Precision spectroscopy of the $A^2Π$ $\leftarrow$ $X^2Σ^+$ transition in BaF

TL;DR

The paper tackles the need for precise BaF molecular constants relevant to laser cooling and electron EDM measurements by performing high-resolution, hyperfine-resolved spectroscopy of the A-X system in a buffer-gas cooled BaF beam, with absolute frequency calibration via a frequency comb. Using two detection zones and carefully controlled Doppler conditions, the authors measure absolute transition frequencies with sub-MHz accuracy for low-J lines in the (0,0) and (1,1) bands and analyze the data with effective Hamiltonians fitted by pgopher. They report improved band origins and spin-orbit constants for the A-state, validated against high-quality prior data and FT-emission results, and demonstrate consistent low- and high-J behavior within ~1 MHz residuals. The results provide essential constants and datasets to support laser cooling schemes and precision eEDM experiments employing BaF as a target species, with data and supplementary materials openly available for community use.

Abstract

High-resolution spectroscopy on the $A^2Π$ - $X^2Σ^+$ electronic system of $^{138}$Ba$^{19}$F is performed using a cold molecular beam produced by a buffer gas source. The hyperfine structure in both $X^2Σ^+$ ground and $A^2Π$ excited states is fully resolved and absolute transition frequencies of individual components are measured at the sub-MHz level making use of frequency-comb laser calibration. Sets of molecular constants for the $X^2Σ^+$($v=0,1$) and $A^2Π$($v=0,1$) levels are determined, with improved accuracy for the $T_{v',v''}$ band origins and spin-orbit interaction constants for the $A^2Π$ excited states, that represent the presently measured highly accurate transitions for low-$J$ states as well as previously determined transition frequencies in Fourier-transform emission studies for rotational levels as high as $J \geq 100$. The extracted molecular constants reproduce the measured transition frequencies at the experimental absolute accuracy of 1 MHz. The work is of relevance for future laser cooling schemes, and is performed in the context of a measurement of the electron dipole moment for which BaF is a target system.

Figures (5)

• Figure 1: Layout of the the experimental setup showing the cryogenic buffer-gas cooled beam source for BaF and the two detection zones for recording spectra. At a distance of 5 mm from the source exit, spectra are recorded in absorption from a two-way pass through the molecular beam. At a distance of 780 mm, laser-induced fluoresence is detected for investigating the $A^2\Pi$$\leftarrow$$X^2\Sigma^+$ transitions, exciting with both 860 nm and 815 nm laser radiation. In this region Doppler shifts are assessed and minimized using overlapping counter-propagating laser beams. For further details see main text and Refs. Mooij2024Mooij2025MooijThesis.
• Figure 2: Absorption measurement (above) and simulation (below) of the $^QQ$ and $^QR$ rotational branches of the $A^2\Pi_{1/2}$$\leftarrow$$X^2\Sigma^+$(0,0) band of BaF. The absorption intensity is the time averaged signal over the duration of the pulse. The simulation includes the five strongest isotopes shown in different colors as indicated in the legend. The black curve shows the combined spectrum.
• Figure 3: Level and transition schemes for the spectroscopic investigation of hyperfine-resolved LIF spectra of $^{138}$Ba$^{19}$F. Excitation from the $N=0, J=1/2$ ground state is depicted for: transition (a) to $A^2\Pi_{1/2}$, $J=1/2$; (b) to $A^2\Pi_{3/2}$, $J=3 /2$. In the experiments, excitation from higher lying rotational levels $N=1-5$ and from $X^2\Sigma^+$, $v=1,2$ are additionally performed. The $\Lambda$-doubling in the $A^2\Pi$ state is not shown.
• Figure 4: Spectra of the $^SR$-branch of the $A^2\Pi_{3/2}$$\leftarrow$$X^2\Sigma^+$(0,0) band at $\lambda = 815$ nm with from (a) to (f) the transitions originating from the $N=0, J=1/2$ to $N=5, J=11/2$ rotational ground states, respectively. Spectra are measured at $z=780$ mm from the buffer gas source exit using LIF detection. The frequency axis is online calibrated with respect to the frequency comb laser. Each data point originates from integration over a single molecular beam pulse while subtracting the integrated background signal observed during the same time interval after the molecular beam pulse has passed. Note that the intensity scale for the different panels (a) - (f) is the same, and the intensity decrease toward larger $N$ reflects the population of rotational states in the beam. The solid red curves show the result of the multi-component fit of Lorentzians to the observed data.
• Figure 5: Recorded spectra of a number of transitions in various bands of BaF. Transitions are in the $A-X$($v',v"$) bands, probe $A^2\Pi_{1/2}$ or $A^2\Pi_{3/2}$ spin-orbit components, and originate from the lowest $N=0,J=1/2$ levels in the $v"$ vibrational states. The identification and extracted frequencies of hyperfine-resolved components for these lines are given in Table \ref{['tab42']}. The spectrum shown in panel (a) results from averaging over 5 shots, while the spectra shown in panel (b) to (d) have been averaged over 20-25 shots. The recorded LIF intensity of the spectrum shown in panel (a) is about an order of magnitude smaller than that shown in Fig. \ref{['fig:A32-X']}(a) due to the lower quantum efficiency of the PMT at 860 nm compared to 815 nm. The intensity of the spectrum shown in panel (b) is about two orders of magnitude smaller than that of the spectrum shown in (a) due to the lower population of the $v=1$ state. Similarly, the spectrum shown in panel (c) is about two orders of magnitude smaller than that of Fig. \ref{['fig:A32-X']}(a), while the spectrum shown in panel (d) is about a factor of 5 less intense than the one shown in (c) due to the even lower population of the $v=2$ state.