Force on a neutral atom near conducting microstructures

We derive the nonretarded energy shift of a neutral atom for two different geometries. For an atom close to a cylindrical wire we find an integral representation for the energy shift, give asymptotic expressions, and interpolate numerically. For an atom close to a semi-infinite half plane we determine the exact Green’s function of the Laplace equation and use it to derive the exact energy shift for an arbitrary position of the atom. These results can be used to estimate the energy shift of an atom close to etched microstructures that protrude from substrates.

Figure 1

An illustration of the geometry of the dipole near a wire. The radius of the wire is $R$, and the distance of the dipole from the center of the wire is $\rho$.

Figure 2

The energy shift due to the $z$ component of the atomic dipole, multiplied by $d^3$, where $d$ is the distance of the dipole to the surface of the wire. The solid line is the exact expression calculated numerically, the dot-dashed line is the $m=0$ term alone, and the dashed line is the $m=0$ term plus the single integral derived through the uniform asymptotic approximation for the Bessel functions, Eq. (20c). The cross on the vertical axis gives the exact value for $d\to 0$.

Figure 3

Same as Fig. 2 but for the energy shift due to the $\rho$ component of the atomic dipole. The solid line is the exact expression calculated numerically, the dot-dashed line is the $m=0$ term alone, and the dashed line is the $m=0$ term plus the single integral derived through the uniform asymptotic approximation for the Bessel functions, Eq. (20a).

Figure 4

Same as Fig. 2 but for the energy shift due to the $\varphi$ component of the atomic dipole. The solid line is the exact expression calculated numerically, the dot-dashed line is the $m=1$ term alone, and the dashed line is the single integral derived through the uniform asymptotic approximation for the Bessel functions, Eq. (20b).

Figure 5

An illustration of the geometry of a dipole near a semi-infinite half plane. The distance of the dipole from the edge is $\rho$, and from the surface of the plane it is $\rho \sin \varphi$.