Enhanced Sensitivity to Ultralight Bosonic Dark Matter in the Spectra of the Linear Radical SrOH

Abstract: Coupling between Standard Model particles and theoretically well-motivated ultralight dark matter (UDM) candidates can lead to time variation of fundamental constants including the proton-to-electron mass ratio $\mu\equiv m_{p}/m_{e}\approx1836$. The presence of nearly-degenerate vibrational energy levels of different character in polyatomic molecules can result in significantly enhanced relative energy shifts in molecular spectra originating from $\partial_{t}\mu$, relaxing experimental complexity required for high-sensitivity measurements. We analyze the amplification of UDM effects in the spectrum of laser-cooled strontium monohydroxide (SrOH). SrOH is the first and, so far, the only polyatomic molecule to be directly laser cooled to sub-millikelvin temperatures, opening the possibility of long experimental coherence times. Because of the high enhancement factors ($\left|Q_{\mu}\right|\approx10^{3}$), measurements of the $\tilde{X}\left(200\right)\leftrightarrow\tilde{X}\left(03^{1}0\right)$ rovibrational transitions of SrOH in the microwave regime can result in $\sim10^{-17}$ fractional uncertainty in $\delta\mu/\mu$ with one day of integration. Furthermore, ultracold SrOH provides a promising platform for suppressing systematic errors. More complex SrOR radicals with additional vibrational modes arising from larger ligands R could lead to even greater enhancement factors.