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 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.
We give a general derivation of the fourth-order DDC formalism (a formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji) for calculating the interaction energy between two ground-state multilevel atoms which are coupled to electromagnetic fields in a thermal bath at temperature T. Both the contributions of the thermal field fluctuations and the radiation reaction of atoms are separately identified. As an application of the formalism, we revisit the interaction energy of two static ground-state two-level atoms in a free space and discover new behaviors such as the $\ensuremath{\sim}T{L}^{\ensuremath{-}2}$ behavior of the van der Waals interaction energy in the region where ${\ensuremath{\lambda}}^{3/4}{T}^{\ensuremath{-}1/4}\ensuremath{\ll}L\ensuremath{\ll}\ensuremath{\lambda}$, with $\ensuremath{\lambda}$ the transition wavelength of the atoms and L the interatomic separation, and an oscillatory behavior of the Casimir-Polder interaction energy as L varies which is superimposed on the monotonic $\ensuremath{\sim}T{L}^{\ensuremath{-}6}$ dependence when $L\ensuremath{\gg}\ensuremath{\lambda}\ensuremath{\gg}{T}^{\ensuremath{-}1}$.
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 have investigated, by separating the contributions from thermal fluctuations (tf) and the radiation reaction (rr), the gravitational Casimir-Polder interaction between a gravitationally polarizable two-level object and an infinite gravitational Dirichlet boundary in a thermal bath at a temperature T. The results indicate that the rr-contribution to the interaction potential is independent of the temperature, whereas the tf-contribution is generally governed by a nontrivial interplay between the thermal corrections and the polarization effect. Here, the object-to-boundary distance, the characteristic transition wavelength of the object and the thermal wavelength of gravitons are denoted by L, λ and β, respectively. In contrast to the vacuum case, where the interaction potential scales as L−5 for L≪λ and L−6 for L≫λ, corresponding to an always repulsive force, qualitatively new behaviors emerge at high temperatures. Particularly, when 4βλ3≪L≪λ and the object is polarizable within the plane perpendicular to the boundary, a novel scaling of TL−1 arises; when βλ≪L≪λ and the object is polarizable along the vertical-to-boundary axis, the interaction force becomes surprisingly attractive. At extremely high temperatures and large distances, i.e. when β≪λ≪L, the potential oscillates with the distance L and thus an attractive or repulsive and even vanishing force can be resulted, depending on the exact values of L. Our work demonstrates that thermal gravitons can act as an active control mechanism for quantum gravitational interactions, and temperature, polarization configuration, and object-to-boundary distance jointly determine the magnitude, scaling law, and even the attractive or repulsive nature of the interaction force.
We study the modification by the presence of a plane wall of energy-level shifts of two-level atoms which are in multipolar coupling with quantized electromagnetic fields in a thermal bath in a formalism which separates the contributions of thermal fluctuations and radiation reaction and allows a distinct treatment to atoms in the ground and excited states. The position-dependent energy shifts give rise to an induced force acting on the atoms. We are able to identify three different regimes where the force shows distinct features and examine, in all regimes, the behaviors of this force in both the low-temperature limit and the high-temperature limit for both the ground-state and excited-state atoms, thus providing some physical insights into the atom-wall interaction at finite temperature. In particular, we show that both the magnitude and the direction of the force acting on an atom may have a clear dependence on the atomic polarization directions. In certain cases, a change in relative ratio of polarizations in different directions may result in a change in direction of the force.
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.
The Casimir-Polder (C-P) interaction between an atom and a surface, described as early as 1948, but observed much later on, is now a topic of broad interest, as connected to fundamental problems of quantum fluctuations, with the atomic energy levels renormalized by the wall-dependent vacuum fluctuations. Dependence of the C-P interaction with the equilibrium temperature is predicted, but had not been observed until now. However, more pronounced effects were predicted in an out-of-equilibrium situation, and were remarkably observed on a Rb BEC, at 6-10 μm from the wall, with the vacuum temperature (~ 300K) strongly differing from the surface temperature (~ 1000 K).