Resonance interaction energy between two accelerated identical atoms in a coaccelerated frame and the Unruh effect

Abstract

We investigate the resonance interaction energy between two uniformly accelerated identical atoms, interacting with the scalar field or the electromagnetic field in the vacuum state, in the reference frame coaccelerating with the atoms. We assume that one atom is excited and the other in the ground state, and that they are prepared in their correlated symmetric or antisymmetric state. Using perturbation theory, we separate, at the second order in the atom-field coupling, the contributions of vacuum fluctuations and radiation reaction field to the energy shift of the interacting system. We show that only the radiation reaction term contributes to the resonance interaction between the two atoms, while Unruh thermal fluctuations, related to the vacuum fluctuations contribution, do not affect the resonance interatomic interaction. We also show that the resonance interaction between two uniformly accelerated atoms, recently investigated in the comoving (locally inertial) frame, can be recovered in the coaccelerated frame, without the additional assumption of the Fulling-Davies-Unruh temperature for the quantum fields (as necessary for the Lamb shift, for example). This indicates, in the case considered, the equivalence between the coaccelerated frame and the locally inertial frame.

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.…”

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

“…The effect of non-equilibrium boundaries on radiative properties of atoms has been also considered [37,38].Another, albeit related, problem, recently addressed in the literature, concerns the equivalence between acceleration and temperature. For example, it has been discussed that non-thermal features (related to a uniform acceleration) manifest in the dispersion (van der Waals/Casimir-Polder) and resonance interaction between non inertial atoms in the free-space [25,26,36,39]. 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 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].…”

Van der Waals and resonance interactions between accelerated atoms in vacuum and the Unruh effect

“…Our results clearly show that the non-inertial motion yields a new scaling of the interaction with the distance between the atoms and, since it is not related to vacuum field fluctuations, this qualitative change is not a thermal effect and goes beyond the usual temperature-acceleration equivalence [24]. The nonthermal nature of the effect of acceleration on the resonance interaction induces us to question at which extent the equivalence between acceleration and temperature is valid [26]. Recent works have concerned with the problem of the equivalence of physical predictions in coaccelerated and comoving frames, and it was argued that a complete equivalence of the two different frames requires assuming in the Rindler frame an Unruh temperature proportional to the acceleration for the quantum fields [27,12].…”

“…We show that, although the vacuum state in the comoving (i.e. locally inertial) and coaccelerated frames is different due to the Unruh effect, the resonance interaction between two atoms as measured by observers in these frames is the same, without the assumption of an Unruh temperature for the quantum field in the comoving frame [26]. This result is at variance with what has been obtained for other radiative effects, such as the spontaneous emission, where vacuum fluctuations are relevant [27].…”