Repulsive Casimir Forces Research Articles

BOUNDARY EFFECTS IN QUANTUM PHYSICS

We analyze the role of boundaries in the infrared behavior of quantum field theories. By means of a novel method we calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary properties. This allows the discrimination between boundary conditions which generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We analyze the effect of the renormalization group flow on these boundary conditions. Even if the Casimirless conformally invariant conditions are physically unstable under renormalization group flow they emerge as a new set of conformally invariant boundary conditions which are anomaly free.

REPULSIVE CASIMIR EFFECTS

Like Casimir's original force between conducting plates in vacuum, Casimir forces are usually attractive. But repulsive Casimir forces can be achieved in special circumstances. These might prove useful in nanotechnology. We give examples of when repulsive quantum vacuum forces can arise with conducting materials.

Vacuum Boundary Effects

The Casimir effect is highly dependent on the shape and structure of space boundaries. This dependence is encoded in the variation of vacuum energy with the different types of boundary conditions. We analyze from a global perspective the properties of the Casimir energy as a function on the largest space of the consistent boundary conditions \(\mathcal{M}_{F}\) for a massless scalar field confined between to homogeneous parallel plates. In particular, we analyze the analytic properties of this function and point out the existence of a third order phase transition at periodic boundary conditions. We also characterize the boundary conditions which give rise to attractive or repulsive Casimir forces. In the interface between both regimes we find a very interesting family of boundary conditions without Casimir effect, and fully characterize the boundary conditions which do not induce any type of Casimir force.

Repulsive Casimir forces with finite-thickness slabs

We use the extended Lifshitz theory to study the behaviors of the Casimir forces between finite-thickness effective medium slabs. We first study the interaction between a semi-infinite Drude metal and a finite-thickness magnetic slab with or without substrate. For no substrate, the large distance $d$ dependence of the force is repulsive and goes as $1/d^5$; for the Drude metal substrate, a stable equilibrium point appears at an intermediate distance which can be tuned by the thickness of the slab. We then study the interaction between two identical chiral metamaterial slabs with and without substrate. For no substrate, the finite thickness of the slabs $D$ does not influence significantly the repulsive character of the force at short distances, while the attractive character at large distances becomes weaker and behaves as $1/d^6$; for the Drude metal substrate, the finite thickness of the slabs $D$ does not influence the repulsive force too much at short distances until $D=0.05\lambda_0$.

Tunable Casimir Repulsion with Three-Dimensional Topological Insulators

In this Letter, we show that switching between repulsive and attractive Casimir forces by means of external tunable parameters could be realized with two topological insulator plates. We find two regimes where a repulsive (attractive) force is found at small (large) distances between the plates, canceling out at a critical distance. For a frequency range where the effective electromagnetic action is valid, this distance appears at length scales corresponding to 1 - ϵ(ω) ∼ (2/π)αθ.

Proposal for measurement of repulsive Casimir forces using silicon membranes

AbstractWe present a procedure to measure the Casimir forces, a direct manifestation of boundary dependence of quantum vacuum due to the alteration by the boundaries of the zero‐point electromagnetic energy, using MEMS. Our approach is based on the measurement of the frequency shift of a silicon membrane caused by Casimir forces. We present theoretically computations of that frequency shift using the Anharmonic Casmir Oscillator model for different experimental configurations. Our main aim is to measure the repulsive Casimir forces using geometric approach and use these repulsive forces to minimize the sticktion of MEMS. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparison of chiral metamaterial designs for repulsive Casimir force

In our previous work [Phys. Rev. Lett. 103, 103602 (2009)], we found that repulsive Casimir forces could be realized by using chiral metamaterials if the chirality is strong enough. In this work, we check four different chiral metamaterial designs (i.e., Twisted-Rosettes, Twisted-Crosswires, Four-U-SRRs, and Conjugate-Swastikas) and find that the designs of Four-U-SRRs and Conjugate-Swastikas are the most promising candidates to realize repulsive Casimir force because of their large chirality and the small ratio of structure length scale to resonance wavelength.

Repulsive Casimir forces between solid materials with high-refractive-index intervening liquids

In order to explore repulsive Casimir/van der Waals forces between solid materials with liquid as the intervening medium, we analyze dielectric data for a wide range of materials as for example PTFE, polystyrene, silica and more than twenty liquids. Although significant variation in the dielectric data from different sources exist, we provide a scheme based on measured static dielectric constants, refractive indices, and applying Kramers Kronig (KK) consistency to dielectric data to create accurate dielectric functions at imaginary frequencies. The latter is necessary for more accurate force calculations via the Lifshitz theory allowing reliable predictions of repulsive Casimir forces.

Nontouching Nanoparticle Diclusters Bound by Repulsive and Attractive Casimir Forces

We present a scheme for obtaining stable Casimir suspension of dielectric nontouching objects immersed in a fluid, validated here in various geometries consisting of ethanol-separated dielectric spheres and semi-infinite slabs. Stability is induced by the dispersion properties of real dielectric (monolithic) materials. A consequence of this effect is the possibility of stable configurations (clusters) of compact objects, which we illustrate via a molecular two-sphere dicluster geometry consisting of two bound spheres levitated above a gold slab. Our calculations also reveal a strong interplay between material and geometric dispersion, and this is exemplified by the qualitatively different stability behavior observed in planar versus spherical geometries.

Quantum Levitation of Graphene Sheet by Repulsive Casimir Forces

We calculate the repulsive Casimir force between a single graphene sheet and a metamaterial slab whose magnetic permeability is expressed by using the Lorentz model, focusing on the possibility of realizing quantum levitation. It is shown that the graphene sheet can be levitated by the repulsive Casimir force because of the very small density of the graphene sheet. The levitation height depends on the magnetic properties of the metamaterial slab, and this height reaches the micrometer range when metamaterials with large permeabilities are used. The possibility of observing quantum levitation in vacuum is also considered. [DOI: 10.1380/ejssnt.2010.57]

Repulsive Casimir forces and the role of surface modes

The Casimir repulsion between a metal and a dielectric suspended in a liquid has been thoroughly studied in recent experiments. In the present paper we consider surface modes in three layered systems modeled by dielectric functions guaranteeing repulsion. It is shown that surface modes play a decisive role in this phenomenon at short separations. For a toy plasma model we find the contribution of the surface modes at all distances.

Repulsive Casimir Force in Chiral Metamaterials

We demonstrate theoretically that one can obtain repulsive Casimir forces and stable nanolevitations by using chiral metamaterials. By extending the Lifshitz theory to treat chiral metamaterials, we find that a repulsive force and a minimum of the interaction energy possibly exist for strong chirality, under realistic frequency dependencies and correct limiting values (for zero and infinite frequencies) of the permittivity, permeability, and chiral coefficients.

Stable Suspension and Dispersion-Induced Transitions from Repulsive Casimir Forces Between Fluid-Separated Eccentric Cylinders

We numerically demonstrate a stable mechanical suspension of a silica cylinder within a metallic cylinder separated by ethanol, via a repulsive Casimir force between the silica and the metal. We investigate cylinders with both circular and square cross sections, and show that the latter exhibit a stable orientation as well as a stable position, via a method to compute Casimir torques for finite objects. Furthermore, the stable orientation of the square cylinder undergoes a 45 degrees transition as the separation length scale is varied, which is explained as a consequence of material dispersion.

Crossover from Attractive to Repulsive Casimir Forces and Vice Versa

Systems described by an O(n) symmetrical varphi;{4} Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes B_{j}, j=1,2, are investigated as functions of film thickness L for generic symmetry-preserving boundary conditions partial differential_{n}phi=c[over composite function]_{j}phi. The L-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form f_{res} approximately D(c_{1}L;{Phi/nu},c_{2}L;{Phi/nu})/L;{d-1} when d<4, where c_{i} are scaling fields associated with the variables c[over composite function]_{i} and Phi is a surface crossover exponent. Explicit two-loop renormalization group results for the function D(c_{1},c_{2}) at d=4- dimensions are presented. These show that (i) the Casimir force can have either sign, depending on c_{1} and c_{2}, and (ii) for appropriate choices of the enhancements c[over composite function]_{j}, crossovers from attraction to repulsion and vice versa occur as L increases.

Repulsive and attractive Casimir forces in a glide-symmetric geometry

We describe a three-dimensional geometry in which both attractive and repulsive Casimir forces arise using ordinary metallic materials, as computed via an exact numerical method (no uncontrolled approximations). The geometry consists of a zipperlike, glide-symmetric structure formed of interleaved metal brackets attached to parallel plates---because of the interleaving pattern, a net repulsive force can arise from a combination of attractive interactions. Depending on the separation, the perpendicular force between the plates and brackets varies from attractive (large separations) to repulsive (intermediate distances) and back to attractive (close separations), with one point of stable equilibrium in the perpendicular direction. This geometry was motivated by a simple intuition of attractive interactions between surfaces, and so we also consider how a rough proximity-force approximation of pairwise attractions compares to the exact calculations.

Influence of negative refractive index materials on repulsive Casimir forces

The influence of negative refractive index materials on repulsive Casimir forces is studied. The repulsive Casimir interaction is determined by the electric and magnetic properties of the material slabs and the intermediate medium. Through theoretical analysis and numerical calculation, the condition for obtaining repulsive forces is presented. For the negative refractive index materials described by dispersive permittivity and permeability of Drude-Lorentz type, repulsive Casimir force can be realized by tuning the characteristic frequencies.

Repulsive and attractive critical Casimir forces

When confining vacuum fluctuations between two identical walls, the Casimir force manifests itself as a mutual attraction of the walls. When confining concentration fluctuations of a binary liquid mixture, an analogous force should exist near the critical temperature T C ; it is called the critical Casimir force. Here we show experimentally that this purely entropic force can be either attractive or repulsive, depending on the boundary conditions for the fluctuations. For symmetrical boundary conditions an attractive force is found while asymmetrical ones lead to a repulsive force. This is observed directly by confining the fluctuations in a thin ( ≈ 100 A ˚ ) wetting film. Depending on the boundary conditions either a thinning or a thickening of the film is observed when T → T C .

Vacuum energy and repulsive Casimir forces in quantum star graphs

Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive. We present three scenarios in which that is not true. Two of these depend on mixing two types of boundary conditions. The other, however, is a simple type of quantum graph in which the sign of the force depends upon the number of edges.

Casimir Forces and Quantum Electrodynamical Torques: Physics and Nanomechanics

This paper discusses recent developments on quantum electrodynamical (QED) phenomena, such as the Casimir effect, and their use in nanomechanics and nanotechnology in general. Casimir forces and torques arise from quantum fluctuations of vacuum or, more generally, from the zero-point energy of materials and their dependence on the boundary conditions of the electromagnetic fields. Because the latter can be tailored, this raises the interesting possibility of designing QED forces for specific applications. After a concise review of the field in an historical perspective, high precision measurements of the Casimir force using microelectromechanical systems (MEMS) technology and applications of the latter to nonlinear oscillators are presented, along with a discussion of its use in nanoscale position sensors. Then, experiments that have demonstrated the role of the skin-depth effect in reducing the Casimir force are presented. The dielectric response of materials enters in a nonintuitive way in the modification of the Casimir-Lifshitz force between dielectrics through the dielectric function at imaginary frequencies epsiv(ixi). The latter is illustrated in a dramatic way by experiments on materials that can be switched between a reflective and a transparent state (hydrogen switchable mirrors). Repulsive Casimir forces between solids separated by a fluid with epsiv(ixi) intermediate between those of the solids over a large frequency range is discussed, including ongoing experiments aimed at its observation. Such repulsive forces can be used to achieve quantum floatation in a virtually frictionless environment, a phenomenon that could be exploited in innovative applications to nanomechanics. The last part of the paper deals with the elusive QED torque between birefringent materials and efforts to observe it. We conclude by highlighting future important directions

Repulsive Casimir forces produced in rectangular cavities: possible measurements and applications

We perform a theoretical analysis of a setup intended to measure the repulsive(outward) Casimir forces predicted to exist inside of perfectly conducting rectangular cavities. We consider the roles of the conductivity of the real metals, of the temperature and surface roughness. The possible use of this repulsive force to reduce friction and wear in micro and nanoelectromechanical systems (MEMS and NEMS) is also considered.