Casimir-Polder interaction between an atom and a dielectric slab

We present an explicit analytic calculation of the energy-level shift of an atom in front of a nondispersive and nondissipative dielectric slab. We work with the fully quantized electromagnetic field, taking retardation into account. We give the shift as a two-dimensional integral and use asymptotic analysis to find expressions for it in various retarded and nonretarded limiting cases. The results can be used to estimate the energy shift of an atom close to layered microstructures.

Figure 1

The geometry of the dielectric slab.

Figure 2

(Color online) By closing the contour $\mathcal{C}$ one can choose a more suitable integration path ${\mathcal{C}}^{\prime }$. In the figure, $\Gamma =\sqrt{n^2-1}/n$.

Figure 3

(Color online) The function $W_{\parallel }^{\text{slab}}$ for various thicknesses of the dielectric slab, with refractive index $n=2$. The uppermost curve is the result for a dielectric half-space, $W_{\parallel }^{\text{HS}}$.

Figure 4

(Color online) The function $W_z^{\text{slab}}$ for various thicknesses of the slab, with refractive index $n=2$. The uppermost curve is for a dielectric half-space, i.e., for $L{E}_{ji}\to \infty$.

Figure 5

(Color online) The function $W_z^{\text{slab}}$ for a slab of thickness $L{E}_{ji}=1$ and various values of the refractive index, $n=1.5,3,5,10$. The uppermost curve $W_z^{\text{PR}}$ is the result for a perfect reflector, i.e., for $n\to \infty$.

Figure 6

(Color online) The function $W_z^{\text{slab}}$ as a function of $L{E}_{ji}$, for an atom located at various fixed distances $\mathcal{Z}{E}_{ji}=1,5,10$ from the surface. The slab has a refractive index of $n=2$.

Figure 7

(Color online) The function $W_z^{\text{slab}}$ as a function of $L{E}_{ji}$, for an atom located at a distance $\mathcal{Z}{E}_{ji}=8$ from the slab and various values for the refractive index $n=1.5,3,5$. In the limit $n\to \infty$ this function approaches a unit step function.