Casimir-Polder interaction energies between a point anisotropically polarizable atom and an annular dielectric are shown to exhibit localized repulsive long-range forces in specific configurations. We show that when the atom is positioned at the center of the annular dielectric, it is energetically favorable for the atom to align its polarizability with respect to that of the dielectric. As the atom moves away from, but along the symmetry axis of the annular dielectric, it encounters a point where the polarizable atom experiences no torque and the energy is free of orientation dependence. At this height, abruptly, the atom prefers to orient its polarizability perpendicular to that of the dielectric. For certain configurations, it encounters another torsion-free point a larger distance away, beyond which it prefers to again point its polarizability with respect to that of the dielectric. We find when the atom is close enough, and oriented such that the energy is close to maximum, the atom could be repelled. For certain annular polarizations, repulsion can happen below or above the torsion-free height. Qualitative features differ when the atom is interacting with a ring, versus a plate of infinite extent with a hole. In particular, the atom can prefer to orient perpendicular to the polarizability of the plate at large distances, in striking contrast to the expectation that it will orient parallel. To gain insight of this discrepancy, we investigate an annular disc, which captures the results of both geometries in limiting cases. These energies are too weak for immediate applications, nevertheless, we elaborate an interesting application on a prototype of a Casimir machine using these configurations.
Repulsion, induced from quantum vacuum fluctuations, for an anisotropically polarizable atom on the symmetry axis of an anisotropically polarizable annular disc is studied. There exists two torsion free points on each side of the annular disc, where the interaction energy is orientation independent. The position of second of the two torsion free points, on either side of the disc, is shown to determine the orientation dependence of the atom at distances far from the plate, revealing a geometrical dependence. In the ring limit of the annular disc, new repulsion emerges.
We demonstrate that the thermal Casimir-Polder forces on molecules near a conducting surface whose transition wavelengths are comparable to the molecule-surface separation are dependent on the ambient temperature and molecular polarization and they can even be changed from attractive to repulsive via varying the temperature across a threshold value for anisotropically polarizable molecules. Remarkably, this attractive-to-repulsive transition may be realized at room temperature. Let us note that the predicted repulsion is essentially a nonequilibrium effect since the force we calculated on a gr…
We determine exactly the non-retarded Casimir-Polder interaction between a neutral but polarizable particle and a perfectly reflecting sheet containing a circular hole. The calculation reveals a strong dependence of the interaction on the orientation of the particle's electric dipole moment with respect to the surface. For a dipole moment that is polarized perpendicularly to the surface the interaction potential has two saddle points lying above and below the plane of the surface, on a line through the centre of the aperture. For a dipole moment that is polarized parallel to the surface there …
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…
We demonstrate that the Casimir-Polder force for a molecule near the surface of a real dielectric substrate out of thermal equilibrium displays distinctive behaviors as compared to that at thermal equilibrium. In particular, when the molecule-substrate separation is much less than the molecular transition wave-length, the CP force in the high temperature limit can be dramatically manipulated by varying the relative magnitude of the temperatures of the substrate and the environment so that the attractive-to-repulsive transition can occur beyond certain a threshold temperature of either the subs…
Recently, the topic of Casimir repulsion has received a great deal of attention, largely because of the possibility of technological application. The general subject has a long history, going back to the self-repulsion of a conducting spherical shell and the repulsion between a perfect electric conductor and a perfect magnetic conductor. Recently it has been observed that repulsion can be achieved between ordinary conducting bodies, provided sufficient anisotropy is present. For example, an anisotropic polarizable atom can be repelled near an aperture in a conducting plate. Here we provide new…
Casimir-Polder interactions are considered in an inhomogeneous, dispersive background. We consider both the interaction between a polarizable atom and a perfectly conducting wall, and between such an atom and a plane interface between two different inhomogeneous dielectric media. Renormalization is achieved by subtracting the interaction with the local inhomogeneous medium by itself. The results are expressed in general form, and generalize the Dzyaloshinskii-Lifshitz-Pitaevskii interaction between a spatially homogeneous dielectric interface and a polarizable atom.
We develop a formalism suitable for studying Maxwell's equations in the presence of a medium that is axially symmetric, in particular with respect to Casimir-Polder interaction energies. As an application, we derive the Casimir-Polder interaction energy between an electric $δ$-function plate and an anisotropically polarizable molecule for arbitrary orientations of the principal axes of polarizabilities of the molecule. We show that in the perfect conductor limit for the plate the interaction is insensitive to the orientation of the polarizabilities of the molecule. We obtain the Casimir-Polder…
We use a derivative expansion for gently curved surfaces to compute the leading and the next-to-leading curvature corrections to the Casimir-Polder interaction between a polarizable small particle and a non-planar surface. While our methods apply to any homogeneous and isotropic surface, explicit results are presented here for perfect conductors. We show that the derivative expansion of the Casimir-Polder potential follows from a resummation of its perturbative series, for small in-plane momenta. We consider the retarded, non-retarded and classical high temperature limits.
We study the Casimir-Polder interaction at finite temperatures between a polarizable small, anisotropic particle and a non-planar surface using a derivative expansion. We obtain the leading and the next-to-leading curvature corrections to the interaction for low and high temperatures. Explicit results are provided for the retarded limit in the presence of a perfectly conducting surface.
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.
In a recent paper we have formulated a theory of non-relativistic quantum electrodynamics in the presence of an inhomogeneous Huttner-Barnett dielectric. Here we generalize the formalism to anisotropic materials and show how it may be modified to include conducting surfaces. We start with the derivation of the photon propagator for a slab of material and use it to work out the energy-level shift near a medium whose conductivity in the direction parallel to the surface far exceeds that in the direction perpendicular to the surface. We investigate the influence of the anisotropy of the material'…
We consider the quantum fluctuations of the Casimir-Polder force between a neutral atom and a perfectly conducting wall in the ground state of the system. In order to obtain the atom-wall force fluctuation we first define an operator directly associated to the force experienced by the atom considered as a polarizable body in an electromagnetic field, and we use a time-averaged force operator in order to avoid ultraviolet divergences appearing in the fluctuation of the force. This time-averaged force operator takes into account that any measurement involves a finite time. We also calculate the …
As part of our program to develop the description of three-body effects in quantum vacuum phenomena, we study the three-body interaction of two anisotropically polarizable atoms with a perfect electrically conducting plate, a generalization of earlier work. Three- and four-scattering effects are important, and lead to nonmonotonic behavior.
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)…
We study the fluctuation-induced dissipative dynamics of the quantized center of mass motion of a polarizable dielectric particle trapped near a surface. The particle's center of mass is treated as an open quantum system coupled to the electromagnetic field acting as its environment, with the resulting system dynamics described by a quantum Brownian motion master equation. The dissipation and decoherence of the particle's center of mass are characterized by the modified spectral density of the electromagnetic field that depends on surface losses and the strength of the classical trap field. Ou…
We investigate the time-dependent Casimir-Polder potential of a polarizable two-level atom placed near a surface of arbitrary material, after a sudden change in the parameters of the system. Different initial conditions are taken into account. For an initially bare ground-state atom, the time-dependent Casimir-Polder energy reveals how the atom is "being dressed" by virtual, matter-assisted photons. We also study the transient behavior of the Casimir-Polder interaction between the atom and the surface starting from a partially dressed state, after an externally induced change in the atomic lev…
Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general "Lifshitz" configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capasso's group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations wh…
We have calculated dynamical Casimir-Polder interaction force between a moving ground state atom and a flat polarizable surface. The velocity of an atom can be close to the velocity of light. The material properties are taken into account using a single oscillator model of the atomic dynamic polarizability and the Drude dielectric function of a metal substrate. The limit cases of nonrelativistic velocities and an ideal metal substrate are also considered. We have found specific dependence of the calculated forces on the velocity (energy), distance and material properties.
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 study the energy shift and the Casimir-Polder force of an atom out of thermal equilibrium near the surface of a dielectric substrate. We first generalize, adopting the local source hypothesis, the formalism proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji, which separates the contributions of thermal fluctuations and radiation reaction to the energy shift and allows a distinct treatment to atoms in the ground and excited states, to the case out of thermal equilibrium, and then use the generalized formalism to calculate the energy shift and the Casimir-Polder force of an isotropically po…
We derive the exact Casimir-Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir-Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0.1$R$, where $R$ is the radius of the cylinder. The developed methods are applicable in the theory of topological defects.
The Casimir-Polder force is an attractive force between a polarizable atom and a conducting or dielectric boundary. Its original computation was in terms of the Lamb shift of the atomic ground state in an electromagnetic field (EMF) modified by boundary conditions along the wall and assuming a stationary atom. We calculate the corrections to this force due to a moving atom, demanding maximal preservation of entanglement generated by the moving atom-conducting wall system. We do this by using non-perturbative path integral techniques which allow for coherent back-action and thus can treat non-M…
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, …
We derive upper and lower bounds on the Casimir--Polder force between an anisotropic dipolar body and a macroscopic body separated by vacuum via algebraic properties of Maxwell's equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We find that the attractive Casimir--Polder force between a polarizable dipole and a uniform planar semi-infinite bulk medium always comes within 10% of the …
In this paper we study an archetypical scenario in which repulsive Casimir-Polder forces between an atom or molecule and two macroscopic bodies can be achieved. This is an extension of previous studies of the interaction between a polarizable atom and a wedge, in which repulsion occurs if the atom is sufficiently anisotropic and close enough to the symmetry plane of the wedge. A similar repulsion occurs if such an atom passes a thin cylinder or a wire. An obvious extension is to compute the interaction between such an atom and two facing wedges, which includes as a special case the interaction…
We review recent results on the low-temperature behaviors of the Casimir-Polder and Casimir free energy an entropy for a polarizable atom interacting with a graphene sheet and for two graphene sheets, respectively. These results are discussed in the wide context of problems arising in the Lifshitz theory of van der Waals and Casimir forces when it is applied to metallic and dielectric bodies. After a brief treatment of different approaches to theoretical description of the electromagnetic response of graphene, we concentrate on the derivation of response function in the framework of thermal qu…
Casimir-Polder potential is investigated for a polarizable microparticle in the geometry of a straight cosmic string with a metallic cylindrical shell. The electromagnetic field Green tensor is evaluated on the imaginary frequency axis. The expressions for the Casimir-Polder potential is derived in the general case of anisotropic polarizability for the both interior and exterior regions of the shell. The potential is decomposed into pure string and shell-induced parts. The latter dominates for points near the shell, whereas the pure string part is dominant near the string and at large distance…
We investigate the Casimir-Polder force acting on a polarizable microparticle in the geometry of a straight cosmic string. In order to develop this analysis we evaluate the electromagnetic field Green tensor on the imaginary frequency axis. The expression for the Casimir-Polder force is derived in the general case of anisotropic polarizability. In dependence of the eigenvalues for the polarizability tensor and of the orientation of its principal axes, the Casimir-Polder force can be either repulsive or attractive. Moreover, there are situations where the force changes the sign with separation.…
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…
Surface Scattering Expansion of the Casimir-Polder Interaction for Magneto-dielectric Bodies: Convergence Properties for Insulators, Conductors and Semiconductors
We derive the low-temperature behavior of the Casimir-Polder free energy for a polarizable atom interacting with graphene sheet which possesses the nonzero energy gap $Δ$ and chemical potential $μ$. The response of graphene to the electromagnetic field is described by means of the polarization tensor in the framework of Dirac model on the basis of first principles of thermal quantum field theory in the Matsubara formulation. It is shown that the thermal correction to the Casimir-Polder energy consists of three contributions. The first of them is determined by the Matsubara summation using the …
The interaction between a polarizable particle and a reflecting wall is examined. A macroscopic approach is adopted in which the averaged force is computed from the Maxwell stress tensor. The particular case of a perfectly reflecting wall and a sphere with a dielectric function given by the Drude model is examined in detail. It is found that the force can be expressed as the sum of a monotonically decaying function of position and of an oscillatory piece. At large separations, the oscillatory piece is the dominant contribution, and is much larger than the Casimir-Polder interaction that arises…
