Open Access Publications from the University of California

## Search for variation of the fine-structure constant and violation of Lorentz symmetry using atomic dysprosium

Abstract

We report on the spectroscopy of radio-frequency transitions between nearly-degenerate, opposite-parity excited states in atomic dysprosium (Dy). Theoretical calculations predict that these states are very sensitive to variation of the fine-structure constant, $\alpha$, owing to large relativistic corrections of opposite sign for the opposite-parity levels. The near degeneracy reduces the relative precision necessary to place constraints on variation of $\alpha$ competitive with results obtained from the best atomic clocks in the world. Additionally, the existence of several abundant isotopes of Dy allows isotopic comparisons that suppress common-mode systematic errors. The frequencies of the 754-MHz transition in $^{164}$Dy and 235-MHz transition in $^{162}$Dy were measured over the span of two years. Linear variation of $\alpha$ is found to be $\dot{\alpha}/\alpha = (-5.8\pm6.9)\times10^{-17}$~yr$^{-1}$, consistent with zero. The same data are used to constrain the dimensionless parameter $k_\alpha$, characterizing a possible coupling of $\alpha$ to a changing gravitational potential. We find that $k_\alpha = (-5.5\pm5.2)\times10^{-7}$, essentially consistent with zero and the best constraint to date.

The same data are used to report a joint test of local Lorentz invariance and the Einstein Equivalence Principle for electrons. We present many-body calculations which demonstrate that the energy splitting of these states is particularly sensitive to violations of both special and general relativity. Lorentz violation for electrons is limited at the level of $10^{-17}$, matching or improving the best laboratory and astrophysical limits by up to a factor of 10, and gravitational redshift anomalies for electrons to the level of $10^{-8}$. With some enhancements, our experiment may be sensitive to Lorentz violation at the level of $9\times 10^{-20}$.

We also report measurements of the differential polarizability between the nearly degenerate, opposite parity states. The differential scalar and tensor polarizabilities due to additional states were measured for the $|M| = 7,\dots,10$ sublevels in $^{164}$Dy and $^{162}$Dy and determined to be $\overline{\balpha}_{\sss BA}^{(0)} = 180\,(45)_\text{stat}\,(8)_\text{sys}$ mHz cm$^2$/V$^2$ and $\overline{\balpha}_{\sss BA}^{(2)} = -163\,(65)_\text{stat}\,(5)_\text{sys}$ mHz cm$^2$/V$^2$, respectively. The average blackbody radiation induced Stark shift of the Zeeman spectrum was measured around 300 K and found to be $-34(4)$~mHz/K and $+29(4)$~mHz/K for the $^{164}$Dy and $^{162}$Dy isotopes, respectively. We conclude that ac-Stark related systematics will not limit the precision of a search for variation of the fine-structure constant, using dysprosium, down to the level of $|\dot{\alpha}/\alpha|=2.6\times10^{-17}$~yr$^{-1}$ for a one-year experiment.