Demonstration of the difference in the Casimir force for samples with different charge-carrier densities

Self-consistent dielectric functions of materials: Toward accurate computation of Casimir-van der Waals forces

Research on theoretical calculation of Casimir-van der Waals (vdW) forces is characterized by a great number of inconsistencies and conflicting reports with widely differing results for many known materials, including water, contradicting experimental measurements. Despite its importance for conceptual advances in both fundamental aspects and practical applications, a universal framework for the accurate determination of Casimir-vdW forces is lacking. Here, we propose a universal theoretical platform for computing Casimir-vdW forces, accounting for the electronic dielectric constant, optical bandgap, density, and chemical composition. Using this methodology, we determine the dielectric function for 55 materials, over a wide range of photon energies, covering an extensive list of common metals, organic and inorganic semiconductors, and insulators. Internal consistency of the compiled data is validated using optical sum rules and Kramers-Kronig relations. We demonstrate that the calculated vdW forces based on these data match remarkably well with the experimentally measured vdW forces.

Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings

Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular silicon gratings. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.

The geometry dependence of the Casimir force could enable applications in nanomechanical systems if the effects can be enhanced. Here, the authors demonstrate that the Casimir force between two interpenetrating nanoscale gratings can exceed the proximity force approximation by a factor of 500.

Casimir free energy of dielectric films: classical limit, low-temperature behavior and control

The Casimir free energy of dielectric films, both free-standing in vacuum and deposited on metallic or dielectric plates, is investigated. It is shown that the values of the free energy depend considerably on whether the calculation approach used neglects or takes into account the dc conductivity of film material. We demonstrate that there are material-dependent and universal classical limits in the former and latter cases, respectively. The analytic behavior of the Casimir free energy and entropy for a free-standing dielectric film at low temperature is found. According to our results, the Casimir entropy goes to zero when the temperature vanishes if the calculation approach with neglected dc conductivity of a film is employed. If the dc conductivity is taken into account, the Casimir entropy takes the positive value at zero temperature, depending on the parameters of a film, i.e. the Nernst heat theorem is violated. By considering the Casimir free energy of SiO₂ and Al₂O₃ films deposited on a Au plate in the framework of two calculation approaches, we argue that physically correct values are obtained by disregarding the role of dc conductivity. A comparison with the well known results for the configuration of two parallel plates is made. Finally, we compute the Casimir free energy of SiO₂, Al₂O₃ and Ge films deposited on high-resistivity Si plates of different thicknesses and demonstrate that it can be positive, negative and equal to zero. The effect of illumination of a Si plate with laser light is considered. Possible applications of the obtained results to thin films used in microelectronics are discussed.

Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate

We demonstrate the Casimir interaction between two ferromagnetic boundary surfaces using the dynamic atomic force microscope. 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. It is shown that for magnetic materials the role of hypothetical patch potentials is opposite to that required for reconciliation of the data with the Drude model.

How to modify the van der Waals and Casimir forces without change of the dielectric permittivity

We propose a new experiment on the measurement of the Casimir force and its gradient between a Au-coated sphere and two different plates made of doped semiconductors. The concentrations of charge carriers in the plates are chosen slightly below and above the critical density at which the Mott-Anderson insulator-metal transition occurs. We calculate changes in the Casimir force and the Casimir pressure due to the insulator-metal transition using the standard Lifshitz theory and the phenomenological approach neglecting the contribution of free charge carriers in the dielectric permittivity of insulator materials (this approach was recently supported by the measurement data of several experiments). It is demonstrated that for the special selection of semiconductor materials (S- or Se-doped Si, B-doped diamond) the calculation results using the two theoretical approaches differ significantly and the predicted effects are easily detectable using the existing laboratory setups. In the case that the prediction of the phenomenological approach is confirmed, this would open opportunities to modify the van der Waals and Casimir forces with almost no change of room temperature dielectric permittivity.

Reduction of the Casimir force from indium tin oxide film by UV treatment

A significant decrease in the magnitude of the Casimir force (from 21% to 35%) was observed after an indium tin oxide sample interacting with an Au sphere was subjected to the UV treatment. Measurements were performed by using an atomic force microscope in high vacuum. The experimental results are compared with theory and a hypothetical explanation for the observed phenomenon is proposed.

Casimir force on a surface with shallow nanoscale corrugations: geometry and finite conductivity effects

We measure the Casimir force between a gold sphere and a silicon plate with nanoscale, rectangular corrugations with a depth comparable to the separation between the surfaces. In the proximity force approximation (PFA), both the top and bottom surfaces of the corrugations contribute to the force, leading to a distance dependence that is distinct from a flat surface. The measured Casimir force is found to deviate from the PFA by up to 10%, in good agreement with calculations based on scattering theory that includes both geometry effects and the optical properties of the material.

Variations of the Lifshitz-van der Waals force between metals immersed in liquids

We present a theoretical calculation of the Lifshitz-van der Waals force between two metallic slabs embedded in a fluid, taking into account the change of the Drude parameters of the metals when in contact with liquids of different index of refraction. For the three liquids considered in this work, water, CCl(3)F and CBr(3)F the change in the Drude parameters of the metal imply a difference of up to 15% in the determination of the force at short separations. These variations in the force are larger for liquids with a higher index of refraction.

Measurement of the Casimir force between a gold sphere and a silicon surface with nanoscale trench arrays

We report measurements of the Casimir force between a gold sphere and a silicon surface with an array of nanoscale, rectangular corrugations using a micromechanical torsional oscillator. At distances between 150 and 500 nm, the measured force shows significant deviations from the pairwise additive formulism, demonstrating the strong dependence of the Casimir force on the shape of the interacting bodies. The observed deviation, however, is smaller than the calculated values for perfectly conducting surfaces, possibly due to the interplay between finite conductivity and geometry effects.

Experimental investigation of the Casimir force beyond the proximity-force approximation

The analysis of all Casimir force experiments using a sphere-plate geometry requires the use of the proximity-force approximation (PFA) to relate the Casimir force between a sphere and a flat plate to the Casimir energy between two parallel plates. Because it has been difficult to assess the PFA's range of applicability theoretically, we have conducted an experimental search for corrections to the PFA by measuring the Casimir force and force gradient between a gold-coated plate and five gold-coated spheres with different radii using a microelectromechanical torsion oscillator. For separations z<300 nm, we find that the magnitude of the fractional deviation from the PFA in the force gradient measurement is, at the 95% confidence level, less than 0.4z/R, where R is the radius of the sphere.