Abstract We study the interaction potential of two nonidentical ground-state atoms coupled to a scalar field in a vacuum by separately calculating the contributions of vacuum fluctuations and those of the radiation reaction of the atoms. Both cases of atoms in a free space and in parallel or vertical alignment to a reflecting boundary are considered. For the former case, we find that the leading-order interaction potential in the region λ A ≪ L ≪ λ B exhibits the same separation-dependence as that in the region L ≪ λ A ≪ λ B , where L, λ A and λ B are respectively the interatomic separation and the transition wavelengths of two atoms with λ A ≪ λ B . For the latter case, we find that boundary-induced modifications are very remarkable when L ≫ z, with z characterizing the separation between the two-atom system and the boundary. Particularly, when L further satisfies L ≫ λ A and L ≫ λ B , the interaction potential in the parallel- and the vertical-alignment cases respectively scales as z 4 L −7 and z 2 L −5, the L-dependence of which is one order higher than those of two atoms in regions where L ≫ z and meanwhile L ≪ λ A or/and L ≪ λ B . Our results suggest that retardation for the interaction potential of two nonidentical atoms with remarkably distinctive transition frequencies happens only when the interatomic separation is much greater than the transition wavelengths of both atoms.
Abstract We study the interaction potential of two nonidentical ground-state atoms coupled to a scalar field in a vacuum by separately calculating the contributions of vacuum fluctuations and those of the radiation reaction of the atoms. Both cases of atoms in a free space and in parallel or vertical alignment to a reflecting boundary are considered. For the former case, we find that the leading-order interaction potential in the region λ A ≪ L ≪ λ B exhibits the same separation-dependence as that in the region L ≪ λ A ≪ λ B , where L, λ A and λ B are respectively the interatomic separation and the transition wavelengths of two atoms with λ A ≪ λ B . For the latter case, we find that boundary-induced modifications are very remarkable when L ≫ z, with z characterizing the separation between the two-atom system and the boundary. Particularly, when L further satisfies L ≫ λ A and L ≫ λ B , the interaction potential in the parallel- and the vertical-alignment cases respectively scales as z 4 L −7 and z 2 L −5, the L-dependence of which is one order higher than those of two atoms in regions where L ≫ z and meanwhile L ≪ λ A or/and L ≪ λ B . Our results suggest that retardation for the interaction potential of two nonidentical atoms with remarkably distinctive transition frequencies happens only when the interatomic separation is much greater than the transition wavelengths of both atoms.
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 investigate the resonance dipole-dipole interaction energy between two identical atoms, one in the ground state and the other in the excited state, interacting with the electromagnetic field in the presence of a perfectly reflecting plane boundary. The atoms are prepared in a correlated (symmetric or antisymmetric) Bell-type state. Following a procedure due to Dalibard et al. [J. Dalibard et al., J. Phys. (Paris) 43, 1617 (1982); J. Phys. (Paris) 45, 637 (1984)], we separate the contributions of vacuum fluctuations and radiation reaction (source) field to the resonance interaction energy between the two atoms and show that only the source field contributes to the interatomic interaction, while vacuum field fluctuations do not. By considering specific geometric configurations of the two-atom system with respect to the mirror and specific choices of dipole orientations, we show that the presence of the mirror significantly affects the resonance interaction energy and that different features appear with respect to the case of atoms in free space, for example, a change in the spatial dependence of the interaction. Our findings also suggest that the presence of a boundary can be exploited to tailor and control the resonance interaction between two atoms, as well as the related energy transfer process. The possibility of observing these phenomena is also discussed.
Abstract We generalize the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji (the DDC formalism) in the fourth order for two atoms in interaction with scalar fields in vacuum to a thermal bath at finite temperature T, and then calculate the interatomic interaction energy of two ground-state atoms separately in terms of the contributions of thermal fluctuations and the radiation reaction of the atoms and analyze in detail the thermal corrections to the van der Waals and Casimir–Polder interactions. We discover a particular region, i.e. λ 3 β 4 ≪ L ≪ λ with L, β and λ denoting the interatomic separation, the wavelength of thermal photons and the transition wavelength of the atoms respectively, where the thermal corrections remarkably render the van der Waals force, which is usually attractive, repulsive, leading to an interesting crossover phenomenon of the interatomic interaction from attractive to repulsive as the temperature increases. We also find that the thermal corrections cause significant changes to the Casimir–Polder force when the temperature is sufficiently high, resulting in an attractive force proportional to TL −3 in the λ ≪ β ≪ L region, and a force that can be either attractive or repulsive and even vanishing in the β ≪ λ ≪ L region depending on the interatomic separation.
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 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 study the resonant dipole–dipole interaction energy between two non-inertial identical atoms, one excited and the other in the ground state, prepared in a correlated Bell-type state, and interacting with the scalar field or the electromagnetic field nearby a perfectly reflecting plate. We suppose the two atoms move with the same uniform acceleration, parallel to the plane boundary, and that their separation is constant during the motion. By separating the contributions of radiation reaction field and vacuum fluctuations to the resonance energy shift of the two-atom system, we show that Unruh thermal fluctuations do not affect the resonance interaction, which is exclusively related to the radiation reaction field. However, non-thermal effects of acceleration in the radiation-reaction contribution, beyond the Unruh acceleration–temperature equivalence, affect the resonance interaction energy. By considering specific geometric configurations of the two-atom system relative to the plate, we show that the presence of the mirror significantly modifies the resonance interaction energy between the two accelerated atoms. In particular, we find that new and different features appear with respect to the case of atoms in the free-space, related to the presence of the boundary and to the peculiar structure of the quantum electromagnetic field vacuum in the locally inertial frame. Our results suggest the possibility to exploit the resonance interaction between accelerated atoms as a probe for detecting the elusive effects of atomic acceleration on radiative processes.