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We report a joint test of local Lorentz invariance and the Einstein equivalence principle for electrons, using long-term measurements of the transition frequency between two nearly degenerate states of atomic dysprosium. We present many-body calculat ions which demonstrate that the energy splitting of these states is particularly sensitive to violations of both special and general relativity. We limit Lorentz violation for electrons at the level of $10^{-17}$, matching or improving the best laboratory and astrophysical limits by up to a factor of 10, and improve bounds on gravitational redshift anomalies for electrons by 2 orders of magnitude, to $10^{-8}$. With some enhancements, our experiment may be sensitive to Lorentz violation at the level of $9times 10^{-20}$.
Radio-frequency electric-dipole transitions between nearly degenerate, opposite parity levels of atomic dysprosium (Dy) were monitored over an eight-month period to search for a variation in the fine-structure constant, $alpha$. The data provide a ra te of fractional temporal variation of $alpha$ of $(-2.4pm2.3)times10^{-15}$ yr$^{-1}$ or a value of $(-7.8 pm 5.9) times 10^{-6}$ for $k_alpha$, the variation coefficient for $alpha$ in a changing gravitational potential. All results indicate the absence of significant variation at the present level of sensitivity. We also present initial results on laser cooling of an atomic beam of dysprosium.
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