The general perturbative expression for the lateral Casimir force between two plates covered by longitudinal corrugations of arbitrary shape is obtained. This expression is applicable for corrugation periods larger than the separation distance. The cases of asymmetric corrugations are considered, which allow to increase the maximum to minimum force ratio and affect the character of equilibrium points. This opens new opportunities to control the lateral Casimir forces for use in microelectromechanical devices based entirely on the vacuum fluctuation properties.
We study the van der Waals (vdW) interaction between a polarizable particle and a grounded conducting corrugated surface. For sinusoidal corrugations, one knows that, under the action of the lateral vdW force, an isotropic particle is always attracted to the nearest corrugation peak, with such behavior called in the present paper as peak regime. Here, considering an anisotropic polarizable particle, and making analytical calculations valid beyond the proximity force approximation (PFA), we show that the attraction is not only toward the peaks, but, for certain particle orientations and distanc…
Lateral Casimir force between sinusoidally corrugated surfaces: Asymmetric profiles, deviations from the proximity force approximation and comparison with exact theory
We examine the lateral Casimir-Polder force acting on a circular rotating emitter near a dielectric plane surface. As the circular motion breaks time-reversal symmetry, the spontaneous emission in a direction parallel to the surface is in general anisotropic. We show that a lateral force arises which can be interpreted as a recoil force because of this asymmetric emission. The force is an oscillating function of the distance between the emitter and the surface, and the lossy character of the dielectric strongly influences the results in the near-field regime. The force exhibits also a populati…
The widely-adopted proximity-force approximation (PFA) to estimate normal Casimir forces is known to be asymptotically exact at vanishing separations. In this letter, we propose a correction to the PFA, which is sufficiently accurate in predicting displacement-induced lateral Casimir forces between a sphere and a grating, for separation-to-radius ratio up to 0.5, far beyond the limit within which the application of PFA is previously restricted. Our result allows convenient estimation of Casimir interactions and thus shall be useful in relevant experimental and engineering Casimir applications.…
We study the lateral Casimir force experienced by a particle that rotates near a planar surface. The origin of this force lies in the symmetry breaking induced by the particle rotation in the vacuum and thermal fluctuations of its dipole moment, and, therefore, in contrast to lateral Casimir forces previously described in the literature for corrugated surfaces, it exists despite the translational invariance of the planar surface. Working within the framework of fluctuational electrodynamics, we derive analytical expressions for the lateral force and analyze its dependence on the geometrical an…
We consider a perfectly conducting infinite cylinder with radius $R$, and investigate the Casimir-Polder (CP) and van der Waals (vdW) interactions with a neutral polarizable particle constrained to move in a plane distant $x_0>R$ from the axis of the cylinder. We show that when the relative curvature $x_0/R \lesssim 6.44$, this particle, under the action of the lateral CP force (which is the projection of the CP force onto the mentioned plane), is attracted to the point on the plane which is closest to the cylinder surface. On the other hand, when $x_0/R \gtrsim 6.44$, we also show that, for c…
Van der Waals forces between atoms and molecules are universally assumed to act along the line separating them. Inspired by recent works on effects which can propel atoms parallel to a macroscopic surface via the Casimir--Polder force, we predict a lateral van der Waals force between two atoms, one of which is in an excited state with non-zero angular momentum and the other is isotropic and in its ground state. The resulting force acts in the same way as a planetary gear, in contrast to the rack-and-pinion motion predicted in works on the lateral Casimir--Polder force in the analogous case, fo…
We show that an isotropic dipolar particle in the vicinity of a substrate made of nonreciprocal plasmonic materials can experience a lateral Casimir force and torque when the particle's temperature differs from that of the slab and the environment. We connect the existence of the lateral force to the asymmetric dispersion of nonreciprocal surface polaritons and the existence of the lateral torque to the spin-momentum locking of such surface waves. Using the formalism of fluctuational electrodynamics, we show that the features of lateral force and torque should be experimentally observable usin…
In a recent paper, it was shown that, under the action of the lateral van der Waals (vdW) force due to a perfectly conducting corrugated surface, a neutral anisotropic polarizable particle in vacuum can be attracted not only to the nearest corrugation peak, but also to a valley, or an intermediate point between a peak and a valley, with such behaviors called peak, valley and intermediate regimes, respectively. In the present paper, we investigate how these regimes are affected by the consideration of two non-dispersive semi-infinite dielectrics $ε_{1}$ and $ε_{2}$, separated by a corrugated in…
We derive the explicit expression for the Casimir energy between a sphere and a 1D grating, in terms of the sphere and grating reflection matrices, and valid for arbitrary materials, sphere radius, and grating geometric parameters. We then numerically calculate the Casimir energy between a metallic (gold) sphere and a dielectric (fused silica) lamellar grating at room temperature, and explore its dependence on the sphere radius, grating-sphere separation, and lateral displacement. We quantitatively investigate the geometrical dependence of the interaction, which is sensitive to the grating hei…
For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which break time-reversal symmetry. These forces are typically very small, unless the bodies are nearly touching, and consequently such effects have never been observed, although lateral Casimir forces have been seen for corrugated surfaces. Partly because of the lack of contact with phenomena, theoretical predictions for the frictional force between parallel plate…
We consider a single slight protuberance in a perfectly conducting plane, and investigate the van der Waals (vdW) interaction between this surface and a neutral polarizable particle. When the protuberance is sufficiently smooth, so that the proximity force approximation (PFA) is well applicable, for a fixed distance of the particle from the plane, the lateral vdW force always points to the protuberance. On the other hand, by making calculations valid beyond the PFA, we show that nontrivial geometric effects arise when we consider an anisotropic particle, and manipulate the ratio between the ch…
Atom-surface forces using excited states have a host of compelling applications, including repulsive and lateral forces. However, such states can be fragile and difficult to prepare. Here we report an explicit normal-mode based calculation of the Casimir-Polder potential between a ground-state atom and a non-dispersive surface in the presence of an external quantised field. The potential we derive shares some features with that of excited-state Casimir-Polder forces even though we consider a ground-state atom. Our work provides a physically transparent and intuitive picture of driven Casimir-P…
Casimir-Lifshitz force between moving plates at different temperatures
在[New J. Phys. 11，033035（2009）]中发现了以任意恒定速度彼此平行移动的两个板之间的零温度Casimir-Lifshitz力。这里的解决方案是推广到的情况下，板在不同的温度。Casimir-Lifshitz力通过计算电磁应力张量获得，使用Antezza等人[Phys.Rev.A77，022901（2008）]针对不同温度下的非移动板采用的方法。作用在平板上的垂直力有来自量子真空和热辐射的贡献;这两种贡献都受到运动的影响。除了垂直力之外，来自运动板的热辐射还产生了卡西米尔-李夫希茨力的横向分量，这是一种没有量子真空贡献的效应。零温度的结果被再现，特别是不存在的量子真空摩擦板之间。
