Precision measurements of electric-field-induced frequency displacements of an ultranarrow optical transition in ions in a solid

We report a series of measurements of the effect of an electric field on the frequency of the ultranarrow linewidth $F70→$ $D50$ optical transition of $Eu3+$ ions in an $Y2SiO5$ matrix at cryogenic temperatures. We provide linear Stark coefficients along two dielectric axes and for the two different substitution sites of the $Eu3+$ ions, with an unprecedented accuracy and an upper limit for the quadratic Stark shift. The measurements, which indicate that the electric field sensitivity is a factor of seven larger for site 1 relative to site 2 for a particular direction of the electric field, are of direct interest in the context of both quantum information processing and laser frequency stabilization with rare-earth doped crystals, in which electric fields can be used to engineer experimental protocols by tuning transition frequencies.