U. Mohideen

New developments in the Casimir effect

Abstract We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus, the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also, the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

Advances in the Casimir effect

1. Introduction I: PHYSICAL AND MATHEMATICAL FOUNDATIONS OF THE CASIMIR EFFECT FOR IDEAL BOUNDARIES 2. Simple models of the Casimir effect 3. Field quantization and vacuum energy in the presence of boundaries 4. Regularization and renormalization of the vacuum energy 5. The Casimir effect at nonzero temperature 6. Approximate and numerical approaches to the Casimir effect 7. The Casimir effect for two ideal metal planes 8. The Casimir effect in rectangular boxes 9. Single spherical and cylindrical boundaries 10. The Casimir force between objects of arbitrary shape 11. Spaces with non-Euclidean topology II: THE CASIMIR FORCE BETWEEN REAL BODIES 12. The Lifshitz theory of van der Waals and Casimir forces between plane dielectrics 13. The Casimir interaction between plates made of real metals at zero temperature 14. The Casimir interaction between real metals at nonzero temperature 15. The Casimir interaction between metal and dielectric 16. The Lifshitz theory of atom-wall interaction 17. The Casimir force between rough and corrugated surfaces III: MEASUREMENTS OF THE CASIMIR FORCE AND THEIR APPLICATIONS IN BOTH FUNDAMENTAL PHYSICS AND NANOTECHNOLOGY 18. General requirements for Casimir force measurements 19. Measurements of the Casimir force between equals 20. Measurements of the Casimir force with semiconductors 21. Measurements of the Casimir force in configurations with corrugated surfaces 22. Measurement of the Casimir-Polder force 23. Applications of the Casimir force in nanotechnology 24. Constraints on hypothetical interactions from the Casimir effect 25. Conclusions and outlook

The Casimir force between real materials: Experiment and theory

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.

Precision measurement of the Casimir force from 0.1 to 0.9 micrometers

We have used an atomic force microscope to make precision measurements of the Casimir force between a metallized sphere of diameter 196 \ensuremath{\mu}m and flat plate. The force was measured for plate-sphere surface separations from 0.1 to 0.9 \ensuremath{\mu}m. 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

Threshold characteristics of semiconductor microdisk lasers

1%

Precision measurement of the Casimir force using gold surfaces

deviation at the smallest separation.

Demonstration of the Lateral Casimir Force

This letter describes the threshold characteristics of InGaAs/InGaAsP microdisk lasers with optical emission near a wavelength λ=1.52 μm. More than 5% of the total spontaneous emission feeds into the lasing mode as the microdisk diameters reach 2 μm.

Casimir and van der Waals forces between two plates or a sphere (lens) above a plate made of real metals

A precision measurement of the Casimir force using metallic gold surfaces is reported. The force is measured between a large gold-coated sphere and flat plate using an atomic force microscope. The use of gold surfaces removes some theoretical uncertainties in the interpretation of the measurement. The forces are also measured at smaller surface separations. The complete dielectric spectrum of the metal is used in the comparison of theory to the experiment. The average statistical precision remains at the same 1% of the forces measured at the closest separation. These results should lead to the development of stronger constraints on hypothetical forces.

Improved precision measurement of the Casimir force

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 microm 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.

GaAs/AlGaAs microdisk lasers

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\char21{}4) nm. More exact values of the Hamaker constant for Al and Au are determined.