Isotope shifts of naturalSr+measured by laser fluorescence in a sympathetically cooled Coulomb crystal

Abstract

We measured by laser spectroscopy the isotope shifts between naturally occurring even isotopes of strontium ions for both the $5s\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ (violet) and the $4d\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}\ensuremath{\rightarrow}5p\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ (infrared) dipole-allowed optical transitions. Fluorescence spectra were taken by simultaneous measurements on a two-component Coulomb crystal in a linear Paul trap containing ${10}^{3}$--${10}^{4}$ laser-cooled ${\mathrm{Sr}}^{+}$ ions. The isotope shifts are extracted from the experimental spectra by fitting the data with the analytical solution of the optical Bloch equations describing a three-level atom interacting with two laser beams. This technique allowed us to increase the precision with respect to previously reported data obtained by optogalvanic spectroscopy or fast atomic-beam techniques. The results for the $5s\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ transition are ${\ensuremath{\nu}}_{88}\ensuremath{-}{\ensuremath{\nu}}_{84}=+378(4)$ MHz and ${\ensuremath{\nu}}_{88}\ensuremath{-}{\ensuremath{\nu}}_{86}=+170(3)$ MHz, in agreement with previously reported measurements. In the case of the previously unexplored $4d\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}\ensuremath{\rightarrow}5p\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ transition we find ${\ensuremath{\nu}}_{88}\ensuremath{-}{\ensuremath{\nu}}_{84}=\ensuremath{-}828(4)$ MHz and ${\ensuremath{\nu}}_{88}\ensuremath{-}{\ensuremath{\nu}}_{86}=\ensuremath{-}402(2)$ MHz. These results provide more data for stringent tests of theoretical calculations of the isotope shifts of alkali-metal-like atoms. Moreover, they simplify the identification and the addressing of ${\mathrm{Sr}}^{+}$ isotopes for ion frequency standards or quantum-information-processing applications in the case of multi-isotope ion strings.