We have used an atomic force microscope to make precision measurements of the Casimir force between a metallized sphere of diameter 196 μm and flat plate. The force was measured for plate-sphere surface separations from 0.1 to 0.9 μm. The experimental results are consistent with present theoretical calculations including the finite conductivity, roughness, and temperature corrections. The root mean square average deviation of 1.6 pN between theory and experiment corresponds to a $1\%$ deviation at the smallest separation.

The physical origin of the Casimir force is connected with the existence of zero-point and thermal fluctuations. The Casimir effect is very general and finds applications in various fields of physics. This review is limited to the rapid progress at the intersection of experiment and theory that has been achieved in the last few years. It includes a critical assessment of the proposed approaches to the resolution of the puzzles arising in the applications of the Lifshitz theory of the van der Waals and Casimir forces to real materials. All the primary experiments on the measurement of the Casimir force between macroscopic bodies and the Casimir-Polder force between an atom and a wall that have been performed in the last decade are reviewed, including the theory needed for their interpretation. The methodology for the comparison between experiment and theory in the force-distance measurements is presented. The experimental and theoretical results described here provide a deeper understanding of the phenomenon of dispersion forces in real materials and offer guidance for the application of the Lifshitz theory to the interpretation of the measurement results.

The lateral Casimir force between a sinusoidally corrugated gold coated plate and large sphere was measured for surface separations between 0.2 to $0.3\mu \mathrm{m}$ using an atomic force microscope. The measured force shows the required periodicity corresponding to the corrugations. It also exhibits the necessary inverse fourth power distance dependence. The obtained results are shown to be in good agreement with a complete theory taking into account the imperfectness of the boundary metal. This demonstration opens new opportunities for the use of the Casimir effect for lateral translation in microelectromechanical systems.

We have made a direct optical observation of pinning and bowing of a single 180° ferroelectric domain wall under a uniform applied electric field using a collection mode near-field scanning optical microscope. The domain wall is observed to curve between the pinning defects, with a radius of curvature determined by the material parameters and the applied electric field. The change in birefringence with applied field is used to infer the orientation of the internal field at the domain wall.

We report an improved precision measurement of the Casimir force. The force is measured between a large Al coated sphere and flat plate using an atomic force microscope. The primary experimental improvements include the use of smoother metal coatings, reduced noise, lower systematic errors, and independent measurement of surface separations. Also the complete dielectric spectrum of the metal is used in the theory. The average statistical precision remains at the same 1% of the forces measured at the closest separation.

The Casimir and van der Waals forces acting between two metallic plates or a sphere (lens) above a plate are calculated, accounting for the finite conductivity of the metals. A simple formalism of surface modes is briefly presented which makes it possible to obtain a generalization of the Lifshitz results for the case of two semispaces covered by thin layers. Additional clarification of the regularization procedure provides the means to obtain reliable results not only for the force but also for the energy density. This, in turn, leads to the value of the force for the configuration of a sphere (lens) above a plate, both of which are covered by additional layers. The Casimir interaction between Al and Au test bodies is recalculated using tabulated optical data for the complex refractive index of these metals. The computations turn out to be in agreement with perturbation theory up to fourth order in the relative penetration depth of electromagnetic zero-point oscillations into the metal. The disagreements between the results recently presented in the literature are resolved. The Casimir force between Al bodies covered by thin Au layers is computed, and the possibility of neglecting spatial dispersion effects is discussed as a function of the layer thickness. The van der Waals force is calculated including the transition region to the Casimir force. The pure nonretarded van der Waals force law between Al and Au bodies is shown to be restricted to a very narrow distance interval from 0.5 nm to (2–4) nm. More exact values of the Hamaker constant for Al and Au are determined.