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arXiv:1806.05344 · Physical review. D/Physical review. D.

Entanglement dynamics for uniformly accelerated two-level atoms in the presence of a reflecting boundary

Shijing Cheng, Hongwei Yu, Jiawei Hu

Published Jul 2, 2018• 29 citations
arXivHTMLPDF

Abstract

We study the entanglement dynamics for two uniformly accelerated two-level atoms in interaction with a bath of fluctuating electromagnetic fields in vacuum in the presence of a reflecting boundary. We consider two different alignments of atoms, i.e., parallel and vertical alignments with respect to the boundary. In particular, we focus on the effects of the boundary, and acceleration on the entanglement dynamics, which are closely related to the orientations of polarization. For the parallel case, the initial entanglement of two transversely polarizable atoms very close to the boundary can be preserved as if it were a closed system, while for two vertically polarizable atoms, the concurrence evolves two times as fast as that in the free space. In the presence of a boundary, entanglement revival is possible for two atoms initially in the symmetric state depending on the orientations of the atomic polarizations, which is in sharp contrast to the fact that the concurrence always decays monotonically in the free space. Interestingly, two initially separable atoms, for which entanglement generation can never happen in the free space with any given acceleration and separation, can get entangled in the presence of a boundary if they are aligned parallel to the boundary. The birth time of entanglement can be noticeably advanced or postponed for the parallel two-atom system placed close to the boundary, while the maximal concurrence during evolution can be significantly enhanced when the atoms are vertically aligned. Moreover, two inertial atoms with different polarizations remain separable all the time, while as the acceleration increases, the delayed birth of entanglement happens, and the nonzero concurrence can be enhanced.

DOI
10.1103/physrevd.98.025001

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We study the entanglement dynamics for two uniformly accelerated two-level atoms in interaction with a bath of fluctuating electromagnetic fields in vacuum in the presence of a reflecting boundary. We consider two different alignments of atoms, i.e., parallel and vertical alignments with respect to the boundary. In particular, we focus on the effects of the boundary, and acceleration on the entanglement dynamics, which are closely related to the orientations of polarization. For the parallel case, the initial entanglement of two transversely polarizable atoms very close to the boundary can be preserved as if it were a closed system, while for two vertically polarizable atoms, the concurrence evolves two times as fast as that in the free space. In the presence of a boundary, entanglement revival is possible for two atoms initially in the symmetric state depending on the orientations of the atomic polarizations, which is in sharp contrast to the fact that the concurrence always decays monotonically in the free space. Interestingly, two initially separable atoms, for which entanglement generation can never happen in the free space with any given acceleration and separation, can get entangled in the presence of a boundary if they are aligned parallel to the boundary. The birth time of entanglement can be noticeably advanced or postponed for the parallel two-atom system placed close to the boundary, while the maximal concurrence during evolution can be significantly enhanced when the atoms are vertically aligned. Moreover, two inertial atoms with different polarizations remain separable all the time, while as the acceleration increases, the delayed birth of entanglement happens, and the nonzero concurrence can be enhanced.
We investigate the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to their separation. The two-atom system is treated as an open system coupled with fluctuating electromagnetic fields in the Minkowski vacuum, and in the Born--Markov approximation the master equation that describes the completely positive time evolution of the two-atom system is derived. In particular, we investigate the phenomena of entanglement degradation, generation, revival and enhancement. As opposed to the scalar-field case, the entanglement dynamics is crucially dependent on the polarization directions of the atoms. For the two-atom system with certain acceleration and separation, the polarization directions of the atoms may determine whether entanglement generation, revival or enhancement happens, while for entanglement degradation, they affect the decay rate of entanglement. A comparison between the entanglement evolution of accelerated atoms and that of static ones immersed in a thermal bath at the Unruh temperature shows that they are the same only when the acceleration is extremely small.
Abstract We study the average rate of change of energy of two accelerated entangled atoms coupled to electromagnetic fields in the presence of a reflecting boundary, which according to the Dalibard, Dupont–Roc and Cohen-Tannoudji formalism is only attributed to the contribution of the radiative reaction of atoms. When the boundary is present, this result can be expressed as the sum of the free-space result and the boundary-induced modifications, and it generally depends on the two-atom initial state, the orientations of atomic dipole moments, as well as the relative scales among atom-boundary distance, interatomic separation and the inverse of atomic acceleration. When the two atoms are vertically aligned and one atom is very close to the boundary, we find that the terms only related to the closer atom are zero for the symmetric state but double the free-space counterpart for the antisymmetric state, if the atom is polarizable parallel to the boundary. However, for the atom polarizable vertically to the boundary, these terms vanish for the antisymmetric state but are twice the free-space counterpart for the symmetric state. Moreover, the terms related to the farther atom exhibit obviously oscillatory behavior, and the terms related to both atoms are vanishing unless the dipole moments of two atoms both have their components vertical to the boundary. When the two atoms are aligned parallel to and very close to the boundary, the terms related to one atom are interatomic-separation-independent and only influenced by the atomic dipole moments. The terms related to both atoms are actually consistent with the counterpart in the vertical-alignment case. In addition, when the two atoms are polarizable along the direction parallel to the boundary, the average rate of change of energy of two parallel-aligned and symmetric entangled atoms vanishes as if the two atoms were a closed system.
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.
We study, in the paradigm of open quantum systems, the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to the separation. The two-atom system is treated as an open system coupled with a bath of fluctuating massless scalar fields in the Minkowski vacuum, and the master equation that governs its evolution is derived. It has been found that, for accelerated atoms with a nonvanishing separation, entanglement sudden death is a general feature when the initial state is entangled, while for those in a separable initial state, entanglement sudden birth only happens for atoms with an appropriate interatomic separation and sufficiently small acceleration. Remarkably, accelerated atoms can get entangled in certain circumstances while the inertial ones in the Minkowski vacuum cannot. A comparison between the results of accelerated atoms and those of static ones in a thermal bath shows that uniformly accelerated atoms exhibit features distinct from those immersed in a thermal bath at the Unruh temperature in terms of entanglement dynamics.
We investigate the influence of environment-induced interactions on the entanglement dynamics of two uniformly accelerated atoms coupled to a fluctuating massless scalar field with a reflecting boundary. The two atoms are aligned vertically to the boundary. The entanglement behaviors are influenced by the competition between the environment-induced interatomic and the environment-induced atom-plate interactions, which can be characterized by certain critical values. The maximum of concurrence generated during evolution decreases non-monotonically with the acceleration, which implies the anti-Unruh phenomenon can exist for some situations even when both environment-induced interatomic and the environment-induced atom-plate interactions are considered.
We investigate, in the framework of open quantum systems, the entanglement dynamics of two circularly accelerated two-level atoms with the same centripetal acceleration interacting with a bath of fluctuating electromagnetic fields in the Minkowski vacuum. We assume that the two atoms rotate synchronically with their separation perpendicular to the rotating plane and study the entanglement degradation, creation, revival, and enhancement by solving the Markovian master equation. In contrast to the scalar-field case, the entanglement dynamics is crucially dependent on the atomic polarizations in the sense that the polarization directions may affect the entanglement decay rate and may determine the occurrences of entanglement creation, revival, and enhancement. Compared with the uniformly accelerated case and the thermal case, the decay rate of entanglement for circularly accelerated atoms is larger, while the revival and enhancement rates are smaller.