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arXiv:1805.04470 · Physical review. D/Physical review. D.

Radiative process of two entanglement atoms in de Sitter spacetime

Xiaobao Liu, Zehua Tian, Jieci Wang, Jiliang Jing

Published May 31, 2018• 31 citations
arXivHTMLPDF

Abstract

We investigate the radiative processes of a quantum system composed by two identical two-level atoms in the de Sitter spacetime, interacting with a conformally coupled massless scalar field prepared in the de Sitter-invariant vacuum. We discuss the structure of the rate of variations of the atomic energy for two static atoms. Following a procedure developed by Dalibard, Dupont-Roc, and Cohen-Tannoudji, our intention is to identify in a quantitative way the contributions of vacuum fluctuations and the radiation reaction to the generation of quantum entanglement and to the degradation of entangled states. We find that when the distance between two atoms larger than the characteristic length scale, the rate of variation of atomic energy in the de Sitter-invariant vacuum behaves differently compared with that in the thermal Minkowski spacetime. In particular, the generation and degradation of quantum entanglement can be enhanced or inhibited, which are dependent not only on the specific entangled state but also on the distance between the atoms.

DOI
10.1103/physrevd.97.105030

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We investigate the radiative processes of a quantum system composed by two identical two-level atoms in the de Sitter spacetime, interacting with a conformally coupled massless scalar field prepared in the de Sitter-invariant vacuum. We discuss the structure of the rate of variations of the atomic energy for two static atoms. Following a procedure developed by Dalibard, Dupont-Roc, and Cohen-Tannoudji, our intention is to identify in a quantitative way the contributions of vacuum fluctuations and the radiation reaction to the generation of quantum entanglement and to the degradation of entangled states. We find that when the distance between two atoms larger than the characteristic length scale, the rate of variation of atomic energy in the de Sitter-invariant vacuum behaves differently compared with that in the thermal Minkowski spacetime. In particular, the generation and degradation of quantum entanglement can be enhanced or inhibited, which are dependent not only on the specific entangled state but also on the distance between the atoms.
We study, in the framework of open quantum systems, the entanglement generation between two mutually independent static two-level atoms in de Sitter spacetime. We treat the two-atom system as an open system in interaction with a bath of fluctuating conformally coupled massless scalar fields in the de Sitter invariant vacuum and derive the master equation that governs its evolution. With the help of the partial transposition criterion, we analyze entanglement generation between the two initially separable atoms and find that static atoms in de Sitter spacetime exhibit distinct characteristics from those in a thermal bath in flat spacetime in terms of entanglement generation. So, in principle, one can tell whether he is in a thermal bath or in de Sitter space by checking the entanglement creation between two initially separable static atoms in certain circumstances.
We consider radiative processes of a quantum system composed by two identical two-level atoms in a black-hole background. We assume that these identical two-level atoms are placed at fixed radial distances outside a Schwarzschild black hole and interacting with a quantum electromagnetic field prepared in one of the usual vacuum states, namely, the Boulware, Unruh, or Hartle-Hawking vacuum states. We study the structure of the rate of variation of the atomic energy. The intention is to identify in a quantitative way the contributions of vacuum fluctuations and the radiation reaction to the entanglement generation between the atoms as well as the degradation of entangled states in the presence of an event horizon. We find that for a finite observation time the atoms can become entangled for the case of the field in the Boulware vacuum state, even if they are initially prepared in a separable state. In addition, the rate of variation of atomic energy is not well behaved at the event horizon due to the behavior of the proper accelerations of the atoms. We show that the thermal nature of the Hartle-Hawking and Unruh vacuum state allows the atoms to get entangled even if they were initially prepared in the separable ground state.
We apply the DDC formalism [proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji] to study the average rate of change of energy of two identical two-level atoms interacting with the vacuum massless scalar field in synchronized motion along stationary trajectories. By separating the contributions of vacuum fluctuations and atomic radiation reaction, we first show that for the two-atom system initially prepared in the factorizable eigenstates ∣gAgB⟩|{g}_{A}{g}_{B}⟩∣gA​gB​⟩ and ∣eAeB⟩|{e}_{A}{e}_{B}⟩∣eA​eB​⟩, where ggg and eee represent the ground state and the excited state of a single atom, respectively, both vacuum fluctuations and atomic radiation reaction contribute to the average rate of change of energy of the two-atom system, and the contribution of vacuum fluctuations is independent of the interatomic separation while that of atomic radiation reaction is dependent on it. This is contrary to the existing results in the literature where vacuum fluctuations are interatomic-separation dependent. However, if the two-atom system is initially prepared in the unfactorizable symmetric/antisymmetric entangled state, the average rate of change of energy of the two-atom system is never perturbed by the vacuum fluctuations, but is totally a result of the atomic radiation reaction. We then consider two special cases of motion of the two-atom system, which is initially prepared in the symmetric/antisymmetric entangled state, i.e., synchronized inertial motion and synchronized uniform acceleration. In contrast to the average rate of change of energy of a single uniformly accelerated atom, the average rate of change of energy of the uniformly accelerated two-atom system is nonthermal-like. The effects of noninertial motion on the transitions of states of the two correlated atoms are also discussed.
We study radiative processes of uniformly accelerated entangled atoms, interacting with an electromagnetic field prepared in the Minkowski vacuum state. We discuss the structure of the rate of variation of the atomic energy for two atoms traveling in different hyperbolic world lines. We identify the contributions of vacuum fluctuations and radiation reaction to the generation of entanglement as well as to the decay of entangled states. Our results resemble the situation in which two inertial atoms are coupled individually to two spatially separated cavities at different temperatures. In addition, for equal accelerations we obtain that one of the maximally entangled antisymmetric Bell state is a decoherence-free state.
We analyze radiative processes of a quantum system composed by two identical two-level atoms interacting with a massless scalar field prepared in the vacuum state in the presence of perfect reflecting flat mirrors. We consider that the atoms are prepared in a stationary maximally entangled state. We investigate the spontaneous transitions rates from the entangled states to the collective ground state induced by vacuum fluctuations. In the empty-space case, the spontaneous decay rates can be enhanced or inhibited depending on the specific entangled state and changes with the distance between the atoms. Next, we consider the presence of perfect mirrors and impose Dirichlet boundary conditions on such surfaces. In the presence of a single mirror the transition rate for the symmetric state undergoes a slight reduction, whereas for the antisymmetric state our results indicate a slightly enhancement. Finally, we investigate the effect of multiple reflections by two perfect mirrors on the transition rates.