Ab initiocalculations off-orbital electron-phonon interaction in laser cooling

Abstract

Results of ab initio calculation of electron-phonon interaction in laser cooling are reported and compared with the values estimated using analytical harmonic potential approximation. Electronic band-structure changes due to normal-mode ligand displacement are used to find the energy change in $f$-orbital optically active electron at the gamma point. The band-structure calculations show that the partial band structure of Yb is flat, indicating limited interaction with the neighboring atoms. The electron-phonon interaction potential calculated is within a factor 2 (larger) of the value using the harmonic potentials and the difference is attributed to the necessary approximations of each method. Single ligand displacement, which simulates one-phonon propagation, is also used and the resulting electron-phonon interaction potentials are in agreement with those from normal-mode vibration of the entire complex. Using these interaction potentials, larger cooling rates of the ion-host pair are calculated.