Measurement of the hyperfine structure and isotope shifts of the3s23p2 3P2→3s3p3 3D3otransition in silicon

Abstract

The hyperfine structure and isotope shifts of the $3{s}^{2}3{p}^{2} {}^{3}{P}_{2}\ensuremath{\rightarrow}3s3{p}^{3} {}^{3}{D}_{3}^{o}$ transition in silicon have been measured. The transition at 221.7 nm was studied by-laser induced fluorescence in an atomic Si beam. For $^{29}\mathrm{Si}$, the hyperfine $A$ constant for the $3{s}^{2}3{p}^{2} {}^{3}{P}_{2}$ level was determined to be $\ensuremath{-}160.1\ifmmode\pm\else\textpm\fi{}1.3$ MHz ($1\ensuremath{\sigma}$ error), and the $A$ constant for the $3s3{p}^{3} {}^{3}{D}_{3}^{o}$ level is $\ensuremath{-}532.9\ifmmode\pm\else\textpm\fi{}0.6$ MHz. The isotope shifts (relative to the abundant isotope $^{28}\mathrm{Si}$) of the transition were determined to be $1753.3\ifmmode\pm\else\textpm\fi{}1.1$ MHz for $^{29}\mathrm{Si}$ and $3359.9\ifmmode\pm\else\textpm\fi{}0.6$ MHz for $^{30}\mathrm{Si}$. This is an improvement by about two orders of magnitude over a previous isotope shift measurement. From these results we are able to predict the hyperfine structure and isotope shift of the radioactive $^{31}\mathrm{Si}$ atom, which is of interest in building a scalable quantum computer.