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arXiv:2001.00750 · Physical review. D/Physical review. D.

Radiation-reaction-induced transitions of two maximally entangled atoms in noninertial motion

Wenting Zhou, Hongwei Yu

Published Jan 16, 2020• 19 citations
arXivHTMLPDF

Abstract

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 $|{g}_{A}{g}_{B}⟩$ and $|{e}_{A}{e}_{B}⟩$, where $g$ and $e$ 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.

DOI
10.1103/physrevd.101.025009

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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 the spontaneous excitation of a uniformly accelerated two-level atom nonlinearly coupled to vacuum Dirac field fluctuations using the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji and generalized by us to the present case in the current paper. We find that a cross term involving both vacuum fluctuations and radiation reaction appears, which is absent in the linear coupling cases such as an atom interacting with vacuum scalar or electromagnetic fluctuations. Furthermore, the contribution of this term actually dominates over that of radiation reaction. Thus, the mean rate of change of the atomic energy can no longer be distinctively separated into only the contributions of vacuum fluctuations and radiation reaction as in the scalar and electromagnetic cases where the coupling is linear. Our result shows that a uniformly accelerated atom interacting with vacuum Dirac fluctuations would spontaneously excite and a unique feature in sharp contrast to the scalar and electromagnetic cases is the appearance of a term in the excitation rate, which is proportional to the quartic acceleration.
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.
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.
We generalize the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji (the DDC formalism) to the fourth order of the coupling constant, which can be used to study the interatomic interaction of two ground-state atoms coupled with the vacuum scalar fields. We show that the interatomic potential can be attributed to the joint effect of both vacuum fluctuations and the radiation reaction of atoms. Remarkably, the formulas we derived for the contributions of vacuum fluctuations and the radiation reaction to the interatomic potential upon which future research on fourth-order effects in particular circumstances can be based differ from those in the existing literature [Phys. Rev. D 95, 085014 (2017)].
We study the resonance interaction between two uniformly accelerated identical atoms, one excited and the other in the ground state, prepared in a correlated (symmetric or antisymmetric) state and interacting with the scalar field or the electromagnetic field in the vacuum state. In this case (resonance interaction), the interatomic interaction is a second-order effect in the atom-field coupling. We separate the contributions of vacuum fluctuations and radiation reaction to the resonance energy shift of the system, and show that only radiation reaction contributes, while Unruh thermal fluctuations do not affect the resonance interaction. We also find that beyond a characteristic length scale related to the atomic acceleration, nonthermal effects in the radiation-reaction contribution change the distance dependence of the resonance interaction. Finally, we find that previously unidentified features appear, compared with the scalar field case, when the interaction with the electromagnetic field is considered, as a consequence of the peculiar nature of the vacuum quantum noise of the electromagnetic field in a relativistically accelerated background.
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.