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±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.