Casimir-Polder force between anisotropic nanoparticles and gently curved surfaces

Abstract

The Casimir-Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO2 and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curvature, temperature, as well as material properties.

Classical Casimir interaction of a perfectly conducting sphere and plate

“…It is worth stressing that the NTLO correction predicted by the DE is also in full agreement with the short distance expansion of the exact sphere-plate and sphere-sphere classical Casimir energies both for Dr bc [19] as well as for P bc in four Euclidean dimensions [20]. The DE has been also used to study curvature effects in the Casimir-Polder interaction of a particle with a gently curved surface [30,31]. The same method has been used very recently to estimate the shifts of the rotational levels of a diatomic molecule due to its van der Waals interaction with a curved dielectric surface [32].…”

Exact Casimir interaction of perfectly conducting three-spheres in four euclidean dimensions

“…The DE for a D and N scalar at zero and finite temperature in any number of space-time dimensions was worked out in [30], while the experimentally important case of dielectric curved surfaces at finite temperature is presented in [31]. The DE has been also used to study curvature effects in the Casimir-Polder interaction of a particle with a gently curved surface [32,33]. The same method has been used very recently to estimate the shifts of the rotational levels of a diatomic molecule due to its van der Waals interaction with a curved dielectric surface [34].…”

Spectroscopic probe of the van der Waals interaction between polar molecules and a curved surface

“…Here we show that a derivative expansion can be used to obtain the asymptotic small-distance form ofḠ (S) ij (d, st ) for any gently curved dielectric surface. The derivative expansion has been recently applied successfully to estimate curvature corrections to the Casimir interaction between two gently curved surfaces [18][19][20], and to the CP interaction of a nanoparticle with a curved surface [5,6]. Here, we apply it to the CP interaction of a quantum particle with a surface.…”

“…[5,6], and based on the following: The derivative expansion in Eqs. (12) and (13) is valid for surfaces of small slope, i.e., for d/R 1 where R is a characteristic radius of curvature.…”