Vacuum force on an atom in a magnetodielectric cavity

We demonstrate that, according to a recently suggested Lorentz-force approach to the Casimir effect, the vacuum force on an atom embedded in a material cavity differs substantially from the force on an atom of the cavity medium. The force on an embedded atom is of the familiar (van der Waals and Casimir-Polder) type, however, more strongly modified by the cavity medium than usually considered. The force on an atom of the cavity medium is of the medium-assisted force type with rather unusual properties, as demonstrated very recently [M. S. Tomaš, Phys. Rev. A 71, 060101(R) (2005)]. This implies similar properties of the vacuum force between two atoms in a medium.

Figure 1

A slab in a planar cavity shown schematically. The (complex) refraction index of the slab is $n_s\left(\omega \right)=\sqrt{{\epsilon }_s\left(\omega \right){\mu }_s\left(\omega \right)}$ and that of the cavity $n\left(\omega \right)=\sqrt{\epsilon \left(\omega \right)\mu \left(\omega \right)}$. The cavity walls are described by their reflection coefficients $r_1^q(\omega ,k)$ and $r_2^q(\omega ,k)$, with $k$ being the in-plane wave vector of a wave. The arrow indicates the direction of the force on the slab.