Lateral Casimir-Polder force with corrugated surfaces

TL;DR

This paper derives the first-order lateral Casimir-Polder force on an atom near a corrugated surface using a scattering approach, highlighting the limitations of common approximations and proposing a measurement method to observe quantum vacuum effects.

Contribution

It introduces a first-order exact calculation of the lateral Casimir-Polder force considering realistic material effects and compares it with traditional approximation methods.

Findings

Proximity force approximation overestimates the force.

Pairwise summation underestimates the force.

Frequency shift measurements can demonstrate geometrical quantum vacuum effects.

Abstract

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.