Inhomogeneous broadening by nuclear spin fields: A new limit for optical transitions in solids

Using a low-strain, isotopically pure crystal of ${\mathrm{YLiF}}_{4}$, we have measured extremely narrow inhomogeneous linewidths (as low as 40 MHz) for the optical transitions of ${\mathrm{Er}}^{3+}$ impurities. Inhomogeneous broadening due to strains and other defects is so low that a new mechanism limits the inhomogeneous linewidth: local magnetic fields due to fluorine nuclear spins. These ultranarrow lines enabled us to make the first direct measurement of the isotope shifts of f-f transitions in a solid, and we find for the isotopes $^{164}\mathrm{Er}$, $^{166}\mathrm{Er}$, $^{168}\mathrm{Er}$, and $^{170}\mathrm{Er}$ a shift of 76\ifmmode\pm\else\textpm\fi{}2 MHz unit mass on the $^{4}$${\mathit{I}}_{15/2}$(1${)}^{4}$${\mathit{F}}_{9/2}$(1) transition. We show that this is consistent with a mechanism of coupling to zero-point vibrations.