We report a series of measurements of the effect of an electric field on the frequency of the ultranarrow linewidth F70D50 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.

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