Complex orientation dependence of Casimir-Polder interaction induced by curvature and optical properties of the surface and the surrounding medium

TL;DR

The paper addresses how curvature and material properties of magneto-dielectric surfaces affect the Casimir-Polder interaction with small anisotropic particles. It develops a multiple scattering expansion (MSE) framework to derive curvature corrections to first order in $d/R_j$ and proves a controlled small-slope expansion that accounts for material responses beyond perfect conductors. The key findings show that surface curvature can both induce and remove preferred particle orientations, with the effect depending on the surrounding medium and temperature, and that thermal fluctuations can wash out quantum orientation switches at higher temperatures. The work provides a principled route to engineer nano-particle orientation near surfaces, with implications for the design of micro- and nano-mechanical devices through a tunable combination of geometry, materials, and temperature.

Abstract

We employ a multiple scattering expansion to systematically derive curvature corrections to the Casimir-Polder (CP) interaction between small an-isotropic particles and general magneto-dielectric surfaces. Our results, validated against exact solutions, reveal a complex, distance-dependent interplay between material properties and surface curvature in determining stable particle orientations. We demonstrate that even small surface curvature can induce or eliminate switches in the preferred orientation, a quantum effect that is diminished by thermal fluctuations. This work provides a crucial understanding of how to engineer nano-particle orientation through tune-able parameters, offering significant implications for micro- and nano-mechanical device design.

Figures (7)

• Figure 1: This figure illustrates the configuration of a small ellipsoidal particle positioned near a gently curved surface. The solid curves on surface $S$ at point $P$ represent the principal directions. The corresponding local radii of curvature, $R_1$ and $R_2$ are positive when the surface curves towards the particle and negative when it curves away.
• Figure 2: Ratio of the curvature expansion of the CP potential $U_k$ up to the k-th power of $d/R$ to the exact potential $U_\text{sphere}$ for an Au sphere of radius $R=30\mu$m at $T=300K$ versus the normalized distance $d/R$.
• Figure 3: Typical surface shapes corresponding to different combinations of $d/R_1$ and $d/R_2$. The coordinate frames indicate the position and orientation of the particle.
• Figure 4: Stability diagram for Au surface in vacuum at $T=0$ K: For a flat surface ($d/R_1=d/R_2=0$) a disk-like (needle-like) particle positions itself with the symmetry axis parallel (perpendicular) to the surface at all distances $d$. For a curved surface, the stable direction can change with distance, depending on the radii of surface curvature.
• Figure 5: Stability diagram for Au surface in Br at $T=0$ K: For a flat surface ($d/R_1=d/R_2=0$) the preferred orientation can change twice with distance, depending on the details of the particle's polarizability: A disk-like (needle-like) particle tends to position itself with the symmetry axis perpendicular (parallel) to the surface at intermediate distances $d$. For a curved surface, the one or both orientation switches can be eliminated, depending on curvature magnitude.