Effect of curvature and confinement on the Casimir-Polder interaction

Abstract

Modifications of Casimir-Polder interactions due to confinement inside a cylindrical cavity and due to curvature in-and outside the cavity are studied. We consider a perfectly conducting cylindrical shell with a single particle (atom or macroscopic sphere) located next to its interior or exterior surface, or two atoms placed inside the shell. By employing the scattering approach, we obtain the particle-cavity interaction and the modification of the two-particle interaction due to the cavity. We consider both retardation and thermal effects. While for the atoms a dipole description is sufficient, for the macroscopic sphere we sum (numerically) over many multipole fluctuations to compute the interaction at short separations. In the latter limit we compare to the proximity approximation and a gradient expansion and find agreement. Our results indicate an confinement induced suppression of the force between atoms. General criteria for suppression and enhancement of Casimir interactions due to confinement are discussed.

Interplay of curvature and temperature in the Casimir–Polder interaction

“…In the special case of a spherical atom near a cylindrical metallic shell at T = 0, the above formula is in full agreement with equation ( 30) of [13], as well as with equations ( 25)-( 26) and ( 38)- (39) or [14]. The magnitude of the thermal corrections depends on the component of the polarizability tensor and the order of the curvature correction.…”

“…(38)- (39) or Ref. [14]. The magnitude of the thermal corrections depends on the component of the polarizability tensor and the order of the curvature correction.…”

“…In Refs. [13,14] analytical results were obtained for the case of a perfectly conducting cylinder. A perturbative approach is presented in [15], where surfaces with smooth corrugations of any shape, but with small amplitude, were studied.…”

“…The example of a uniaxially corrugated surface was studied numerically in [11] within a toy scalar field theory, while rectangular dielectric gratings were considered in [12]. In [13,14] analytical results were obtained for the case of a perfectly conducting cylinder. A perturbative approach is presented in [15], where surfaces with smooth corrugations of any shape, but with small amplitude, were studied.…”