Vibrational Branching Ratios for Laser-Cooling of Nonlinear Strontium-Containing Molecules

TL;DR

This study measures vibrational branching ratios (VBRs) from the lowest excited electronic state for three nonlinear Sr-containing molecules—SrOCH$_3$, SrNH$_2$, and SrSH—using dispersed laser-induced fluorescence and corroborates the results with high-level ab initio calculations (EOMEA-CCSD with X2C, FCSQUARE, and VPT2, including DVC effects). By applying symmetry analysis for C$_{3v}$, C$_{2v}$, and Cs groups, the authors assess rotational closure and identify rotational leakage pathways, highlighting SrNH$_2$ as the most favorable candidate for future deep laser cooling and parity-doublet-based BSM experiments, while SrOCH$_3$ and SrSH face larger challenges from additional vibrational modes and perturbations. The results indicate that rotational and vibrational leakage can be controlled in SrNH$_2$, potentially enabling ~10^4 optical cycles with a manageable repumping scheme, whereas SrSH suffers from strong perturbations that create multiple leaky channels, complicating deep cooling. Overall, the work provides a quantitative framework linking molecular symmetry, vibronic coupling, and laser-cooling viability, guiding the selection of polyatomic candidates for high-precision EDM searches and informing the design of next-generation cooling schemes for nonlinear molecules.

Abstract

The vibrational branching ratios from the lowest excited electronic state for $\textrm{SrOCH}_3$, $\textrm{SrNH}_2$, and $\textrm{SrSH}$ are measured at the $< 0.1\%$ level. Spectra are obtained by driving the $\tilde{X} - \tilde{A}$ transitions and dispersing the fluorescence on a grating spectrometer. We also perform $\textit{ab initio}$ calculations for the energies of vibrational levels relevant for laser cooling, as well as branching ratios to support the interpretations of all molecular spectra. Symmetry group analysis is applied in conjunction with our data to study rotational closure in these molecules. These analyses indicate favorable prospects for laser cooling $\textrm{SrNH}_2$ and other similar alkaline-earth(-like) amides for future beyond the Standard Model physics searches using polyatomic molecules with long-lived parity doublets.

Figures (4)

• Figure 1: Schematic showing the apparatus as viewed from above. A strontium metal target, located inside a cryogenic copper cell, is ablated by an Nd:YAG laser. The strontium atoms then react with the reactant gas to form the molecule of interest. The molecules are thermalized to the cell temperature by helium buffer gas, and exit the cell rotationally cold. A laser beam excites molecules to the lowest excited electronic state, and the fluorescence from the subsequent decay is collected into a spectrometer.
• Figure 2: Schematics showing the relevant rotational structure in a) $\textrm{SrOCH}_3$, b) $\textrm{SrNH}_2$, and c) $\textrm{SrSH}$. Dashed lines show known rotational decay channels, and identify states that will need to be addressed in order to photon cycle in each species. The asymmetric top states are labeled as $N_{K_a K_c}$. In these molecules, the opposite parity states are not shown due to strict parity selection rules. Note also that these are only the confirmed decay channels; see Appendix \ref{['app:symmetry']} for all possible loss channels given the excitations used here. Even when perturbations are taken into account, $\textrm{SrNH}_2$ requires the fewest rotational repumps per vibrational decay channel.
• Figure 3: VBR data for (a) $\textrm{SrOCH}_3$, (b) $\textrm{SrNH}_2$, and (c) $\textrm{SrSH}$. Insets show the same spectra at higher resolution. Accompanying VBRs are found in Tables \ref{['tab:SrOCH3-VBR-peak']}--\ref{['tab:SrSH-VBR-peak']}. States are labeled according to the modes in Table \ref{['tab:statesym']}. State labels separated by commas indicate transitions to different states that are unresolved by the spectrometer.
• Figure 4: Comparison of rotational branching for four rotational levels in the $\textrm{SrSH}$$\tilde{A} ^2A'$$0_0$ state to the $\tilde{X} ^2A'$$0_0$ state. Each peak corresponds to a decay to a different $K_a$ level in the ground state. Dashed lines indicate the energies of $K_a$ levels using the measured $A$ constant Brazier2000. Note that four decays only happen for $K_a' = 1$and$J' = 3/2$. The other states show only three decays.