Vacuum fluctuations and radiation reaction contributions to the resonance dipole-dipole interaction between two atoms near a reflecting boundary

Abstract

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 anti-symmetric) Bell-type state. Following a procedure due to Dalibard et. al. [J. Dalibard et. al., J. Phys. (Paris) 43, 1617; 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.

Boundarylike behaviors of the resonance interatomic energy in a cosmic string spacetime

“…Dalibard, Dupont-Roc and Cohen Tannoudji(DDC) proposed that a symmetric ordering should be exploited, so that the contributions of field fluctuations and radiation reaction can be distinctively separated [72,73]. This formalism has been widely used to study the spontaneous transition rates and energy shifts of a single atom interacting with quantum fields in various environments [2, 6-12, 15-19, 22-24], and very recently, it was generalized to study the resonance interaction between two atoms prepared in an entangled state in the Minkowski spacetime [4,71,[79][80][81][82] and in the Schwarzschild spacetime [25,82]. Here we introduce the DDC formalism with which we will investigate the resonance interaction energy of two atoms in the Minkowski and cosmic string spacetimes.…”

“…Very recently, we studied the resonance interaction energy between two static atoms interacting with quantum electromagnetic fields near a perfectly reflecting boundary and correlated by an entangled state. We discovered that for some specific geometric configurations of the two-atom system with respect to the mirror, the resonance interaction energy exhibits new behaviors as compared with those of two static ones in an unbounded Minkowski spacetime [70,71].…”

Resonance Dipole-Dipole Interaction Between Two Accelerated Atoms in the Presence of a Reflecting Plane Boundary

“…The first term on the right-hand side of Equation (29) coincides with that for atoms uniformly accelerating in free-space [25], while the second new term is related to the boundary. In the static (inertial) limit, we recover the expression of the resonance interaction for atoms at rest near the mirror for the configuration considered [44]: It is worth noting that the expression of δE (z, D, a) given by Equation (29) is formally equal to that obtained for δE ⊥ (z, L, a) in Equation (22), provided R is replaced by R. This is indeed expected, as the distance R = √ D 2 + 4z 2 is the distance between one atom and the image of the other. In order to compare the results obtained in the two geometric configurations, in Figure 3 are plotted Equations (22) and (29) of the resonance interaction energy (in units of eV/λ 2 ), as a function of the atomic acceleration.…”

“…These investigations reveal that the effects of a uniform acceleration are not always equivalent to Unruh thermal effects.Motivated by these issues, in this paper, we investigate the effect of a non-inertial motion on the resonance interaction between two atoms, that accelerate with the same constant acceleration, parallel to a reflecting plate. The imposition of boundary conditions on the quantum field on the plate changes vacuum field fluctuations and the density of states of the quantized radiation field, and, thus, it can significantly influence radiative properties of atoms placed nearby [40][41][42][43][44][45]. Our aim is to investigate in detail physical manifestations of atomic acceleration in the radiation-mediated resonance interaction between the two atoms located in the proximity of a reflecting plate.Resonance and dispersion Casimir-Polder interactions are long-range interactions involving neutral objects such as atoms or molecules [46,47], due to the zero-point fluctuations of the quantum electromagnetic field or to the source field [47][48][49].…”

“…The possibility to manipulate (enhance or inhibit) the dispersion and resonance interactions through a structured environment has been also recently investigated [57][58][59][60][61].We consider two atoms moving with the same uniform proper acceleration in a direction parallel to a reflecting boundary and interacting with the quantum scalar and the electromagnetic field in the vacuum state. Following a procedure originally introduced by Dalibard, 63], we identify the contribution of self reaction and vacuum fluctuations to the resonance energy shift of the two accelerated atoms [25,39,44,64]. This approach has been recently used to investigate radiative process of atoms at rest in the presence of a boundary [44,65] or in a cosmic string spacetime [66], and it has been recently generalized to the fourth order to evaluate the dispersion Casimir-Polder interaction between two atoms accelerating in the vacuum space [36].…”