms of the entanglement generation is deprived of by the consideration of the environment-induced interatomic interaction.
The entanglement generated for a uniformly accelerated two-atom system in vacuum during its evolution may increase with acceleration, while that for a static one in a thermal bath always decreases monotonically with temperature. This phenomenon is named as the anti-Unruh effect in terms of the entanglement generated. In this paper, we study the effects of the interatomic interaction induced by the electromagnetic vacuum fluctuations on the entanglement dynamics of two uniformly accelerated atoms. We show that the anti-Unruh phenomenon may exist or disappear depending critically on the configuration of the orientation of the atomic polarization and the directions of the uniform acceleration and the interatomic separation. This is in sharp contrast to the scalar-field case, in which the anti-Unruh phenomenon is always lost when the environment-induced interatomic interaction is considered.
Considering environment-induced interatomic interaction, we study the entanglement dynamics of two uniformly accelerated atoms that interact with fluctuating massless scalar fields in the Minkowski vacuum in the presence of a reflecting boundary. The two atoms are initially prepared in a state such that one is in the ground state and the other is in the excited state, which is separable. When the acceleration is small, the rate of entanglement generation at the initial time and the maximum of concurrence generated during evolution oscillate with the distance between the atoms and the boundary before reaching a stable value, and may decrease non-monotonically with the acceleration, which means the anti-Unruh phenomenon can exist for some situations even when environmental considerations are taken into account. The results show that there exists the competition of the vacuum fluctuations caused by the boundary and the acceleration. In addition, the time evolution of concurrence will not be affected by the environment-induced interatomic interaction under certain conditions. For a larger acceleration, when the environment-induced interatomic interaction is considered, the concurrence may disappear later compared with the result when the environment-induced interatomic interaction is neglected.
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.