We show the influence of surface plasmons on the Casimir effect between two plane parallel metallic mirrors at arbitrary distances. Using the plasma model to describe the optical response of the metal, we express the Casimir energy as a sum of contributions associated with evanescent surface plasmon modes and propagative cavity modes. In contrast to naive expectations, the plasmonic modes contribution is essential at all distances in order to ensure the correct result for the Casimir energy. One of the two plasmonic modes gives rise to a repulsive contribution, balancing out the attractive contributions from propagating cavity modes, while both contributions taken separately are much larger than the actual value of the Casimir energy. This also suggests possibilities to tailor the sign of the Casimir force via surface plasmons.
In this paper we study the role of surface plasmon modes in the Casimir effect. The Casimir energy can be written as a sum over the modes of a real cavity and one may identify two sorts of modes, two evanescent surface plasmon modes and propagative modes. As one of the surface plasmon modes becomes propagative for some choice of parameters we adopt an adiabatic mode definition where we follow this mode into the propagative sector and count it together with the surface plasmon contribution, calling this contribution "plasmonic". We evaluate analytically the contribution of the plasmonic modes t…
In this paper we study the role of surface plasmon modes in the Casimir effect. First we write the Casimir energy as a sum over the modes of a real cavity. We may identify two sorts of modes, two evanescent surface plasmon modes and propagative modes. As one of the surface plasmon modes becomes propagative for some choice of parameters we adopt an adiabatic mode definition where we follow this mode into the propagative sector and count it together with the surface plasmon contribution, calling this contribution "plasmonic". The remaining modes are propagative cavity modes, which we call "photo…
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 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…
A new model for calculating the Casimir-Lifshitz force per unit length for two dielectric rods is proposed, based on the Green function method of classical electrodynamics and the Lorentz model for permittivity.
We investigate the Casimir force between two dissimilar plane mirrors the material properties of which are described by Drude or Lorentz models. We calculate analytically the short and long distance asymptote of the force and relate its behavior to the influence of interacting surface plasmons. In particular we discuss conditions under which Casimir repulsion could be achieved.
We investigate the role of surface plasmons in the electromagnetic Casimir effect at finite temperature, including situations out of global thermal equilibrium. The free energy is calculated analytically and expanded for different regimes of distances and temperatures. Similar to the zero-temperature case, the interaction changes from attraction to repulsion with distance. Thermal effects are shown to be negligible for small plate separations and at room temperature, but become dominant and repulsive at large values of these parameters. In configurations out of global thermal equilibrium, we s…
Applying a sum-over-modes approach to the Casimir interaction between two plates with finite conductivity, we isolate and study the contributions of surface plasmons and Foucault (eddy current) modes. We show in particular that for the TE-polarization eddy currents provide a repulsive force that cancels, at high temperatures, the Casimir free energy calculated with the plasma model.
Electromagnetic vacuum fluctuations have observable consequences, like the Casimir force between mirrors in vacuum. This force is now measured with good accuracy and agreement with theory when the effect of imperfect reflection of mirrors is properly taken into account. We discuss the simple case of bulk metallic mirrors described by a plasma model and show that simple scaling laws are obtained at the limits of long and short distances. The crossover between the short and long-distance laws is quite similar to the crossover between Van der Waals and Casimir-Polder forces for two atoms in vacuu…
Polarisable atoms and molecules experience the Casimir-Polder force near magnetoelectric bodies, a force that is induced by quantum fluctuations of the electromagnetic field and the matter. Atoms and molecules in relative motion to a magnetoelectric surface experience an additional, velocity-dependent force. We present a full quantum-mechanical treatment of this force and identify a generalised Doppler effect, the time delay between photon emission and reabsorption, and the Roentgen interaction as its three sources. For ground-state atoms, the force is very small and always decelerating, hence…
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 demonstrate the fundamental links existing between two different descriptions of quantum electrodynamics in inhomogeneous, lossy and dispersive dielectric media which are based either on the Huttner-Barnett formalism for polaritons [B. Huttner and S. M. Barnett, Phys.Rev. A 46, 4306 (1992)] or the Langevin noise approach using fluctuating currents [T. Gruner and D.-G. Welsch, Phys.Rev.A 53, 1818 (1996)]. In this work we demonstrate the practical equivalence of the two descriptions by introducing the concept of effective photon state associated with some specific noise current distribution. …
We compare theory and experiment in the Casimir force measurement between gold surfaces performed with the atomic force microscope. Both random and systematic experimental errors are found leading to a total absolute error equal to 8.5 pN at 95% confidence. In terms of the relative errors, experimental precision of 1.75% is obtained at the shortest separation of 62 nm at 95% confidence level (at 60% confidence the experimental precision of 1% is confirmed at the shortest separation). An independent determination of the accuracy of the theoretical calculations of the Casimir force and its appli…
We show that an isotropic dipolar particle in the vicinity of a substrate made of nonreciprocal plasmonic materials can experience a lateral Casimir force and torque when the particle's temperature differs from that of the slab and the environment. We connect the existence of the lateral force to the asymmetric dispersion of nonreciprocal surface polaritons and the existence of the lateral torque to the spin-momentum locking of such surface waves. Using the formalism of fluctuational electrodynamics, we show that the features of lateral force and torque should be experimentally observable usin…
Perturbative corrections to the Casimir free energy due to macroscopic roughness of dielectric interfaces are obtained in the framework of an effective low-energy field theory. It describes the interaction of electromagnetic fields with materials whose plasma frequency $ω_p$ determines the low-energy scale. The naïve perturbative expansion of the single-interface scattering matrix in the variance of the profile is sensitive to short wavelength components of the roughness correlation function. We introduce generalized counter terms that subtract and correct these high-momentum contributions to …
We separate Maxwell's equations for background media that allow for both electric and magnetic time-dependence in a generalized Lorenz gauge. In a process analogous to the dynamical Casimir effect (DCE) we discuss how surface plasmon polaritons (SPP)s can be created out of vacuum, via the time-dependent variation of a dielectric and magnetic insulator at a metal interface for TM and TE branches, respectively. We suggest how to extend currently proposed DCE experiments to set up and detect these excitations. Numerical simulations (without any approximation) indicate that vacuum excited SPPs can…
The aim of this paper is to show that within the open-system framework the sum-over-modes approach á la Casimir leads to the Lifshitz formula for the Casimir free energy. A general result applicable to arbitrary geometries is obtained through the use of Ford, Lewis, & O'Connell's remarkable formula. Additionally, we address the possibility for obtaining the Casimir energy as a sum over complex "modes". We show in this case that the standard sum-over-modes formula must be suitably generalized to avert unphysical complex energies. Finally, we apply our results to several standard examples.
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.
This work deals with the problem of photon detection generated from the mirror-induced Dynamical Casimir Effect. Particularly we are interested in measurement of those statistical characteristics of a generated intracavity field which may confirm its nonthermal properties. Here an indirect protocol for quadrature dispersion measurement is presented.
In this paper we derive a general expression for the acoustic Casimir pressure between two parallel slabs made of arbitrary materials and whose acoustic reflection coefficients are not equal. The formalism is based on the calculation of the local density of modes using a Green's function approach. The results for the Casimir acoustic pressure are generalized to a sphere/plate configuration using the proximity theorem
We propose a new theory of thermal Casimir effect, holding for the experimentally important case of metallic surfaces with a roughness having a spatial scale smaller than the skin depth. The theory is based on a simple phenomenological model for a rough conductor, that explicitly takes account of the fact that ohmic conduction in the immediate vicinity of the surface of a conductor is much impeded by surface roughness, if the amplitude of roughness is smaller than the skin depth. As a result of the new model, we find that surface roughness strongly influences the magnitude of the thermal corre…
We present a modal approach to calculate finite temperature Casimir interactions between two periodically modulated surfaces. The scattering formula is used and the reflection matrices of the patterned surfaces are calculated decomposing the electromagnetic field into the natural modes of the structures. The Casimir force gradient from a deeply etched silicon grating is evaluated using the modal approach and compared to experiment for validation. The Casimir force from a two dimensional periodic structure is computed and deviations from the proximity force approximation examined.
The finite conductivity corrections to the Casimir force in two configurations are calculated in the third and fourth orders in relative penetration depth of electromagnetic zero oscillations into the metal. The obtained analytical perturbation results are compared with recent computations. Applications to the modern experiments are discussed.
We investigate the Casimir energy between two dissipative mirrors in term of a sum over mode formula which can be interpreted by analogy to a quantum dissipative oscillator. We also show that metamaterials engineered at scales between the nanometer and the micron seem a promising way to achieve a repulsive force.
We derive an analytic behavior of the Casimir free energy, entropy and pressure of metallic films in vacuum at low temperature. It is shown that this behavior differs significantly depending on whether the plasma or the Drude model is used to describe the dielectric properties of film metal. For metallic films described by the lossless plasma model the thermal corrections to the Casimir energy and pressure drop to zero exponentially fast with increasing film thickness. There is no classical limit in this case. The Casimir entropy satisfies the Nernst heat theorem. For metallic films with perfe…
We discuss the Casimir effect between two identical, parallel slabs, emphasizing the role of dissipation and temperature. Starting from quite general assumptions, we analyze the behavior of the Casimir entropy in the limit T->0 and link it to the behavior of the slab's reflection coefficients at low frequencies. We also derive a formula in terms of a sum over modes, valid for dissipative slabs that can be interpreted in terms of a damped quantum oscillator.
We calculate the corrections to the Casimir force between two metals due to the spatial dispersion of their response functions. We employ model-independent expressions for the force in terms of the optical coefficients. We express the non-local corrections to the Fresnel coefficients employing the surface $d_\perp$ parameter, which accounts for the distribution of the surface screening charge. Within a self-consistent jellium calculation, spatial dispersion increases the Casimir force significatively for small separations. The nonlocal correction has the opposite sign than previously predicted…
A matter-field theory of the Casimir force is formulated in which the electromagnetic field and collective modes of dielectric media are treated on an equal footing. In our theory, the Casimir force is attributed to zero-point energies of the combined matter-field modes. We analyze why some of the existing theories favor the interpretation of the Casimir force as originating from zero-point energies of the electromagnetic field and others from those of the matter.
The Casimir interaction energy for a class of discrete self-similar configuration of parallel plates is evaluated using existing methods. The similarities to characteristics of an attractive Casimir force is deduced only at infinite range of configuration. Further, the emergence of Casimir-like energy is qualitatively described for a Gaussian model of Landau-Ginzburg scalar field. Its relevance to self-similarity in the statistical field is shown at infinite range of fluctuations.
Isoelectronic differential force measurements provide a unique opportunity to probe controversial features of the thermal Casimir effect, that are still much debated in the current literature. Isolectronic setups offer two major advantages over conventional Casimir setups. On one hand they are immune from electrostatic forces caused by potential patches on the plates surfaces, that plague present Casimir experiments especially for separations in the micron range. On the other hand they can strongly enhance the discrepancy between alternative theoretical models that have been proposed to estima…
We consider the Casimir effect of a massive vector field between two semi-infinite dielectric slabs. We first derive the generalization of the Lifshitz formula that gives the Casimir interaction energy of two magnetodielectric slabs separated by a magnetodielectric medium due to the vacuum fluctuations of a massive vector field. We then discuss the asymptotic behaviors of the Casimir energy and the Casimir force in various limits, such as low temperature, high temperature, small mass, large mass, up to the first order in the finite conductivity correction, for two real metal semispaces whose d…
The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically within a microscopic realistic model of dielectrics for an arbitrary physically possible frequency dispersion of dielectric permittivity. Divergences are absent in calculations, a minimum interatomic distance is a physical cut-off. Casimir surface force is proved to be attractive. A physical definition of the Casimir energy is discussed.
We compute the Casimir energy of a real scalar field in the presence of a pair of partially transparent plane mirrors, modeled by Dirac delta potentials.
We compute the Casimir Energy of a spherical region using a Surface Impedance approach. We characterize the Surface Impedance of the boundary using plasma model. Exact analytical formulae are obtained by means of the zeta function regularization method and all the divergencies are explicitly computed. We find that it is possible to have negative Casimir energy for some range of values of the relevant parameter. Limits of applicability of the model are discussed.
The attractive force between metallic surfaces, predicted by Casimir in 1948, seems to indicate the physical existence and measurability of the quantized electromagnetic field's zero-point energy. It is shown in this article, that the measurements of that force do not confirm Casimir's model, but in fact disprove it's foundational assumption that metal plates may be represented in the theory by quantum-field-theoretical boundaries. The consequences for the cosmological constant problem are discussed.
In this paper the Casimir energy of two parallel plates made by materials of different penetration depth and no medium in between is derived. We study the Casimir force density and derive analytical constraints on the two penetration depths which are sufficient conditions to ensure repulsion. Compared to other methods our approach needs no specific model for dielectric or magnetic material properties and constitutes a complementary analysis.
Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive, but we present several counterexamples, notably a simple type of quantum graph in which the sign of the force depends upon the number of edges. We also show that Casimir forces in quantum graphs can be reliably computed by summing over the classical orbits, and study the rate of convergence of the periodic orbit expansion. In generic situations where no analytic expression is available, the sign and approximate magnitude…
It was recently found that thermodynamic anomalies which arise in the Casimir effect between metals described by the Drude model can be attributed to the interaction of fluctuating Foucault (or eddy) currents [Phys. Rev. Lett. 103, 130405 (2009)]. We show explicitly that the two leading terms of the low-temperature correction to the Casimir free energy of interaction between two plates, are identical to those pertaining to the Foucault current interaction alone, up to a correction which is very small for good metals. Moreover, a mode density along real frequencies is introduced, showing that t…
We study the lateral dependence of the Casimir energy for different corrugated gratings of arbitrary periodic profile. To this end we model the profiles as stacks of horizontal rectangular slices following the profiles' shape and evaluate numerically the Casimir energy between them for different relative lateral displacements of the two corrugated plates. We compare our results with predictions obtained within the proximity force approximation (PFA). At comparable separation of the corrugated plates and geometric parameters, we find a strong dependence of the Casimir energy on the shape of the…
The finite temperature Casimir effect for a scalar field in the bulk region of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the Casimir energy and the Casimir force for two parallel plates with separation $a$ on the visible brane in the RSI model. High-temperature and low-temperature cases are covered. Attractiveness versus repulsiveness of the temperature correction to the force is discussed in the typical special cases of Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions at low temperature. The Abel-Plana summation formula is made use o…
The thermal Casimir-Lifshitz force among two bodies held at different temperatures displays striking features that are absent in systems in thermal equilibrium. The manifestation of this force has been observed so far only in Bose-Einstein condensates close to a heated substrate, but never between two macroscopic bodies. Observation of the thermal Casimir-Lifhitz force out of thermal equilibrium with conventional Casimir setups is very difficult, because for experimentally accessible separations the thermal force is small compared to the zero-temperature quantum Casimir force, unless prohibiti…
Modes have steadily influenced the understanding of physical systems through time. At least since the prediction of the Casimir effect, they also play a very important role in Casimir Physics and in the understanding of the different phenomena typical of this research field. At equilibrium modes provide a direct connection between the zero-point energy and the existence of irreducible fluctuations in a quantum system, offering an anatomic view into the physics of the interaction. In nonequilibrium systems, modes can be decisive to understand the behavior of quantum fluctuation-induced phenomen…
The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, the are no TM discrete modes t…
Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive. We present three scenarios in which that is not true. Two of these depend on mixing two types of boundary conditions. The other, however, is a simple type of quantum graph in which the sign of the force depends upon the number of edges.
The Casimir repulsion between a metal and a dielectric suspended in a liquid has been thoroughly studied in recent experiments. In the present paper we consider surface modes in three layered systems modeled by dielectric functions guaranteeing repulsion. It is shown that surface modes play a decisive role in this phenomenon at short separations. For a toy plasma model we find the contribution of the surface modes at all distances.
In this paper we discuss the computation of Casimir energy on a quantum computer. The Casimir energy is an ideal quantity to calculate on a quantum computer as near term hybrid classical quantum algorithms exist to calculate the ground state energy and the Casimir energy gives physical implications for this quantity in a variety of settings. Depending on boundary conditions and whether the field is bosonic or fermionic we illustrate how the Casimir energy calculation can be set up on a quantum computer and calculated using the Variational Quantum Eigensolver algorithm with IBM QISKit. We compa…
We derive exact expressions for the Casimir scalar interaction energy between media-separated eccentric dielectric cylinders and for the media-separated cylinder-plane geometry using a mode-summation approach. Similarly to the electromagnetic Casimir-Lifshitz interaction energy between fluid-separated planar plates, the force between cylinders is attractive or repulsive depending on the relative values of the permittivities of the three intervening media.
Using recently developed techniques based on scattering theory, we find the electromagnetic Casimir energy for geometries involving semi-infinite planes, a case that is of particular interest in the design of microelectromechanical devices. We obtain both approximate analytic formulae and exact results requiring only modest numerical computation. Using these results, we analyze the effects of edges and orientation on the Casimir energy. We also demonstrate the accuracy, simplicity, and utility of our approximation scheme, which is based on a multiple reflection expansion.
Zero-point energy is generally known to be unphysical. Casimir effect, however, is often presented as a counterexample, giving rise to a conceptual confusion. To resolve the confusion we study foundational aspects of Casimir effect at a qualitative level, but also at a quantitative level within a simple toy model with only 3 degrees of freedom. In particular, we point out that Casimir vacuum is not a state without photons, and not a ground state for a Hamiltonian that can describe Casimir force. Instead, Casimir vacuum can be related to the photon vacuum by a non-trivial Bogoliubov transformat…
We use the mode summation method together with zeta-function regularization to compute the Casimir energy of a dilute dielectric cylinder. The method is very transparent, and sheds light on the reason the resulting energy vanishes.
The Casimir effect is investigated in cylindrical and toroidal carbon nanotubes within the framework of the Dirac-like model for the electronic states. The topological Casimir energy is positive for metallic cylindrical nanotubes and is negative for semiconducting ones. The toroidal compactification of a cylindrical nanotube along its axis increases the Casimir energy for metallic-type (periodic) boundary conditions along its axis and decreases the Casimir energy for the semiconducting-type compactifications. For finite length metallic nanotubes the Casimir forces acting on the tube edges are …
We develop a diagrammatic representation of the Casimir energy of a multibody configuration. The diagrams represent multiple reflections between the objects and can be organized by a few simple rules. The lowest-order diagrams (or reflections) give the main contribution to the Casimir interaction which proves the usefulness of this expansion. Among some applications of this, we find analytical formulae describing the interaction between "edges", i.e. semi-infinite plates, where we also give a first example of blocking in the context of the Casimir energy. We also find the interaction of edges …
We derive a general procedure for finding the electromagnetic normal modes in layered structures. We apply this procedure to planar, spherical and cylindrical structures. These normal modes are important in a variety of applications. They are the only input needed in calculations of Casimir interactions. We present explicit expression for the condition for modes and Casimir energy for a large number of specific geometries. The layers are allowed to be two-dimensional so graphene and graphene-like sheets as well as two-dimensional electron gases can be handled within the formalism. Also forces …
The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We devoleped a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions. The Casimir energy for a massless scalar field between the closely spaced two concentric spheres coincides with the Casimir energy of the parallel plates for a massless scalar field in the limit when the dimensionless paramete…
We consider the Casimir effect between two parallel plates localized on a brane. In order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the KK modes. When no massless mode appears in the spectrum, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. Here we illustrate a new method to compute the correction to the Casimir energy between two parallel …
In this article we compute the Casimir force between two finite-width mirrors at finite temperature, working in a simplified model in 1+1 dimensions. The mirrors, considered as dissipative media, are modeled by a continuous set of harmonic oscillators which in turn are coupled to an external environment at thermal equilibrium. The calculation of the Casimir force is performed in the framework of the theory of quantum open systems. It is shown that the Casimir interaction has two different contributions: the usual radiation pressure from vacuum, which is obtained for ideal mirrors without dissi…
The Casimir energy for a massless scalar field between the closely spaced two concentric D-dimensional (for D>3) spheres is calculated by using the mode summation with contour integration in the complex plane of eigenfrequencies and the generalized Abel-Plana formula for evenly spaced eigenfrequency at large argument. The sign of the Casimir energy between closely spaced two concentric D-dimensional spheres for a massless scalar field satisfying the Dirichlet boundary conditions is strictly negative. The Casimir energy between D-1 dimensional surfaces close to each other is regarded as interes…
The Casimir energy is the first-order-in-\hbar correction to the energy of a time-independent field configuration in a quantum field theory. We study the Casimir energy in a toy model, where the classical field is replaced by a separable potential. In this model the exact answer is trivial to compute, making it a good place to examine subtleties of the problem. We construct two traditional representations of the Casimir energy, one from the Greens function, the other from the phase shifts, and apply them to this case. We show that the two representations are correct and equivalent in this mode…
