Quadrupole transitions near an interface: General theory and application to an atom inside a planar cavity

Quadrupole radiation of an atom in an arbitrary environment is investigated within classical as well as quantum electrodynamical approaches. Analytical expressions for decay rates are obtained in terms of the Green’s function of Maxwell equations. The equivalence of both approaches is shown. General expressions are applied to analyze the quadrupole decay rate of an atom placed between two half spaces with arbitrary dielectric constant. It is shown that in the case where the atom is close to the surface, the total decay rate is inversely proportional to the fifth power of distance between an atom and a plane interface.

Figure 1

Some kinds of quadrupoles and the corresponding quadrupole momentum tensors.

Figure 2

Geometry of the problem of quadrupole radiation of an atom placed in a planar cavity.

Figure 3

Contours of integration in the case of ideally conducting mirrors.

Figure 4

The quadrupole decay rates of different quadrupoles versus their position in the case of a hypothetic material with $ϵ=-200+0.1i$, and in the case of an ideal conductivity (dotted line).

Figure 5

The quadrupole decay rates of different quadrupoles versus their position between two thick silver ($\mathrm{Ag}:ϵ=-15.37+0.231i$, $\lambda =632.8\mathrm{nm}$ [22]) mirrors (dotted lines correspond to the case of the ideally conducting walls).

Figure 6

The spontaneous decay rates of different quadrupoles versus their position between two quartz half-spaces with $ϵ=2.1+0.000000001i$ (silica) in the case of a microresonator $(kL=10)$.

Figure 7

The spontaneous decay rates of different quadrupoles versus their position between two quartz half-spaces with $ϵ=2.1+0.000000001i$ (silica) in the case of a nanoresonator $(kL=1)$.