Investigation of the gravitational-potential dependence of the fine-structure constant using atomic dysprosium

Radio-frequency $E1$ transitions between nearly degenerate, opposite-parity levels of atomic dysprosium (Dy) were monitored over an 8-month period to search for a variation in the fine-structure constant $\alpha$. During this time period, data were taken at different points in the gravitational potential of the Sun. The data are fitted to the variation in the gravitational potential yielding a value of $(-8.7\pm 6.6)\times {10}^{-6}$ for $k_{\alpha }$, the variation of $\alpha$ in a changing gravitational potential. This value gives the first laboratory limit independent of assumptions regarding other fundamental constants. In addition, our value of $k_{\alpha }$ combined with other experimental constraints is used to extract the first limits on $k_e$ and $k_q$. These coefficients characterize the variation of $m_e∕m_p$ and $m_q∕m_p$ in a changing gravitational potential, where $m_e$, $m_p$, and $m_q$ are electron, proton, and quark masses. The results are $k_e=(4.9\pm 3.9)\times {10}^{-5}$ and $k_q=(6.6\pm 5.2)\times {10}^{-5}$. All these results indicate the absence of significant variation at the present level of sensitivity.