Casimir Force Calculations Research Articles

Comparison of the Casimir force between SiC plates with different permittivity models: Lorentz model and Palik data

Accurate calculation of Casimir forces is essential for the development of micro- and nanoelectromechanical systems. Silicon carbide (SiC) is an excellent material for fabricating microsensors due to its high durability, high stiffness, and low thermal expansion. The permittivity of the SiC could be characterized by the Lorentz model or the Palik data. However, the influence of the two models of calculating permittivity on the Casimir force has not been discussed. In this work, we calculate the Casimir force between SiC plates by the Lorentz model and the Palik data, respectively. The Casimir force calculated by the Lorentz model could be 4 times greater than the Palik data for SiC at a gap distance of 10 nm. The difference of the permittivity in the ultraviolet lead to different Casimir forces. This work demonstrates the difference between the two models of permittivity for calculating the SiC-based Casimir force, and provides a reliable base for more accurate Casimir force calculations.

Fluctuation-induced dispersion forces on thin DNA films.

In this work, the calculation of Casimir forces across thin DNA films is carried out based on the Lifshitz theory. The variations of Casimir forces due to the DNA thicknesses, volume fractions of containing water, covering media, and substrates are investigated. For a DNA film suspended in air or water, the Casimir force is attractive, and its magnitude increases with decreasing thickness of DNA films and the water volume fraction. For DNA films deposited on a dielectric (silica) substrate, the Casimir force is attractive for the air environment. However, the Casimir force shows unusual features in a water environment. Under specific conditions, switching sign of the Casimir force from attractive to repulsive can be achieved by increasing the DNA-film thickness. Finally, the Casimir force for DNA films deposited on a metallic substrate is investigated. The Casimir force is dominated by the repulsive interactions at a small DNA-film thickness for both the air and water environments. In a water environment, the Casimir force turns out to be attractive for a large DNA-film thickness, and a stable Casimir equilibrium can be found. The influences of electrolyte screening on the Casimir pressure of DNA films are also discussed at the end. In addition to the adhesion stability, our finding could be applicable to the problems of condensation and decondensation of DNA, due to fluctuation-induced dispersion forces.

Casimir Force: Vacuum fluctuation, zero-point energy, and computational electromagnetics

The understanding of the Casimir force foretells applications in micro/nanoelectromechanical sensors and quantum friction. We review the history of quantum theory and Casimir force modeling and, using the homomorphism between electromagnetic oscillations and a linear pendulum with simple harmonic oscillation, we explore various concepts needed for Casimir force calculations. Through the argument principle, we simplify the derivation of Casimir energy and, hence, the Casimir force. Then, we discuss the connection between the Casimir force and computational electromagnetics (CEM), focusing on the method of moments (MOM). Finally, we consider the marriage of these concepts with recently developed broadband fast algorithms. The resulting approaches illustrate that the Casimir force calculation is for various highly complex structures.

The effect of patch potentials in Casimir force measurements determined by heterodyne Kelvin probe force microscopy

Measurements of the Casimir force require the elimination of the electrostatic force between the surfaces. However, due to electrostatic patch potentials, the voltage required to minimize the total force may not be sufficient to completely nullify the electrostatic interaction. Thus, these surface potential variations cause an additional force, which can obscure the Casimir force signal. In this paper, we inspect the spatially varying surface potential of e-beamed, sputtered, sputtered and annealed, and template stripped gold surfaces with Heterodyne amplitude modulated Kelvin probe force microscopy (HAM-KPFM). It is demonstrated that HAM-KPFM improves the spatial resolution of surface potential measurements compared to amplitude modulated Kelvin probe force microscopy. We find that patch potentials vary depending on sample preparation, and that the calculated pressure can be similar to the pressure difference between Casimir force calculations employing the plasma and Drude models.

Born-series approach to the calculation of Casimir forces

The Casimir force between two objects is notoriously difficult to calculate in anything other than parallel-plate geometries due to its non-additive nature. This means that for more complicated, realistic geometries one usually has to resort to approaches such as making the crude proximity force approximation (PFA). Another issue with calculation of Casimir forces in real-world situations (such as with realistic materials) is that there are continuing doubts about the status of the standard Lifshitz treatment as a true quantum theory. Here we demonstrate an alternative approach to calculation of Casimir forces for arbitrary geometries which sidesteps both these problems. Our calculations are based upon a Born expansion of the Green's function of the quantised electromagnetic vacuum field, interpreted as multiple scattering, with the relevant coupling strength being the difference in the dielectric functions of the various materials involved. This allows one to consider arbitrary geometries in single or multiple scattering simply by integrating over the desired shape, meaning that extension beyond the PFA is trivial. This work is mostly dedicated to illustration of the method by reproduction of known parallel-slab results -- a process that turns out to be non-trivial and provides several useful insights. We also present a short example of calculation of the Casimir energy for a more complicated geometry, namely that of two finite slabs.

MONTE CARLO CALCULATION OF THE LATERAL CASIMIR FORCES BETWEEN RECTANGULAR GRATINGS WITHIN THE FORMALISM OF LATTICE QUANTUM FIELD THEORY

We propose a new Monte Carlo method for calculation of the Casimir forces. Our method is based on the formalism of noncompact lattice quantum electrodynamics. This approach has been tested in the simplest case of two ideal conducting planes. After this the method has been applied to the calculation of the lateral Casimir forces between two ideal conducting rectangular gratings. We compare our calculations with the results of PFA and "Optimal" PFA methods.

Casimir forces between spheres

We discuss the calculation of Casimir forces between a collection of N dielectric spheres. This is done by evaluating directly the force on a sphere constructed from a stress tensor, rather than an interaction energy. Two- and three-body forces between the spheres are evaluated for setups of two- and three-sphere systems, respectively. An approximate large-N limit is also obtained for the functional dependence on the number of spheres.

Theoretical ingredients of a Casimir analog computer.

We derive a correspondence between the contour integration of the Casimir stress tensor in the complex-frequency plane and the electromagnetic response of a physical dissipative medium in a finite real-frequency bandwidth. The consequences of this correspondence are at least threefold: First, the correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard imaginary-frequency point of view based on Wick rotations. Second, it forms the starting point of finite-difference time-domain numerical techniques for calculation of Casimir forces in arbitrary geometries. Finally, this correspondence is also key to a technique for computing quantum Casimir forces at micrometer scales using antenna measurements at tabletop (e.g., centimeter) scales, forming a type of analog computer for the Casimir force. Superficially, relationships between the Casimir force and the classical electromagnetic Green's function are well known, so one might expect that any experimental measurement of the Green's function would suffice to calculate the Casimir force. However, we show that the standard forms of this relationship lead to infeasible experiments involving infinite bandwidth or exponentially growing fields, and a fundamentally different formulation is therefore required.

Multiple scattering Casimir force calculations: Layered and corrugated materials, wedges, and Casimir–Polder forces

Various applications of the multiple scattering techniques to calculating the Casimir energy are described. These include the interaction between dilute bodies of various sizes and shapes, temperature dependence, interactions with multilayered and corrugated bodies, and new examples of exactly solvable separable bodies.

Improved finite-difference computation of the van der Waals force: One-dimensional case

We present an improved demonstration of the calculation of Casimir forces in one-dimensional systems based on the recently proposed numerical imaginary frequency Green's function computation approach. The dispersion force on two thick lossy dielectric slabs separated by an empty gap and placed within a perfectly conducting cavity is obtained from the Green's function of the modified Helmholtz equation by means of an ordinary finite-difference method. In order to demonstrate the possibility to develop algorithms to explore complex geometries in two and three dimensions to higher order in the mesh spacing, we generalize existing classical electromagnetism algebraic methods to generate the difference equations for dielectric boundaries not coinciding with any grid points. Diagnostic tests are presented to monitor the accuracy of our implementation of the method and follow-up applications in higher dimensions are introduced.

On the accuracy of the PFA: Analogies between Casimir and electrostatic forces

We present an overview of the validity of the Proximity Force Approximation (PFA) in the calculation of Casimir forces between perfect conductors for different geometries, with particular emphasis for the configuration of a cylinder in front of a plane. In all cases we compare the exact numerical results with those of PFA, and with asymptotic expansions that include the next to leading order corrections. We also discuss the similarities and differences between the results for Casimir and electrostatic forces.

Frequency-dependent Drude damping in Casimir force calculations

The Casimir force is calculated between Au thin films that are described by a Drude model with a frequency dependent damping function. The model parameters are obtained from available experimental data for Au thin films. Two cases are considered; annealed and nonannealed films that have a different damping function. Compared with the calculations using a Drude model with a constant damping parameter, we observe changes in the Casimir force of a few percent. This behavior is only observed in films of no more than 300 Å thick.

Casimir force calculations near the insulator-conductor transition in gold thin films

We present theoretical calculations of the Casimir force for Au thin films near the insulator-conductor transition that has been observed experimentally. The dielectric function of the Au thin films is described by the Drude-Smith model. The parameters needed to model the dielectric function such as the relaxation time, plasma frequency, and the backscattering constant depend on the thickness of the film. The Casimir force decreases as the film thickness decreases until it reaches a minimum after which the force increases again. The minimum of the force coincides with the critical film thickness where a percolation conductor-insulator occurs.

The Casimir effect as a scattering problem

We show that Casimir-force calculations for a finite number of non-overlapping obstacles can be mapped onto quantum-mechanical billiard-type problems which are characterized by the scattering of a fictitious point particle off the very same obstacles. With the help of a modified Krein trace formula the genuine/finite part of the Casimir energy is determined as the energy-weighted integral over the log-determinant of the multi-scattering matrix of the analog billiard problem. The formalism is self-regulating and inherently shows that the Casimir energy is governed by the infrared end of the multi-scattering phase shifts or the spectrum of the fluctuating field. The calculation is exact and in principle applicable for any separation(s) between the obstacles. In practice, it is more suited for large- to medium-range separations. We report especially about the Casimir energy of a fluctuating massless scalar field between two spheres or a sphere and a plate under Dirichlet and Neumann boundary conditions. But the formalism can easily be extended to any number of spheres and/or planes in three or arbitrary dimensions, with a variety of boundary conditions or non-overlapping potentials/non-ideal reflectors.

Bose-Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs

We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of ħ. At finite temperatures the Casimir force for our system depends on ħ. For the calculation of Casimir force we consider only the Dirichlet boundary condition. We show that below condensation temperature (Tc) the Casimir force for this non-interacting system decreases with temperature (T) and at $T\gtrsim T_c$ , it is independent of temperature. We also discuss the Casimir effect on 3-d highly anisotropic harmonically trapped ideal Bose gas.

Exact surface impedance formulation of the Casimir force: Application to spatially dispersive metals

We show that exact results are obtained for the calculation of Casimir forces between arbitrary materials using the concept of surface impedances, obtaining in a trivial way the force in the limit of perfect conductors and also Lifshitz formula in the limit of semi-infinite media. As an example we present a full and rigorous calculation of the Casimir force between two metallic half-spaces described by a hydrodynamic nonlocal dielectric response.

Casimir Forces in Nanostructures

We present a theoretical calculation of Casimir forces in structures made of parallel slabs that can be made of dispersive and absorptive materials. The materials are characterized by the reflectivity amplitude coefficients of the vacuum modes between the slabs. In particular, we present results for an antisymmetric configuration in which one plate is a metal and the other one a dielectric material. As a reference, we also calculate the force for the symmetric case (two metallic or two dielectric slabs). Our results show that the Casimir force could have a relevant contribution to the interaction between the tip and sample in atomic force microscopy experiments.