One- and Two-Photon Transitions of Atoms in Solids

Abstract

The theory of one- and two-photon transitions between a given pair of impurity levels of the same parity is developed. As is well known, lattice vibrations assist the otherwise forbidden one-photon transition, increasing its intensity with temperature. The two-photon transition rate is shown to have a complementary decrease with increasing temperature. A measurement of both temperature dependences determines the effective frequency and coupling constant for the interaction. The formalism is applied to predicting the two-photon transition rate for the $4{d}^{10}\ensuremath{-}4{d}^{9}5s$ transition of the silver ion in NaCl:Ag. For an experiment using a ruby laser and an ultraviolet beam the maximum absorption coefficient predicted for the ultraviolet beam is $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}48}\mathrm{FN}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ at low temperatures, where $F$ is the flux (photons/${\mathrm{cm}}^{2}$ sec) of the laser and $N$ is the ${\mathrm{Ag}}^{+}$ concentration. This should be within reach of present experimental techniques.