The van der Waals potential of two atoms in the presence of an arbitrary arrangement of dispersing and absorbing magnetodielectric bodies is studied. Starting from a polarizable atom placed within a given geometry, its interaction with a second polarizable/magnetizable atom is deduced from its Casimir-Polder interaction with a weakly polarizable/magnetizable test body. The general expressions for the van der Waals potential hence obtained are illustrated by considering first the case of two atoms in free space, with special emphasis on the interaction between (i) two polarizable atoms and (ii) a polarizable and a magnetizable atom. Furthermore, the influence of magnetodielectric bodies on the van der Waals interaction is studied in detail for the example of two atoms placed near a perfectly reflecting plate or a magnetodielectric half space, respectively.
By modeling a linear polarizable and magnetizable medium (magneto-dielectric) with two quantum fields, namely E and M, electromagnetic field is quantized in such a medium consistently and systematically. A Hamiltonian is proposed from which, using the Heisenberg equations, Maxwell and constitutive equations of the medium are obtained. For a homogeneous medium, the equation of motion of the quantum vector potential, $\vec{A}$, is derived and solved analytically. Two coupling functions which describe the electromagnetic properties of the medium are introduced. Four examples are considered showin…
Modeling an anisotropic spatially and temporarily dispersive magnetodielectric medium by two independent collections of three dimensional vector fields, we demonstrate a fully canonical quantization of electromagnetic field in the presence of such a medium. Two tensor fields which couple the electromagnetic field with the medium and have an important role in this quantization method are introduced. The electric and magnetic polarization fields of the medium naturally are concluded in terms of the coupling tensors and the dynamical variables modeling the magnetodielectric medium. In Heisenberg …
We find the low-temperature behavior of the Casimir-Polder free energy for a polarizable and magnetizable atom interacting with a plate made of ferromagnetic dielectric material. It is shown that the corresponding Casimir-Polder entropy goes to zero with vanishing temperature, i.e., the Nernst heat theorem is satisfied, if the dc conductivity of the plate material is disregarded in calculations. If the dc conductivity is taken into account, the Nernst theorem is violated. These results are discussed in light of recent experiments.
We derive analytic expressions for the classical Casimir-Polder free energy and force for a polarizable (magnetizable) atom (microparticle) interacting with thin films, made of different materials, or graphene. It is shown that for an isolated dielectric film the free energy and force decrease quicker with separation, as compared to the case of atom interacting with a thick plate (semispace). For metallic films some peculiar features depending on the model of a metal used are analyzed. For an atom interacting with graphene we demonstrate that at room temperature the classical regime is achieve…
Highly polarizable metastable He* ($\mathrm{2^3S}$) and Ne* ($\mathrm{2^3P}$) atoms have been diffracted from a 100 nm period silicon nitride transmission grating and the van der Waals coefficients $C_3$ for the interaction of the excited atoms with the silicon nitride surface have been determined from the diffraction intensities out to the 10th order. The results agree with calculations based on the non-retarded Lifshitz formula.
The van der Waals interaction between two ground-state atoms is calculated for two electrically or magnetically polarizable particles embedded in a dispersive magneto-dielectric medium. Unlike previous calculations which infer the atom-atom interaction from the dilute-medium limit of the macroscopic, many-body van der Waals interaction, the interaction is calculated directly for the system of two atoms in a magneto-dielectric medium. Two approaches are presented, the first based on the quantized electromagnetic field in a dispersive medium without absorption and the second on Green functions t…
We study single- and two-atom van der Waals interactions of ground-state atoms which are both polarizable and paramagnetizable in the presence of magneto-electric bodies within the framework of macroscopic quantum electrodynamics. Starting from an interaction Hamiltonian that includes particle spins, we use leading-order perturbation theory for the van der Waals potentials expressed in terms of the polarizability and magnetizability of the atom(s). To allow for atoms embedded in media, we also include local-field corrections via the real-cavity model. The general theory is applied to the poten…
We study the van der Waals (vdW) interaction between a polarizable particle and a grounded conducting corrugated surface. For sinusoidal corrugations, one knows that, under the action of the lateral vdW force, an isotropic particle is always attracted to the nearest corrugation peak, with such behavior called in the present paper as peak regime. Here, considering an anisotropic polarizable particle, and making analytical calculations valid beyond the proximity force approximation (PFA), we show that the attraction is not only toward the peaks, but, for certain particle orientations and distanc…
We calculate the van der Waals dispersive interaction between a neutral but polarizable atom and a perfectly conducting isolated sphere in the nonretarded case. We make use of two separate models, one being the semiclassical fluctuating-dipoles method, the other using ordinary quantum mechanics.
Initially, we make a detailed historical survey of van der Waals forces, collecting the main references on the subject. Then, we review a method recently proposed by Eberlein and Zietal to compute the dispersion van der Waals interaction between a neutral but polarizable atom and a perfectly conducting surface of arbitrary shape. This method has the advantage of relating the quantum problem to a corresponding classical one in electrostatics so that all one needs is to compute an appropriate Green function. We show how the image method of electrostatics can be conveniently used together with th…
The van der Waals interaction between two polarizable atoms is considered. In three dimensions the standard form with an attractive $1/|R|^6$ potential is obtained from second-order quantum perturbation theory. When the electron motion is restricted to lower dimensions (but the $1/|R|$ Coulomb potential is retained), new terms in the expansion appear and alter both the sign and the $|R|$ dependence of the interaction.
A unified approach to the calculation of dispersive forces on ground-state bodies and atoms is given. It is based on the ground-state Lorentz force density acting on the charge and current densities attributed to the polarization and magnetization in linearly, locally, and causally responding media. The theory is applied to dielectric macro- and micro-objects, including single atoms. Existing formulas valid for weakly polarizable matter are generalized to allow also for strongly polarizable matter. In particular when micro-objects can be regarded as single atoms, well-known formulas for the Ca…
The analytic expressions for the free energy and entropy of the Casimir-Polder interaction between a polarizable and magnetizable atom and a graphene sheet are found in the limiting case of low temperature. In so doing, the response of graphene to electromagnetic fluctuations is described in the framework of the Dirac model by means of the polarization tensor in (2+1)-dimensional space-time. It is shown that the dominant contribution to the low-temperature behavior is given by an explicit dependence of the polarization tensor on temperature as a parameter. We demonstrate that the Lifshitz theo…
We calculate the non-retarded dispersion force exerted on an electrically polarizable quantum particle by a perfectly conducting toroid, which is one of the most common objects exhibiting a non-trivial topology. We employ a convenient method developed by Eberlein and Zietal that essentially relates the quantum problem of calculating dispersion forces between a quantum particle and a perfectly conducting surface of arbitrary shape to a corresponding classical problem of electrostatics. Considering the quantum particle in the symmetry axis of the toroid, we use this method to find an exact analy…
In a recent paper, it was shown that, under the action of the lateral van der Waals (vdW) force due to a perfectly conducting corrugated surface, a neutral anisotropic polarizable particle in vacuum can be attracted not only to the nearest corrugation peak, but also to a valley, or an intermediate point between a peak and a valley, with such behaviors called peak, valley and intermediate regimes, respectively. In the present paper, we investigate how these regimes are affected by the consideration of two non-dispersive semi-infinite dielectrics $ε_{1}$ and $ε_{2}$, separated by a corrugated in…
We consider a single slight protuberance in a perfectly conducting plane, and investigate the van der Waals (vdW) interaction between this surface and a neutral polarizable particle. When the protuberance is sufficiently smooth, so that the proximity force approximation (PFA) is well applicable, for a fixed distance of the particle from the plane, the lateral vdW force always points to the protuberance. On the other hand, by making calculations valid beyond the PFA, we show that nontrivial geometric effects arise when we consider an anisotropic particle, and manipulate the ratio between the ch…
In this paper, dedicated to the career of Iver Brevik, we review the derivation of the retarded van der Waals or Casimir-Polder interaction between polarizable molecules from the general multiple scattering formulation of Casimir interactions between bodies. We then apply this van der Waals potential to examine the interaction between tenuous cylindrical bodies, including eccentric cylinders, and revisit the vanishing self-energy of a tenuous dielectric cylinder. In each case, closed-form expressions are obtained.
We investigate the lateral van der Waals (vdW) force between an anisotropic polarizable particle and a perfectly conducting plane with a hemispherical protuberance with radius $R$. We predict, via an exact calculation, a sign inversion in the lateral vdW force, in the sense that, instead of pointing to the protuberance, in certain situations this force points to the opposite direction. In the literature, predictions of sign inversions in the lateral vdW force were based on perturbative solutions, valid when the height of the protuberance is very small when compared to the distance $z_0$ betwee…
We consider a perfectly conducting infinite cylinder with radius $R$, and investigate the Casimir-Polder (CP) and van der Waals (vdW) interactions with a neutral polarizable particle constrained to move in a plane distant $x_0>R$ from the axis of the cylinder. We show that when the relative curvature $x_0/R \lesssim 6.44$, this particle, under the action of the lateral CP force (which is the projection of the CP force onto the mentioned plane), is attracted to the point on the plane which is closest to the cylinder surface. On the other hand, when $x_0/R \gtrsim 6.44$, we also show that, for c…
Since general relativity is a consistent low energy effective field theory, it is possible to compute quantum corrections to classical forces. Here we compute a quantum correction to the gravitational potential between a pair of polarizable objects. We study two distant bodies and compute a quantum force from their induced quadrupole moments due to two graviton exchange. The effect is in close analogy to the Casimir-Polder and London-van der Waals forces between a pair of atoms from their induced dipole moments due to two photon exchange. The new effect is computed from the shift in vacuum ene…
In this paper, we consider some second-order effective Hamiltonians describing the interaction of the quantum electromagnetic field with atoms or molecules in the nonrelativistic limit. Our procedure is valid only for off-energy-shell processes, specifically virtual processes such as those relevant for ground-state energy shifts and dispersion van der Waals and Casimir-Polder interactions, while on-energy-shell processes are excluded. These effective Hamiltonians allow for a considerable simplification of the calculation of radiative energy shifts, dispersion, and Casimir-Polder interactions, …
The retarded Van der Waals force between a polarizable particle and a perfectly conducting plate is re-examined. The expression for this force given by Casimir and Polder represents a mean force, but there are large fluctuations around this mean value on short time scales which are of the same order of magnitude as the mean force itself. However, these fluctuations occur on time scales which are typically of the order of the light travel time between the atom and the plate. As a consequence, they will not be observed in an experiment which measures the force averaged over a much longer time. I…
Fluctuation electromagnetic interaction between a small rotating particle and a polarizable surface produces the friction torque on the particle, changes the attraction force (van -der -Waals force) and the rate of heat exchange in this system. In this paper we consider the case where the rotation axis is parallel to the surface. We present general theoretical basis allowing to obtain characteristics of the interaction at an arbitrary orientation of the rotation axis. In comparison to the case where the rotation axis is perpendicular to the surface (arXiv: 1208.2603), the obtained integral exp…
Dispersion interactions are long-range interactions between neutral ground-state atoms or molecules, or polarizable bodies in general, due to their common interaction with the quantum electromagnetic field. They arise from the exchange of virtual photons between the atoms, and, in the case of three or more atoms, are not additive. In this review, after having introduced the relevant coupling schemes and effective Hamiltonians, as well as properties of the vacuum fluctuations, we~outline the main properties of dispersion interactions, both in the nonretarded (van der Waals) and retarded (Casimi…
