Probing New Forces with Nuclear Clocks

Abstract

Clocks based on nuclear isomer transitions promise exceptional stability and precision. The low transition energy of the thorium-229 isomer makes it an ideal candidate, as it has been excited by a vacuum-ultraviolet laser and is highly sensitive to subtle interactions. This enables the development of powerful tools for probing new forces, which we call {\it quintessometers}. In this work, we demonstrate the potential of nuclear clocks, particularly solid-state variants, to surpass existing limits on scalar field couplings, exceeding the sensitivity of current fifth-force searches at submicron distances and significantly improving equivalence-principle tests at kilometer scales and beyond. Additionally, we highlight the capability of transportable nuclear clocks to detect scalar interactions at distances beyond $10\,$km, complementing space-based missions.

Figures (3)

• Figure 1: Projected sensitivities of nuclear clock-based quintessometers on the scalar couplings $d_{g}$ (top) and $d_e$ (bottom). The gray-shaded regions represent the parameter space excluded by fifth-force experiments Spero:1980zzMostepanenko:1990edBordag:1993htqLamoreaux:1996whBordag:1998nvEderth:2000zzHarris:2000zzFischbach:2001ryChiaverini:2002cbAdelberger:2003zxLong:2003dxKapner:2006siYang:2012zzbChen:2014odaTan:2020vpfLee:2020zjt (lighter gray) and EP tests Schlamminger:2007htSmith:1999crBerge:2017ovy (darker gray). The yellow-shaded regions indicate the unexplored parameter space that could be explored by quintessometers with a sensitivity of $\delta \nu/\nu\sim 10^{-19}$, and assuming $K_{g,e}= 10^5$. See \ref{['fig:large_dist']} and \ref{['fig:small_dist']} for zoomed-in views of the large- and short-distance regions, respectively. The red dotted line represents the ultimate quintessometer's sensitivity to scalar fields sourced by the Earth at this frequency uncertainty. The dashed blue line denotes the sensitivity of the isotope comparison discussed in \ref{['sec:host crystals that differ by isotope']}, achievable once nuclear effects are properly accounted for.
• Figure 2: Zoomed-in view of the large-distance region of \ref{['fig:moneyplots']}, illustrating the reach of the proposed nuclear clock-based quintessometers (yellow) compared to existing bounds from relative acceleration (dark gray). A nuclear clock operating on earth for one year covers the region enclosed by the red line, due to the Earth's eccentric orbit around the Sun. Similarly, a satellite clock with high orbital eccentricity extents the reach to the area enclosed by the thick orange line. If the satellite clock is both stable and accurate to the quoted level, the reach further extends to the thin orange line. An Earth-based transportable experiment, where the height of the clock is varied from sea level to a 4 altitude, is shown in purple.
• Figure 3: Zoomed-in view of the small-distance region of \ref{['fig:moneyplots']}, illustrating the expected sensitivities from placing a rotating disk at a distance of $10\nm$ from a nuclear clock (green), and from CaF$_2$ crystals made of different Ca isotopes doped with $^{229}$Th. The cyan area represents the bound derived from the non-observation of a Mössbauer shift in ZnO due to enrichment (see \ref{['sec:Moessbauer classic']}). The light gray region is constrained by fifth-force searches Ederth:2000zzHarris:2000zzFischbach:2001ryChen:2014oda and neutron scattering experiments Nesvizhevsky:2007by.