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

We measured by laser spectroscopy the isotope shifts between naturally-occurring even-isotopes of strontium ions for both the $5s\,\,^2S_{1/2}\to 5p\,\,^2P_{1/2}$ (violet) and the $4d\,\,^2D_{3/2}\to 5p\,\,^2P_{1/2}$ (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 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 in interaction 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 $5s\,\,^2S_{1/2}\to 5p\,\,^2P_{1/2}$ transition are $\nu_{88}-\nu_{84}=+378(4)$~MHz and $\nu_{88}-\nu_{86}=+170(3)$~MHz, in agreement with previously reported measurements. In the case of the previously unexplored $4d\,\,^2D_{3/2}\to 5p\,\,^2P_{1/2}$ transition we find $\nu_{88}-\nu_{84}=-828(4)$~MHz and $\nu_{88}-\nu_{86}=-402(2)$~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 Sr$^+$ isotopes for ion frequency standards or quantum-information-processing applications in the case of multi-isotope ion strings.