A novel formalism for the evaluation of the Casimir-Polder potential in an arbitrary gauge of vector potentials is introduced. The ground state energy of a neutral atom in the presence of an infinite two-dimensional plane with Chern-Simons interaction is derived at zero temperature. The essential feature of the result is its dependence on the antisymmetric part of a dipole moment correlation function.
Various applications of the multiple scattering technique to calculating Casimir energy are described. These include the interaction between dilute bodies of various sizes and shapes, temperature dependence, interactions with multilayered and corrugated bodies, and new examples of exactly solvable separable bodies.
It has been increasingly becoming clear that Casimir and Casimir-Polder entropies may be negative in certain regions of temperature and separation. In fact, the occurrence of negative entropy seems to be a nearly ubiquitous phenomenon. This is most highlighted in the quantum vacuum interaction of a nanoparticle with a conducting plate or between two nanoparticles. It has been argued that this phenomenon does not violate physical intuition, since the total entropy, including the self-entropies of the plate and the nanoparticle, should be positive. New calculations, in fact, seem to bear this ou…
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.
This Resource Letter provides a guide to the literature on van der Waals and Casimir-Polder forces. Journal articles, books, and other documents are cited on the following topics: van der Waals forces, retarded dispersion forces or Casimir-Polder forces between atoms or molecules, Casimir-Polder forces between a molecule and a dielectric or conducting body, the summation of Casimir-Polder forces as leading to the Casimir and Lifshitz forces between conducting and dielectric bodies, Casimir friction, applications to nanotechnology, the nature of the quantum vacuum, and experimental tests of the…
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.
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 propose a method to separate enantiomers using parity violation in the Casimir-Polder potential between chiral mirrors and chiral molecules. The proposed setup involves a molecular beam composed of chiral molecules passing through a planar cavity consisting of two chiral mirrors. Enantiomers of opposite handedness are deflected differently due to a chiral dependence of the Casimir-Polder potential resulting in the separation of the enantiomers. Our setup provides an alternative experimental tool for enantiomer separation, as well as shedding light on the fundamental properties of the Casimi…
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 Casimir and Casimir-Polder interactions are investigated in a stack of equally spaced graphene layers. The optical response of the individual graphene is taken into account using gauge invariant components of the polarization tensor extended to the whole complex frequency plane. The planar symmetry for the electromagnetic boundary conditions is further used to obtain explicit forms for the Casimir energy stored in the stack and the Casimir-Polder energy between an atom above the stack. Our calculations show that these fluctuation induced interactions experience strong thermal effects due t…
It has always been conventionally understood that, in the dilute limit, the Casimir energy of interaction between bodies or the Casimir self-energy of a dielectric body could be identified with the sum of the van der Waals or Casimir-Polder energies of the constituents of the bodies. Recently, this proposition for self-energies has been challenged by Avni and Leonhardt [Ann.\ Phys.\ {\bf 395}, 326 (2018)], who find that the energy or self-stress of a homogeneous dielectric ball with permittivity $\varepsilon$ begins with a term of order $\varepsilon-1$. Here we demonstrate that this cannot be …
We discuss the scalar analogue of the Casimir-Polder force between a sphere and a uniaxially corrugated surface with Dirichlet boundary conditions. Presenting a formulation that is nonperturbative in the height profile of the surface, we give explicit numerical results for a sinuosoidal corrugation profile.
We apply general formalism of quantum field theory and addition theorem for Bessel functions to derive formula for the Casimir-Polder energy of interaction between a polarizable particle and a dilute dielectric ball and Casimir energy of a dilute dielectric ball. The correspondence between the Casimir-Polder formula and Casimir energy of a dilute dielectric ball is shown. Different approaches to the problem of Casimir energy of a dielectric ball are reviewed and analysed by use of addition theorem for Bessel functions.
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 present the derivation of the Casimir-Polder interactions mediated by a massive photon between two neutral systems described in terms of their atomic polarizability tensors. We find a compact expression for the leading term at large distances between the two systems. Our result reduces, in the mass-less photon limit, to the standard Casimir-Polder. We discuss implications of our findings with respect to recent scenarios of physics beyond the standard model such as universal extra dimensions, Randall-Sundrum and scale-invariant models. For each model we compute the correction to the Casimir-…
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 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…
In our paper [Ann. Phys. (NY) 395, 326 (2018)] we calculate the Casimir stress on a sphere immersed in a homogeneous background, assuming dispersionless dielectrics. Our results appear to challenge the conventional picture of Casimir forces. The paper [arXiv:1909.05721] criticises our approach without offering an alternative. In particular, the paper [arXiv:1909.05721] claims that we have made an unjustified mathematical step. This brief comment clarifies the matter.
The low temperature expansion of the free energy of atom/plane system is considered for general symmetric form of tensor conductivity of the plane. It is shown that the first correction is proportional to second order of the temperature $\sim T^2$ and comes from TM mode. The agreement of the expansion and exact expressions for different models of conductivity is numerically demonstrated.
We develop the scattering approach to calculate the exact dispersive Casimir-Polder potential between a ground-state atom and a rectangular grating. Our formalism allows, in principle, for arbitrary values of the grating amplitude and period, and of the atom-grating distance. We compute numerically the potential for a Rb atom on top of a Si grating and compare the results with the potential for a flat surface taken at the local atom-surface distance (proximity force approximation). Except for very short separation distances, the potential is nearly sinusoidal along the direction transverse to …
We predict a repulsive Casimir-Polder-type dispersion interaction between a single neutron and a metal or dielectric surface. We consider a scenario where a single neutron is subject to an external magnetic field. Due to its intrinsic magnetic moment, the neutron then forms a magnetisable two-level system which can exchange virtual photons with a nearby surface. The resulting dispersion interaction between a purely magnetic object (neutron) and a purely electric one (surface) is found to be repulsive, in contrast to the typical attractive interaction between electric objects. Its magnitude is …
The thermal correction to the energy of Casimir-Polder interaction of atoms with a suspended graphene membrane described by the Dirac model is investigated. We show that a major impact on the thermal correction is made by the size of the gap in the energy spectrum of graphene quasiparticles. Specifically, if the temperature is much smaller than the gap parameter (alternatively, larger or of the order of the gap parameter), the thermal correction is shown to be relatively small (alternatively, large). We have calculated the free energy of the thermal Casimir-Polder interaction of atoms of He, N…
Generalized uncertainty relations are known to provide a minimal length $\hbar\sqrtβ$. The effect of such minimal length in the Casimir-Polder interactions between neutral atoms (molecules) is studied. The first order correction term in the minimal uncertainty parameter is derived and found to describe an attractive potential scaling as $r^{-9}$ as opposed to the well known $r^{-7}$ long range retarded potential.
We demonstrate that the static ground state atom, which interacts with a conformally coupled massless scalar field in the de Sitter invariant vacuum, can obtain a position-dependent energy-level shift and this shift could cause a Casimir-Polder-like force on it. Interestingly no such force arises on the inertial atom bathed in a thermal radiation in the Minkowski universe. Thus, although the energy-level shifts of the static atom for these two cases are structurally the same, whether the energy-level shift causes the Casimir-Polder-like force, in principle, could be as an indicator to distingu…
We derive the Casimir-Polder force and Casimir torque expressions for an anisotropic molecule close to a conducting plane with a tensorial conductivity. We apply our general expressions to the case of a carbon dioxide CO$_2$ molecule close to a plane with pure Hall conductivity and to graphene. We show that the equilibrium position of this linear molecule is with its main axis perpendicular to the surface. We hence conjecture a possible way to exploit the Casimir torque to mechanically improve the performance of CO$_2$ separation membranes useful for an efficient atmospheric CO$_2$ reduction.
The Casimir-Polder interaction potential is evaluated for a polarizable microparticle and a conducting wall in the geometry of a cosmic string perpendicular to the wall. The general case of the anisotropic polarizability tensor for the microparticle is considered. The corresponding force is a function of the wall-microparticle and cosmic string-microparticle distances. Depending on the orientation of the polarizability tensor principal axes the force can be either attractive or repulsive. The asymptotic behavior of the Casimir-Polder potential is investigated at large and small separations com…
We investigate the Dirichlet-scalar equivalent of Casimir-Polder forces between an atom and a surface with arbitrary uniaxial corrugations. The complexity of the problem can be reduced to a one-dimensional Green's function equation along the corrugation which can be solved numerically. Our technique is fully nonperturbative in the height profile of the corrugation. We present explicit results for experimentally relevant sinusoidal and sawtooth corrugations. Parameterizing the deviations from the planar limit in terms of an anomalous dimension which measures the power-law deviation from the pla…
We consider the low-temperature expansion of the Casimir-Polder free energy for an atom and graphene by using the Poisson representation of the free energy. We extend our previous analysis on the different relations between chemical potential $μ$ and mass gap parameter $m$. The key role plays the dependence of graphene conductivities on the $μ$ and $m$. For simplicity, we made the manifest calculations for zero values of the Fermi velocity. For $μ>m$ the thermal correction $\sim T^2$ and for $μ< m$ we confirm the recent result of Klimchitskaya and Mostepanenko, that the thermal correction $\si…
