Casimir-Polder interaction between an atom and a small magnetodielectric sphere

On the basis of macroscopic quantum electrodynamics and point-scattering techniques, we derive a closed expression for the Casimir-Polder force between a ground-state atom and a small magnetodielectric sphere in an arbitrary environment. To allow for the presence of both bodies and media, local-field corrections are taken into account. Our results are compared with the known van der Waals force between two ground-state atoms. To continuously interpolate between the two extreme cases of a single atom and a macroscopic sphere, we also derive the force between an atom and a sphere of variable radius that is embedded in an Onsager local-field cavity. Numerical examples illustrate the theory.

Figure 1

Models of polarizable systems: (i) neutral arrangement of point charges (atom), (ii) cluster of atoms, (iii) dielectric sphere inside medium, (iv) atom in empty cavity surrounded by medium (Onsager real-cavity model), and (v) dielectric sphere in empty cavity surrounded by medium.

Figure 2

(i) Green tensor of the combined system of magnetodielectric sphere and arbitrary background environment and (ii) Green tensor of the same system without the sphere.

Figure 3

CP potential $U(r_{\mathit{AS}})$ of a nonmagnetic atom in front of a dielectric sphere in an empty cavity embedded in bulk material vs. $q=R/R_{\mathrm{C}}$ for different atom-sphere separations, $r_{\mathit{AS}}{\omega }_{10}/c$. Other parameters are ${\omega }_T/{\omega }_{10}=1.03$, ${\omega }_{\mathit{TS}}/{\omega }_{10}=1.0$, ${\omega }_{\mathit{PS}}/{\omega }_{10}=6.0$, ${\omega }_P/{\omega }_{10}=0.1$, and ${\gamma }_{(S)}/{\omega }_{10}=0.001$.

Figure 4

$U(r_{\mathit{AS}})$ vs. $r_{\mathit{AS}}{\omega }_{10}/c$ for different ratios $q$. Other parameters are the same as in Fig. 3.