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Register a new userCorrected Proximity-Force Approximation for Lateral Casimir Forces
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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 also study the PFA for gradient gratings, and we find that the inhomogeneity-induced lateral Casimir force is beyond the corrected PFA.
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We predict the existence of lateral drag forces near the flat surface of an absorbing slab of an anisotropic material. The forces originate from the fluctuations of the electromagnetic field, when the anisotropy axis of the material forms a certain angle with the surface. In this situation, the spatial spectra of the fluctuating electromagnetic fields becomes asymmetric, different for positive and negative transverse wave vectors components. Differently from the case of van der Waals interactions in which the forward-backward symmetry is broken due to the particle movement or in quantum noncontact friction where it is caused by the mutual motion of the bodies, in our case the lateral motion results merely from the anisotropy of the slab. This new effect, of particular significance in hyperbolic materials, could be used for the manipulation of nanoparticles.
We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference implementation of this approach, we obtain both agreement with past results for cylinder-plate geometries, and also present results for new geometries. In particular, we examine a piston-like problem involving two dielectric and metallic squares sliding between two metallic walls, in two and three dimensions, respectively, and demonstrate non-additive and non-monotonic changes in the force due to these lateral walls.
Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general Lifshitz configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capassos group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations where repulsion could be achieved between ordinary conducting and dielectric bodies in vacuum. The status of the field of Casimir repulsion with emphasis on recent developments will be surveyed. Here, stress will be placed on analytic developments, especially of Casimir-Polder (CP) interactions between anisotropically polarizable atoms, and CP interactions between anisotropic atoms and bodies that also exhibit anisotropy, either because of anisotropic constituents, or because of geometry. Repulsion occurs for wedge-shaped and cylindrical conductors, provided the geometry is sufficiently asymmetric, that is, either the wedge is sufficiently sharp or the atom is sufficiently far from the cylinder.
Lateral Casimir force near a laterally-inhomogeneous plate is first revealed by both rigorous simulations and proximity approximations. The inhomogeneity-induced lateral Casimir force provides a novel method to control the lateral motion of nano-objects above the plate, and makes source-free manipulations of them possible. When incorporated with the Casimir repulsion in a fluid, the lateral Casimir force is shown to dominate over Brownian motion and enables long-distance quantum propulsion and firm quantum trapping of nano-objects. Gratings of varying filling factors to mimic micro-scale inhomogeneity also confirm those effects. The idea to design asymmetric distributions of nano-structures paves the way to sophisticated tailoring of the lateral Casimir force.
We derive the lateral Casimir-Polder force on a ground state atom on top of a corrugated surface, up to first order in the corrugation amplitude. Our calculation is based on the scattering approach, which takes into account nonspecular reflections and polarization mixing for electromagnetic quantum fluctuations impinging on real materials. We compare our first order exact result with two commonly used approximation methods. We show that the proximity force approximation (large corrugation wavelengths) overestimates the lateral force, while the pairwise summation approach underestimates it due to the non-additivity of dispersion forces. We argue that a frequency shift measurement for the dipolar lateral oscillations of cold atoms could provide a striking demonstration of nontrivial geometrical effects on the quantum vacuum.
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