Scalar Casimir-Polder forces for uniaxial corrugations

TL;DR

This paper studies the Casimir-Polder forces between an atom and a uniaxially corrugated surface using a nonperturbative numerical approach, revealing universal behavior at large distances due to averaging over surface structures.

Contribution

It introduces a fully nonperturbative method to compute Casimir-Polder forces for arbitrary uniaxial corrugations, including sinusoidal and sawtooth profiles, and analyzes their universal large-distance behavior.

Findings

Up to order-one anomalous dimensions at small and intermediate scales.

Universal regime at larger distances due to averaging effects.

Method applicable to various uniaxial corrugation profiles.

Abstract

We investigate the Dirichlet-scalar equivalent of Casimir-Polder forces between an atom and a surface with arbitrary uniaxial corrugations. The complexity of the problem can be reduced to a one-dimensional Green's function equation along the corrugation which can be solved numerically. Our technique is fully nonperturbative in the height profile of the corrugation. We present explicit results for experimentally relevant sinusoidal and sawtooth corrugations. Parameterizing the deviations from the planar limit in terms of an anomalous dimension which measures the power-law deviation from the planar case, we observe up to order-one anomalous dimensions at small and intermediate scales and a universal regime at larger distances. This large-distance universality can be understood from the fact that the relevant fluctuations average over corrugation structures smaller than the atom-wall distance.