Template-stripped gold surfaces with 0.4 nm rms roughness suitable for force measurements. Application to the Casimir force in the 20-100 nm range

Using a template-stripping method, macroscopic gold surfaces with root-mean-square (rms) roughness less than 0.4 nm have been prepared, making them useful for studies of surface interactions in the nanometer range. The utility of such substrates is demonstrated by measurements of the Casimir force at surface separations between 20 and 100 nm, resulting in good agreement with theory. The significance and quantification of this agreement is addressed, as well as some methodological aspects regarding the measurement of the Casimir force with high accuracy.Comment: 7 figure

Partially Annealed Disorder and Collapse of Like-Charged Macroions

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.Comment: 21 pages, 2 figure

Geometry and material effects in Casimir physics - Scattering theory

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, to nonzero temperatures, and to spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. This approach, which combines methods of statistical physics and scattering theory, is well suited to analyze many diverse phenomena. We illustrate its power and versatility by a number of examples, which show how the interplay of geometry and material properties helps to understand and control Casimir forces. We also examine whether electrodynamic Casimir forces can lead to stable levitation. Neglecting permeabilities, we prove that any equilibrium position of objects subject to such forces is unstable if the permittivities of all objects are higher or lower than that of the enveloping medium; the former being the generic case for ordinary materials in vacuum.Comment: 44 pages, 11 figures, to appear in upcoming Lecture Notes in Physics volume in Casimir physic

Sample-to-sample torque fluctuations in a system of coaxial randomly charged surfaces

Polarizable randomly charged dielectric objects have been recently shown to exhibit long-range lateral and normal interaction forces even when they are effectively net neutral. These forces stem from an interplay between the quenched statistics of random charges and the induced dielectric image charges. This type of interaction has recently been evoked to interpret measurements of Casimir forces in vacuo, where a precise analysis of such disorder-induced effects appears to be necessary. Here we consider the torque acting on a randomly charged dielectric surface (or a sphere) mounted on a central axle next to another randomly charged surface and show that although the resultant mean torque is zero, its sample-to-sample fluctuation exhibits a long-range behavior with the separation distance between the juxtaposed surfaces and that, in particular, its root-mean-square value scales with the total area of the surfaces. Therefore, the disorder-induced torque between two randomly charged surfaces is expected to be much more pronounced than the disorder-induced lateral force and may provide an effective way to determine possible disorder effects in experiments, in a manner that is independent of the usual normal force measurement.Comment: 7 pages, 3 fig

Repulsive Casimir-Polder forces from cosmic strings

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 show that for an isotropic polarizability tensor the force is always repulsive. At large separations between the microparticle and the string, the force varies inversely as the fifth power of the distance. In the non-retarded regime, corresponding to separations smaller than the relevant transition wavelengths, the force decays as the inverse fourth power of the distance. In the case of anisotropic polarizability, the dependence of the Casimir-Polder potential on the orientation of the polarizability tensor principal axes also leads to the moment of force acting on the particle.Comment: 16 pages, 2 figure

Characterization of optical properties and surface roughness profiles: The Casimir force between real materials

The Lifshitz theory provides a method to calculate the Casimir force between two flat plates if the frequency dependent dielectric function of the plates is known. In reality any plate is rough and its optical properties are known only to some degree. For high precision experiments the plates must be carefully characterized otherwise the experimental result cannot be compared with the theory or with other experiments. In this chapter we explain why optical properties of interacting materials are important for the Casimir force, how they can be measured, and how one can calculate the force using these properties. The surface roughness can be characterized, for example, with the atomic force microscope images. We introduce the main characteristics of a rough surface that can be extracted from these images, and explain how one can use them to calculate the roughness correction to the force. At small separations this correction becomes large as our experiments show. Finally we discuss the distance upon contact separating two rough surfaces, and explain the importance of this parameter for determination of the absolute separation between bodies.}Comment: 33 pages, 14 figures, to appear in Springer Lecture Notes in Physics, Volume on Casimir Physics, edited by Diego Dalvit, Peter Milonni, David Roberts, and Felipe da Ros