We consider the Casimir-Polder potential of particles placed inside a metallic cylindrical cavity at finite temperatures, taking account of thermal non-equilibrium effects. In particular, we study how the resonant (thermal non-equilibrium) potential and transition rates can be enhanced by fine-tuning the radius of the cavity to match the transition wavelength of the dominant transition of the particle. Numerical calculations show that the CP potential acting atoms prepared in low-lying Rydberg states can be enhanced beyond 30 kHz, which is within the range of observability of modern experiments. Because the magnitude of the resonance peaks depend sensitively on the low frequency dissipation of the cavity metal, experiments in this set-up could be a critical test of the disputed thermal correction to the Casimir force between metal plates.
We consider the resonant Casimir-Polder interaction of an excited alkali-type atom which has a single (electric dipole) transition with a Chern insulator. The Chern insulator has a nonzero, time reversal symmetry breaking Hall conductance, leading to an additional contribution to the resonant Casimir-Polder interaction which depends on the coupling between the Hall conductance and the circular polarization state of the atomic transition. We find that the resonant Casimir-Polder shift can be significantly enhanced for de-excitation frequencies near values associated with the van Hove singularit…
The Casimir-Polder force between two atoms with equal uniform acceleration and separated by a constant distance R is considered. We show that, in the low-acceleration limit, while the near-zone R^{-6} behavior of the interatomic interaction energy is not changed by the acceleration of the atoms, the far-zone interaction energy decreases as R^{-5} instead of the well-known R^{-7} behavior for inertial atoms. Possibility of an indirect detection of the Unruh effect through measurements of the Casimir-Polder force between the two accelerating atoms is also suggested. We also consider a heuristic …
The chiral component of the Casimir-Polder potential is derived within the framework of macroscopic quantum electrodynamics. It is shown to exist only if the particle and the medium are both chiral. Furthermore, the chiral component of the Casimir-Polder potential can be attractive or repulsive, depending on the chirality of the molecule and the medium. The theory is applied to a cavity geometry in the non-retarded limit with the intention of enantiomer separation. For a ground state molecule the chiral component is dominated by the electric component and thus no explicit separation will happe…
Different non-equilibrium situations have recently been considered when studying the thermal Casimir--Polder interaction with a body. We show that the Keldysh Green function method provides a very general common framework for such studies where non-equilibrium of either the atom or the body with the environment can be accounted for. We apply the results to the case of ground state polar molecules out of equilibrium with their environment, observing several striking effects. We consider thermal Casimir--Polder potentials in planar configurations, and new results for a molecule in a cylindrical …
We study the nonequilibrium Casimir-Polder force on an atom prepared in an incoherent superposition of internal energy-eigenstates, which is placed in a magnetoelectric environment of nonuniform temperature. After solving the coupled atom--field dynamics within the framework of macroscopic quantum electrodynamics, we derive a general expression for the thermal Casimir-Polder force.
We propose a new method to measure Casimir-Polder force in an optical cavity by means of atomic excitations. We utilize a framework in which Unruh-DeWitt Hamiltonian mimics the full matter-field interaction and find a connection between the excitation rate of the two-level atom and the Casimir-Polder energy, allowing to map one onto the other. We argue that such a realization opens a route to study Casimir-Polder potentials through measurement of excited state's population in large, spatially compact ensembles of atoms.
We study the effect of two non-interacting impurity atoms near by a one-dimensional nanowire, which is modeled as a tight-binding hopping model. The virtual single-electron hopping between two impurities will induce an additional energy depending on the distance of two impurities, which gives a electronic Casimir-Polder effect. We find that the Casimir-Polder force between the two impurities decreases with the impurity-impurity distance exponentially. And the effects of nanowire and finite temperature on the Casimir-Polder force are also discussed in detail, respectively.
We consider the three-body Casimir-Polder interaction between three atoms during their dynamical self-dressing. We show that the time-dependent three-body Casimir-Polder interaction energy displays nonlocal features related to quantum properties of the electromagnetic field and to the nonlocality of spatial field correlations. We discuss the measurability of this intriguing phenomenon and its relation with the usual concept of stationary three-body forces.
We consider vacuum fluctuations of the quantum electromagnetic field in the presence of an infinite and perfectly conducting plate. We evaluate how the change of vacuum fluctuations due to the plate modifies the Casimir-Polder potential between two atoms placed near the plate. We use two different methods to evaluate the Casimir-Polder potential in the presence of the plate. They also give new insights on the role of boundary conditions in the Casimir-Polder interatomic potential, as well as indications for possible generalizations to more complicated boundary conditions.
We show that the Casimir-Polder interaction may induce coherent oscillations between degenerate atomic states. We illustrate this effect by computing the Casimir-Polder induced Rabi frequency on a $^{87}$Rb atom as it interacts with a reflecting surface. The atom oscillates between two Zeeman sublevels of its ground state undergoing a periodic exchange of angular momentum with the vacuum photons.
The three-body Casimir-Polder potential between one excited and two ground-state atoms is evaluated. A physical model based on the dressed field correlations of vacuum fluctuations is used, generalizing a model previously introduced for three ground-state atoms. Although the three-body potential with one excited atom is already known in the literature, our model gives new insights on the nature of non-additive Casimir-Polder forces with one or more excited atoms.
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…
Making use of the quantum correlators associated with the Maxwell field vacuum distorted by the presence of plane parallel material surfaces we derive the Casimir-Polder interaction in the presence of plane parallel conducting walls and in the presence of a conducting wall and a magnetically permeable one.
We review different aspects of the atom-atom and atom-wall Casimir-Polder forces. We first discuss the role of a boundary condition on the interatomic Casimir-Polder potential between two ground-state atoms, and give a physically transparent interpretation of the results in terms of vacuum fluctuations and image atomic dipoles. We then discuss the known atom-wall Casimir-Polder force for ground- and excited-state atoms, using a different method which is also suited for extension to time-dependent situations. Finally, we consider the fluctuation of the Casimir-Polder force between a ground-stat…
We investigate the dispersive Casimir-Polder interaction between a Rubidium atom and a suspended graphene sheet subjected to an external magnetic field B. We demonstrate that this concrete physical system allows for an unprecedented control of dispersive interactions at micro and nanoscales. Indeed, we show that the application of an external magnetic field can induce a 80% reduction of the Casimir-Polder energy relative to its value without the field. We also show that sharp discontinuities emerge in the Casimir-Polder interaction energy for certain values of the applied magnetic field at low…
A time-dependent Casimir-Polder force is shown to arise during the time evolution of a partially dressed two-level atom. The partially dressed atom is obtained by a rapid change of an atomic parameter such as its transition frequency, due to the action of some external agent. The electromagnetic field fluctuations around the atom, averaged over the solid angle for simplicity, are calculated as a function of time, and it is shown that the interaction energy with a second atom yields a dynamical Casimir-Polder potential between the two atoms.
We develop a dynamical approach to study the Casimir-Polder force between a initially bare molecule and a magnetodielectric body at finite temperature. Switching on the interaction between the molecule and the field at a particular time, we study the resulting temporal evolution of the Casimir-Polder interaction. The dynamical self-dressing of the molecule and its population-induced dynamics are accounted for and discussed. In particular, we find that the Casimir-Polder force between a chiral molecule and a perfect mirror oscillates in time with a frequency related to the molecular transition …
We demonstrate that Casimir-Polder potentials can be entirely independent of temperature even when allowing for the thermal photon numbers to become large at the relevant molecular transition frequencies. This statement holds for potentials that are due to low-energy transitions of a molecule placed near a plane metal surface. For a molecule in an energy eigenstate, the temperature-invariance is a consequence of strong cancellations between nonresonant potential components and those due to evanescent waves. For a molecule with a single dominant transition in a thermal state, upward and downwar…
We critically discuss the common belief that the thermal Casimir-Polder force can always be represented as a Matsubara sum, as it is true for the Casimir force. On the contrary, an exact treatment of the atom-field coupling reveals that for a ground-state atom, terms associated with virtual-photon absorption contribute to the force which are identified as a signature of non-equilibrium dynamics. Even the equilibrium force on a thermalized atom or molecule may be overestimated when using the ground-state polarizability instead of its thermal counterpart.
We consider the Casimir-Polder interaction between two atoms, one in the ground state and the other in its excited state. The interaction is time-dependent for this system, because of the dynamical self-dressing and the spontaneous decay of the excited atom. We calculate the dynamical Casimir-Polder potential between the two atoms using an effective Hamiltonian approach. The results obtained and their physical meaning are discussed and compared with previous results based on a time-independent approach which uses a non-normalizable dressed state for the excited atom.
We propose a method to probe dispersive atom-surface interactions by measuring via two-photon Bragg spectroscopy the dynamic structure factor of a Bose-Einstein condensate above corrugated surfaces. This method takes advantage of the condensate coherence to reveal the spatial Fourier components of the lateral Casimir-Polder interaction energy.
An ultracold atom above a horizontal mirror experiences quantum reflection from the attractive Casimir-Polder interaction, which holds it against gravity and leads to quantum levitation states. We analyze this system by using a Liouville transformation of the Schrödinger equation and a Langer coordinate adapted to problems with a classical turning point. Reflection on the Casimir-Polder attractive well is replaced by reflection on a repulsive wall and the problem is then viewed as an ultracold atom trapped inside a cavity with gravity and Casimir-Polder potentials acting respectively as top an…
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.
Using a recently developed theory of the Casimir force (Raabe C and Welsch D-G 2005 Phys. Rev. A 71 013814), we calculate the force that acts on a plate in front of a planar wall and the force that acts on the plate in the case where the plate is part of matter that fills the space in front of the wall. We show that in the limit of a dielectric plate whose permittivity is close to unity, the force obtained in the former case reduces to the ordinary, i.e., unscreened Casimir-Polder force acting on isolated atoms. In the latter case, the theory yields the Casimir-Polder force that is screened by…
Within leading-order perturbation theory, the Casimir-Polder potential of a ground-state atom placed within an arbitrary arrangement of dispersing and absorbing linear bodies can be expressed in terms of the polarizability of the atom and the scattering Green tensor of the body-assisted electromagnetic field. Based on a Born series of the Green tensor, a systematic expansion of the Casimir-Polder potential in powers of the susceptibilities of the bodies is presented. The Born expansion is used to show how and under which conditions the Casimir-Polder force can be related to microscopic many-at…
We develop a new theory for Casimir-Lifshitz and Casimir-Polder interactions with semiconductor surfaces that takes into account charge drift in the bulk material. The corresponding frequency-dependent dispersion relations describe a crossover between Lifshitz results for dielectrics and for good conductors. In the quasi-static limit, our calculated reflection amplitudes coincide with those recently computed to account for Debye screening in the thermal Lifshitz force with conducting surfaces with small density of carriers.
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 take a closer look at the fundamental Casimir-Polder interaction between quantum particles and dispersive dielectric surfaces with surface polariton or plasmon resonances. Linear response theory shows that in the near field, van der Waals, regime the free energy shift of a particle contains a thermal component that depends exclusively on the population/excitation of the evanescent surface polariton/plasmon modes. Our work makes evident the link between particle surface interaction and near field thermal emission and demonstrates how this can be used to engineer Casimir-Polder forces. We als…
We investigate the possibility to trap ultracold atoms near the outside of a metallic carbon nanotube (CN) which we imagine to use as a miniaturized current-carrying wire. We calculate atomic spin flip lifetimes and compare the strength of the Casimir-Polder potential with the magnetic trapping potential. Our analysis indicates that the Casimir-Polder force is the dominant loss mechanism and we compute the minimum distance to the carbon nanotube at which an atom can be trapped.
We report on the first measurement of a temperature dependence of the Casimir-Polder force. This measurement was obtained by positioning a nearly pure 87-Rb Bose-Einstein condensate a few microns from a dielectric substrate and exciting its dipole oscillation. Changes in the collective oscillation frequency of the magnetically trapped atoms result from spatial variations in the surface-atom force. In our experiment, the dielectric substrate is heated up to 605 K, while the surrounding environment is kept near room temperature (310 K). The effect of the Casimir-Polder force is measured to be ne…
We investigate the magnetic dipole coupling between a metallic surface and an atom in a thermal state, ground state and excited hyperine state. This interaction results in a repulsive correction and - unlike the electrical dipole contribution - depends sensitively on the Ohmic dissipation in the material.
We investigate how the combination of nonequilibrium effects and material properties impacts on the Casimir-Polder interaction between an atom and a surface. By addressing systems with temperature inhomogeneities and laser interactions, we show that nonmonotonous energetic landscapes can be produced where barriers and minima appear. Our treatment provides a self-consistent quantum theoretical framework for investigating the properties of a class of nonequilibrium atom-surface interactions.
We investigate theoretically the Casimir-Polder potential of an atom which is driven by a laser field close to a surface. This problem is addressed in the framework of macroscopic quantum electrodynamics using the Green's tensor formalism and we distinguish between two different approaches, a perturbative ansatz and a method based on Bloch equations. We apply our results to a concrete example, namely an atom close to a perfectly conducting mirror, and create a scenario where the tunable Casimir-Polder potential becomes similar to the respective potential of an undriven atom due to fluctuating …
The Casimir-Polder (CP) potential and transition rates of a Rydberg atom above a plane metal surface at finite temperature are discussed. As an example, the CP potential and transition rates of a rubidium atom above a copper surface at room temperature is computed. Close to the surface we show that the quadrupole correction to the force is significant and increases with increasing principal quantum number n. For both the CP potential and decay rates one finds that the dominant contribution comes from the longest wavelength transition and the potential is independent of temperature. We provide …
We study the resonant Casimir--Polder potential of an excited atom near a half space containing magneto-electric meta-material of various kinds on the basis of macroscopic quantum electrodynamics. Analytical results are obtained in the nonretarded and retarded distance regimes and numerical examples are given. We compare our findings with the potential of an excited atom near a left-handed superlens.
The problem of nonlocality in the dynamical three-body Casimir-Polder interaction between an initially excited and two ground-state atoms is considered. It is shown that the nonlocal spatial correlations of the field emitted by the excited atom during the initial part of its spontaneous decay may become manifest in the three-body interaction. The observability of this new phenomenon is discussed.
Atom-surface forces using excited states have a host of compelling applications, including repulsive and lateral forces. However, such states can be fragile and difficult to prepare. Here we report an explicit normal-mode based calculation of the Casimir-Polder potential between a ground-state atom and a non-dispersive surface in the presence of an external quantised field. The potential we derive shares some features with that of excited-state Casimir-Polder forces even though we consider a ground-state atom. Our work provides a physically transparent and intuitive picture of driven Casimir-P…
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 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 …
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…
Diffraction of matter-waves is an important demonstration of the fact that objects in nature possess a mixture of particle-like and wave-like properties. Unlike in the case of light diffraction, matter-waves are subject to a vacuum-mediated interaction with diffraction obstacles. Here we present a detailed account of this effect through the calculation of the attractive Casimir-Polder potential between a dielectric sphere and an atomic beam. Furthermore, we use our calculated potential to make predictions about the diffraction patterns to be observed in an ongoing experiment where a beam of in…
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…
We study the interaction between a neutral atom or molecule and a conductor-patched dielectric surface. We model this system by a perfectly reflecting disc lying atop of a non-dispersive dielectric half-space, both interacting with the neutral atom or molecule. We assume the interaction to be non-retarded and at zero temperature. We find an exact solution to this problem. In addition we generate a number of other useful results. For the case of no substrate we obtain the exact formula for the van der Waals interaction energy of an atom near a perfectly conducting disc. We show that the Casimir…
In this paper we calculate the Casimir-Polder force density (force per unit area acting on the elements of the surface) on a metallic plate placed in front of a neutral atom. To obtain the force density we use the quantum operator associated to the electromagnetic stress tensor. We explicitly show that the integral of this force density over the plate reproduces the total force acting on the plate. This result shows that, although the force is obtained as a sum of surface element-atom contributions, the stress-tensor method includes also nonadditive components of Casimir-Polder forces in the e…
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.
For the first time, we have studied the impact of magnetic polarizability of a neutral metallic particle on the dynamical Casimir-Polder force, when the particle is uniformly moving with relativistic velocity parallel to the surface of an ideally conducting plate. The material properties of particle are taken into account within the Drude model approach.
We propose a scheme to actively cool the fundamental flexural (out-of-plane) mode of a graphene sheet via vacuum forces. Our setup consists in a cold atom cloud placed close to a graphene sheet at distances of a few micrometers. The atoms couple to the graphene membrane via Casimir-Polder forces. By deriving a self-consistent set of equations governing the dynamics of the atomic gas and the flexural modes of the graphene, we show to be possible to cool graphene from room temperatures by actively (laser) cooling an atomic gas. By choosing the right set of experimental parameter we are able to c…
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.
Based on the idea that the vacuum fluctuations of electromagnetic fields can induce instantaneous correlated dipoles, we study the far-zone Casimir-Polder potential between two atoms in the Boulware, Unruh and Hartle-Hawking vacua outside a Schwarzschild black hole. We show that, at spatial infinity, the Casimir-Polder potential in the Boulware vacuum is similar to that in the Minkowski vacuum in flat spacetime with a behavior of $R^{-7}$, so is in the Unruh vacuum as a result of the backscattering of the Hawking radiation from the black hole off the spacetime curvature. However, the interatom…
We consider the out-of-thermal-equilibrium Casimir-Polder interaction between atoms of He$^*$, Na, Cs, and Rb and a cavity wall made of sapphire coated with a vanadium dioxide film which undergoes the dielectric-to-metal phase transition with increasing wall temperature. Numerical computations of the Casimir-Polder force and its gradient as the functions of atom-wall separation and wall temperature are made when the latter exceeds the temperature of the environment. The obtained results are compared with those in experiment on measuring the gradient of the Casimir-Polder force between $^{87}$R…
We show that the claims expressed in the Comment arXiv:0810.3244v1 by R.S. Decca et al against our paper, D.A.R. Dalvit and S.K. Lamoreaux, Phys. Rev. Lett. {\bf 101}, 163203 (2008), are wrong and manifestly inconsistent with basic principles of statistical physics.
We have considered the interaction of a pair of spatially separated two-level atoms with the electromagnetic field in its vacuum state and we have analyzed the amount of entanglement induced between the two atoms by the non local field fluctuations. This has allowed us to characterize the quantum nature of the non local correlations of the electromagnetic field vacuum state as well as to link the induced quantum entanglement with Casimir-Polder potentials.
We study the influence of thermal Casimir-Polder forces on the near-surface trapping of cold polar molecules, with emphasis on LiH and YbF near an Au surface at room temperature. We show that for a molecule initially prepared in its electronic and rovibrational ground state, the Casimir-Polder force oscillates with the molecule-wall separation. The non-resonant force contribution and the evanescent part of the resonant force contribution almost exactly cancel at high temperature which results in a saturation of the (attractive) force in this limit. A dynamical calculation reveals how the spati…
We evaluate the Casimir-Polder potential between two atoms in the presence of an infinite perfectly conducting plate and at nonzero temperature. In order to calculate the potential, we use a method based on equal-time spatial correlations of the electric field, already used to evaluate the effect of boundary conditions on interatomic potentials. This method gives also a transparent physical picture of the role of a finite temperature and boundary conditions on the Casimir-Polder potential. We obtain an analytical expression of the potential both in the near and far zones, and consider several …
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…
