Effect of boundaries on vacuum field fluctuations and radiation-mediated interactions between atoms

Abstract

In this paper we discuss and review several aspects of the effect of boundary conditions and structured environments on dispersion and resonance interactions involving atoms or molecules, as well as on vacuum field fluctuations. We first consider the case of a perfect mirror, which is free to move around an equilibrium position and whose mechanical degrees of freedom are treated quantum mechanically. We investigate how the quantum fluctuations of the mirror's position affect vacuum field fluctuations for both a one-dimensional scalar and electromagnetic field, showing that the effect is particularly significant in the proximity of the moving mirror. This result can be also relevant for possible gravitational effects, since the field energy density couples to gravity. We stress that this interaction-induced modification of the vacuum field fluctuations can be probed through the Casimir-Polder interaction with a polarizable body, thus allowing to detect the effect of the mirror's quantum position fluctuations. We then consider the effect of an environment such as an isotropic photonic crystal or a metallic waveguide, on the resonance interaction between two entangled identical atoms, one excited and the other in the ground state. We discuss the strong dependence of the resonance interaction with the relative position of the atomic transition frequency with the gap of the photonic crystal in the former case, and with the cut-off frequency of waveguide in the latter.

Dispersion Interaction between Two Hydrogen Atoms in a Static Electric Field

“…These ubiquitous interactions have great relevance in many areas of physics, and applications in biology [10,11], chemistry [12] and nanotechnologies [13][14][15]. A striking property of these interactions is that they can be controlled and tailored through the external environment, for example a cavity or a wall [16][17][18][19][20], a waveguide [21][22][23][24][25], or a photonic crystal [26,27]. Of special interest is to investigate the possibility of making Casimir interactions repulsive, in particular for applications in nanotechnological devices, where a repulsive Casimir interaction could help to prevent stiction [28].…”

Dispersion Interactions between Neutral Atoms and the Quantum Electrodynamical Vacuum

“…All this is relevant because these methods can provide very useful computational tools to evaluate dispersion interactions in complicated geometries, also allowing the possibility to change and manipulate radiation-mediated interactions between atoms or molecules through the environment. This is still more striking for the resonance interaction, where the exchange of real photons is also present [43,112,113].…”

“…We have already seen in Section IV that the presence of the plate changes vacuum fluctuations; mathematically, this is due to the necessity of setting appropriate boundary conditions on the field operators at the plate surface. Due to the deep relation of dispersion interactions to field fluctuations, shown in Section VII, we must expect that also the van der Waals and Casimir-Polder force (and any other radiation-mediated interaction) will change due to the plate [7,43]. A fourth-order perturbative calculation has been done in Ref.…”

Collective spontaneous emission of two entangled atoms near an oscillating mirror

“…Very recently, the influence of a perfect reflector on the cooperative spontaneous emission process of two atoms located nearby has been discussed [16]. The effect of a surface or a structured environment, or of an external static electric field on other radiative processes, such as dispersion or resonance interactions between atoms, have been recently studied [17][18][19][20][21][22][23].…”