Modified atomic decay rate near absorptive scatterers at finite temperature

The change in the decay rate of an excited atom that is brought about by extinction and thermal-radiation effects in a nearby dielectric medium is determined from a quantum-mechanical model. The medium is a collection of randomly distributed thermally excited spherical scatterers with absorptive properties. The modification of the decay rate is described by a set of correction functions for which analytical expressions are obtained as sums over contributions from the multipole moments of the scatterers. The results for the modified decay rate as a function of the distance between the excited atom and the dielectric medium show the influence of absorption, scattering and thermal-radiation processes. Some of these processes are found to be mutually counteractive. The changes in the decay rate are compared to those following from an effective-medium theory in which the discrete scatterers are replaced by a continuum.

Figure 1

Decay-rate correction function $F_{\perp }\left(\zeta \right)$ (with $\zeta =kr)$ for cold scatterers and its constituents $F_{d,\perp }\left(\zeta \right)$ $\left(---\right)$ and $F_{r,\perp }\left(\zeta \right)$ $\left(–––\right)$ for a spherical domain with dimensionless radius $kR=6$ containing cold absorbing spheres of dimensionless radius $ka=0.5$ and dielectric constant $\varepsilon =3.0+0.5i$.

Figure 2

Decay-rate correction function $F_{\perp }\left(\zeta \right)$ for cold scatterers and its constituents $F_{d,\perp }\left(\zeta \right)$ $\left(---\right)$ and $F_{r,\perp }\left(\zeta \right)$ $\left(–––\right)$ for $kR=6,ka=0.5$, and $\varepsilon =3.0+0.1i$.

Figure 3

Decay-rate correction function $F_{\perp }\left(\zeta \right)$ for cold scatterers and its constituents $F_{d,\perp }\left(\zeta \right)$ $\left(---\right)$ and $F_{r,\perp }\left(\zeta \right)$ $\left(–––\right)$ for $kR=6,ka=0.5$, and $\varepsilon =3.0+0.01i$.

Figure 4

Total decay-rate correction function $F_{\perp }\left(\zeta \right)$ for scatterers at finite temperature and its constituents $[e^{\beta \hslash \omega }/(e^{\beta \hslash \omega }-1)]F_{d,\perp }\left(\zeta \right)$ $\left(---\right)$ and $F_{r,\perp }\left(\zeta \right)$ $\left(–––\right)$, for $kR=6,ka=0.5,\varepsilon =3.0+0.5i$, and $\beta \hslash \omega =1$.

Figure 5

Decay-rate correction function $F_{\parallel }\left(\zeta \right)$ for cold scatterers and its constituents $F_{d,\parallel }\left(\zeta \right)$ $\left(---\right)$ and $F_{r,\parallel }\left(\zeta \right)$ $\left(–––\right)$ for $kR=6,ka=0.5$, and $\varepsilon =3.0+0.5i$.

Figure 6

Total decay-rate correction function $F_{\parallel }\left(\zeta \right)$ for scatterers at finite temperature and its constituents $[e^{\beta \hslash \omega }/(e^{\beta \hslash \omega }-1)]F_{d,\parallel }\left(\zeta \right)$ $\left(---\right)$ and $F_{r,\parallel }\left(\zeta \right)$ $\left(–––\right)$ for $kR=6,ka=0.5,\varepsilon =3.0+0.5i$, and $\beta \hslash \omega =1$.

Figure 7

Comparison of the decay-rate correction function $F_{\perp }^{\left(\mathrm{eff}\right)}\left(\zeta \right)$ (—) for a cold effective medium and its constituents $F_{d,\perp }^{\left(\mathrm{eff}\right)}\left(\zeta \right)$ $\left(---\right)$, $F_{r,\perp }^{\left(\mathrm{eff}\right)}\left(\zeta \right)$ $\left(–––\right)$ with their scattering-medium counterparts $F_{\perp }\left(\zeta \right),F_{d,\perp }\left(\zeta \right),F_{r,\perp }\left(\zeta \right)$ $\left(······\right)$ for cold scatterers, as taken from Fig. 2, for $kR=6,ka=0.5$, and $\varepsilon =3.0+0.1i$.