Session R41: Casimir Forces

Measurement of the Casimir force between ferromagnetic surfaces

We have measured the Casimir interaction between two ferromagnetic boundary surfaces using the dynamic atomic force microscope in the frequency shift technique. The experimental data are found to be in excellent agreement with the predictions of the Lifshitz theory for magnetic boundary surfaces combined with the plasma model approach for the free electrons in the metal. In an important difference from non-magnetic metals, the Drude description of the free electrons leads to a Casimir force that is less than that from the plasma model approach. Thus the role of hypothetical patch potentials will be opposite to that required for reconciliation of the data with the Drude model.   

Validity of effective medium theories in Casimir force calculations

Effective medium theories have been used extensively to describe the dielectric response of inhomogeneous media. This is media that is composed of a mixture of materials with different dielectric functions. The possibility of using inhomogeneous media to control or tune Casimir forces has been discussed in the literature. In this paper we present results for the Casimir force between two inhomogeneous plates described by different effective medium models. In particular we show how the force depends on the model used. This has implications on the comparison between theoretical and experimental results. Furthermore, we calculate the force between an inhomogeneous sphere like multi layered nano shells and a plane to study the effects of effective models when using the proximity force approximations. The conditions under which effective medium models can be used in the context of the Casimir force are discussed in detail.   

Experiments on Sphere Cylinder Geometry Dependence in the Electromagnetic Casimir Effect

We report on ongoing experimental investigations on the geometry dependence of the electromagnetic Casimir force in the sphere-cylinder configuration. A gold coated hollow glass sphere which forms one surface is attached to a Silicon AFM cantilever. The cylinder, which is constructed from tapered optical fiber is also gold coated.~ The resonance frequency shift of the cantilever is measured as a function of the sphere-cylinder surface separation.~ The sphere-cylinder electrostatic force is used for alignment of the sphere and the cylinder and also for calibrating the system. The results are compared to numerical simulations in the framework of the Proximity Force Approximation (PFA).   

Sum-over-modes approach to the Casimir effect in dissipative systems

We show that, within the open-system framework, the sum-over-modes approach \`{a} 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.   

Influence of Casimir-Lifshitz forces on actuation dynamics of MEMS

Electromagnetic fluctuations generate forces between neutral bodies known as Casimir-Lifshitz forces, of which van der Waals forces are special cases, and which can become important in micromechanical systems (MEMS). For surface areas big enough but gaps small enough, the Casimir force can possibly draw and lock MEMS components together, an effect called stiction, causing device malfunction. Alternatively, stiction can also be exploited to add new functionalities to MEMS architecture. Here, using as inputs the measured frequency dependent dielectric response and surface roughness statistics from Atomic Force Microscopy (AFM) images, we perform the first realistic calculation of MEMS actuation. For our analysis the Casimir force is combined with the electrostatic force between rough surfaces to counterbalance the elastic restoring force. It is found that, even though surface roughness has an adverse effect on the availability of (stable) equilibria, it ensures that those stable equilibria can be reached more easily than in the case of flat surfaces. Hence our results can have significant implications on how to design MEM surfaces. The author would like this abstract to appear in a Casimir related session.   

Scattering Theory Calculations of Casimir Energies at High Curvature

Scattering theory provides a powerful tool for capturing the response of an object to electromagnetic charge and field fluctuations. Techniques based on scattering theory have made possible a wide range of new calculations of Casimir energies. In this approach, the Casimir interaction energy for a collection of objects can be expressed in terms of the scattering T-matrices for each object individually, combined with universal translation matrices describing the objects' relative positions and orientations. These translation matrices are derived from an expansion of the free Green's function in an appropriate coordinate system, independent of the details of the objects themselves. This method proves particularly valuable for geometries involving high curvature, such as edges and tips. I will describe this approach in general terms and then give results from several problems to which it has been applied successfully. I will also discuss new developments in scattering theory that have been motivated by these problems.   

Investigation of electrostatic ``patches'' on Au samples: Effects on the Casimir measurements

It has been argued by Behunin and co-workers that the measurements done of the Casimir force on Au coated surfaces could suffer from substantial systematic errors arising from the presence of so called electrostatic ``patches'' (i.e. an electrostatic potential distribution on the surface of the Au layer). While these effects can be minimized, in principle they cannot be nullified by the application of uniform potential differences between the investigated surfaces. We present Kelvin probe microscopy studies of Au samples on Si. Au samples (about 200 nm thick) were deposited by thermal evaporation and sputtering. A thin (about 10 nm thick) layer of Cr is used as an adhesion layer. We will discuss the methodology used. We will show that that irrespectively of sample deposition method, there is two characteristic scales for the potential distribution: One, with spatial size of about 100 nm, associated with grain sizes and the other one, typical dimension 1 $\mu$m, most likely associated with unavoidable sample contamination. The effect of this potentials is found to be too small to affect the conclusions found in precision measurements of the Casimir effect.   

Casimir effect between Topological Insulators: a proposal for quantum levitation

In this talk I will study the Casimir interaction between Topological Insulators (TIs). I will start with a brief description of the TIs, to explain what a TI is, and why they are interesting from a Casimir effect point of view. In particular, a three dimensional Topological Insulator is characterized by its topological magnetoelectric coupling $\theta \ne $0. We will discuss the electromagnetic response of the TIs, how a magnetoelectric coupling between TE and TM modes appears in this material and its consequences. We will show how, by tuning the parameter $\theta $ of the TI, we will be able to change the behavior of the Casimir energy between Tis from attraction to repulsion for all distances, and even the appearance of an equilibrium distance in the system. Then TIs can be potentially used to obtain ``quantum levitation'' and to avoid the sticking phenomena in NEMS.   

Three-body Casimir effects and repulsion

The Casimir effect arises from quantum fluctuations in the electromagnetic field and results in forces between atoms (van der Waals and Casimir-Polder forces), between atoms and surfaces (Casimir-Polder forces), and between conducting and dielectric surfaces (Casimir-Lifshitz forces). In the past few years, there has been a revolution in our ability to calculate forces between different bodies. Pairwise summation of interatomic forces in general is very inadequate to describe the physics. In particular three-body effects can be large. Two-body forces, for example, between a dielectric sphere and a dielectric plane, can be calculated by a combination of analytic and numerical techniques; non-monotonic effects can occur when three-body interactions are considered. Anisotropic objects with ordinary electrical properties can give rise to repulsive quantum vacuum forces, which might have application in nanotechnology. This talk will focus on the overlap of the three-body force regime and Casimir repulsion, for example, the interaction between an anisotropically polarizable atom and a pair of facing conducting wedges, or two conducting half-planes constituting an aperture.   

Electromagnetic fluctuation-induced interactions with metallic gratings

In this talk I will discuss electromagnetic equilibrium and non-equilibrium fluctuation-induced interactions involving metallic gratings. In particular, I will describe a modal approach [1] to compute Casimir forces between metallic gratings and discuss the description of a recent Casimir force experiment with nanostructures that shows a strong force reduction. I will also discuss the related non-equilibrium problem of nanoscale heat transfer in metallic gratings from a modal approach point of view [2].\\[4pt] [1] {\it Quasi-analytical modal approach for computing Casimir interactions in periodic nanostructures}, F. Intravaia, P.S. Davids, R.S. Decca, V.A Aksyuk, D. Lopez, and D.A.R. Dalvit, Phys. Rev. A 86, 042101 (2012).\\[0pt] [2] {\it Enhanced radiative heat transfer between nanostructured gold plates}, R. Guerout, J. Lussange, F.S.S. Rosa, J.-P. Hugonin, D.A.R. Dalvit, J.-J. Greffet, A. Lambrecht, and S. Reynaud, Phys. Rev. B85, 180301(R) (2012).   

Fundamental limitations on force sensing due to patch potentials

In this talk I will discuss some of the current methods used for measuring non-Newtonian corrections to gravity at short separation. When polycrystalline metallic test masses are used in these experiments patch potentials may provide a large source of noise. I'll present a simple model to quantify patch effects from which insights may be gained for minimizing deleterious effects on force signal to noise in these experiments.   

Measurement of the Casimir force between gold surfaces using a Frequency-Modulation technique

The Casimir force arises from the interactions between fluctuating dipoles in two media separated by a gap. We measure the derivative of the Casimir force with respect to sample separation between a gold-coated sphere and a gold-coated planar substrate using a non-contact Frequency-Modulation (FM) method of Atomic Force Microscopy (AFM) in a thermally controlled environment. The resonant frequency of the cantilever is tracked as the sphere is brought close to the surface. At each distance from the surface, the bias voltage of the sphere is swept, both to measure the distance between the sphere and the plate and to mitigate the effect of any contact potential difference. We will present recently obtained experimental data and discuss the various artifacts associated with Casimir force measurements.   

Shape and material effects in Casimir forces

Casimir forces depend non-trivially on shape and material properties. Using ideas from electromagnetic scattering theory and conformal mappings, we have derived a number of novel analytical and numerical results for Casimir interactions. We shall give a brief overview of the general approach and present explicit results for some generic examples, including short- and long-distance expansions, interaction of perfect conductors with sharp edges and tips, and exact solutions in two and three dimensions. The predictions are compared to recent experiments.   

Heat transfer and non-equilibrium Casimir force in nanostructured surfaces

I'll review recent calculations for Casimir interactions between nanostructured surfaces both at thermodynamic equilibrium and out of equilibrium in the framework of the scattering theory. I'll emphasize on the interplay between the thermal Casimir force and the geometry of the surfaces. We predict an enhancement in the heat transfer between metallic gratings due to the appearance of spoof surface plasmons modes. We also show that the thermal component of the Casimir force arise at shorter separation distance in the case of nanostructured surfaces.