Optical pumping and laser slowing of a heavy molecule

TL;DR

The study tackles enabling high-precision eEDM measurements with heavy BaF molecules by building a laser-cooling and slowing pathway toward a 3D MOT. It performs a comprehensive leakage analysis across vibrational and rotational channels and implements a microwave-optical hybrid pumping scheme to suppress leakage to $\sim10^{-5}$. Using frequency-chirped laser slowing, a subset of BaF molecules is slowed from roughly $80~\mathrm{m\,s^{-1}}$ to near-zero velocity, a crucial step for MOT loading. This work establishes a solid technical foundation for precision eEDM measurements with laser-cooled heavy molecules and points to further improvements, such as optical rotational pumping to mitigate diffraction-related issues with microwaves.

Abstract

Precision measurements of the electron's electric dipole moment (eEDM) are critical for testing fundamental symmetries in particle physics, and heavy polar molecules-such as barium monofluoride (BaF)-have emerged as promising candidates for advancing the sensitivity. However, the achievement of a 3D magneto-optical trap (MOT) required slowing BaF molecules to near-zero velocity by scattering over 10^4 photons per molecule, demanding a quasi-cycling transition with minimal leakage. We present a detailed study of the leakage channels, including higher vibrational and rotational states. By combining microwave remixing with optical pumping of rotational and vibrational dark states, we reduced the total leakage fraction to 10^-5. Using frequency-chirped laser slowing, we slowed a subset of buffer-gas-cooled BaF molecules from approximately 80 m/s to near-zero velocity, which is critical for efficient MOT loading. This work establishes the technical foundation for precision eEDM measurements using laser-cooled heavy molecules.

Figures (6)

• Figure 1: The energy levels relevant to the laser slowing of BaF molecules. The red line denotes the main cooling laser. The brown lines stand for the repump lasers, where the label $L_{vN}$ indicates the vibrational and rotational quantum numbers of the corresponding dark state. The green lines denote the microwaves, and the grey lines indicate the principal leakage pathways to higher rotational and vibrational states.
• Figure 2: Laser slowing experimental setup and molecular velocity distribution. (a) The experimental setup consists of a cryogenic buffer gas source and a series of vacuum chambers. Slowing, probe, and ablation lasers are employed in the experiment via different optical accesses. (b) The time-velocity density plot of the light-induced fluorescence (LIF) of BaF molecules at a helium flow rate of 0.5 SCCM. The vertical axis represents molecular velocity, and the horizontal axis represents molecular arrival time at the probe region after laser ablation. The dashed curve is a guideline, depicting arrival times calculated from molecular velocity $v$ and apparatus geometry $t=0.5\text{ ms}+1.25\text{ m}\cdot v^{-1}$ for ease of experimental data comparison and analysis. The orange circles in panel (c) are obtained by integrating data in panel (b) from 5 ms to 20 ms. The orange curve is a Gaussian fitting. The error bars represent the standard error of the mean.
• Figure 3: Typical leakage measurement data showing laser-induced fluorescence signals for selected molecular states. The data features laser-induced fluorescence (LIF) signals for the states $|v=2,N=1,-\rangle$(a, b), $|v=0,N=2,+\rangle$(c, d), $|v=1,N=2,+\rangle$(e, f), and $|v=0,N=3,-\rangle$(g, h). In all the panels, the red curve represents the LIF signal with all repump lasers on, while the blue curve shows the LIF signal with one specific repump laser switched off at $t=0$ ms. The data in panels (a), (c), (e), (g) were obtained via the slowing laser method, with insets displaying the normalized LIF signals fitted with exponential decays. The data in panels (b), (d), (f), (h) were acquired using the magneto-optical trap (MOT) method with exponential decay fits. All data are averages over $\sim200$ experimental cycles. For clarity, panels (c), (e), (g) were smoothed using a moving average with a 0.8 ms window.
• Figure 4: Experimental results of laser slowing. The red circles (blue squares) represent the intensity of light-induced fluorescence (LIF) of slowed (unperturbed) molecular beams at different velocities. The solid curves are Gaussian fittings. (a) White light slowing starts at 0 ms and ends at 6.5 ms in the absence of both microwave remixing and higher-order optical repumping. (b) White light slowing starts at 0 ms and ends at 6.5 ms with microwave remixing and higher-order optical repumping. (c) Chirped slowing from 110 $\text{m }\text{s}^{-1}$ (-128 MHz) to 65 $\text{m }\text{s}^{-1}$ (-76 MHz) in 11 ms with microwave remixing and higher-order optical repumping. The error bars represent the standard error of the mean.
• Figure 5: Microwave remixing schemes and laser slowing data. (a) shows the hyperfine structure of the BaF molecule. Red arrows represent possible transitions between $X(N=1,-)$ and $A(J=1/2,+)$ states. Green arrows represent microwave transitions between $X(N=0,+)$ and $X(N=1,-)$ states. Here, the arrow for $A(J=1/2,F=1)\leftarrow X(N=1,J=3/2,F=1)$ is plotted in light red because this transition is nearly forbidden. Arrow a is labelled as "fixed" because the microwave frequency it corresponds to remains activated throughout all experimental runs. Two distinct microwave remixing schemes are used in the experiments: Slowing results with frequency components a and b activated are shown in panel (b); those with frequency components a and c activated are shown in panel (c). The frequencies of microwaves a, b, and c are 12.906 GHz, 12.838 GHz, and 12.953 GHz, respectively. The red circles (blue squares) represent the intensity of light-induced fluorescence (LIF) of slowed (unperturbed) molecular beams at different velocities. The solid curves are Gaussian fittings. The frequency of the slowing laser is chirped from a velocity corresponding to 140 $\text{m }\text{s}^{-1}$ (-163 MHz) to 90 $\text{m }\text{s}^{-1}$ (-105 MHz) in 10 ms. The error bars represent the standard error of the mean.