Constraints on the Variation of Physical Constants, Equivalence Principle Violation, and a Fifth Force from Atomic Experiments

The aim of this paper is to derive limits on various forms of ``new physics'' using atomic experimental data. Interactions with dark energy and dark matter fields can lead to space-time variations of fundamental constants, which can be detected through atomic spectroscopy. In this study, we examine the effects of a varying nuclear mass $m_{N}$ and nuclear radius $r_{N}$ on two transition ratios: the comparison of the two-photon transition in atomic hydrogen with the hyperfine transition in $^{133}$Cs based clocks, and the ratio of optical clock frequencies in in Al$^{+}$ and Hg$^{+}$. The sensitivity of these frequency ratios to changes in $m_{N}$ and $r_{N}$ enables us to derive new limits on the variations of the proton mass, quark mass, and the QCD parameter $\theta$. Additionally, we consider the scalar field generated by the Yukawa-type interaction of feebly interacting hypothetical scalar particles with Standard Model particles in the presence of massive bodies such as the Sun and Moon. Using the data from the Al$^{+}$/Hg$^{+}$, Yb$^{+}$/Cs and Yb$^{+}$(E2)/Yb$^{+}$(E3) transition frequency ratios, we place constraints on the interaction of the scalar field with photons, nucleons, and electrons for a range of scalar particle masses. We also investigate limits on the Einstein Equivalence Principle (EEP) violating term ($c_{00}$) in the Standard Model Extension (SME) Lagrangian and the dependence of fundamental constants on gravity.