Casimir effect between ponderable media as modeled by the standard model extension

TL;DR

This paper investigates how Lorentz-violating modifications to Maxwell's electrodynamics influence the Casimir effect between media, revealing novel phenomena like a non-trivial Kerr effect and vacuum phase interactions.

Contribution

It derives the modified Fresnel coefficients and computes the Casimir energy density considering Lorentz violation, including effects on vacuum phases and force directions.

Findings

Casimir energy density is affected by Lorentz-violating coefficients.

The Casimir force can be positive, zero, or negative depending on LV coefficients.

New effects such as a non-trivial Kerr effect and vacuum phase interactions are observed.

Abstract

The CPT-even sector of the standard model extension amounts to extending Maxwell electrodynamics by a gauge invariant term of the form $- \frac{1}{4} (k _{F}) _{\alpha \beta \mu \nu} F ^{\alpha \beta} F ^{\mu \nu}$, where the Lorentz-violating (LV) background tensor $(k _{F}) _{\alpha \beta \mu \nu}$ possesses the symmetries of the Riemann tensor. The electrodynamics in ponderable media is still described by Maxwell equations in matter with modified constitutive relations which depend on the coefficients for Lorentz violation. We study the effects of this theory on the Casimir force between two semi-infinite ponderable media. The Fresnel coefficients characterizing the vacuum-medium interface are derived, and with the help of these, we compute the Casimir energy density. At leading-order in the LV coefficients, the Casimir energy density is numerically evaluated and successfully compared with the standard result. We also found a variety of intriguing effects, such as a non-trivial Kerr effect and the Casimir effect between two phases of the electromagnetic vacuum. We consider a bubble of Lorentz-symmetric (Maxwell) vacuum embedded in the infinite Lorentz-violating vacuum, and we calculate the Casimir energy at leading order, which in this case is quadratic in the LV coefficients. The Casimir force can be positive, zero, or negative, depending on the relative strengths between the LV coefficients.