Optimization of experimental parameters for laser-slowing and magneto-optical trapping of MgF molecules

TL;DR

The paper tackles the challenge of bringing MgF molecules to ultracold temperatures by jointly optimizing laser slowing and MOT parameters through Bayesian optimization on a complete slowing–MOT simulation. Rate‑equation modeling (via PyLCP) is used to compute optical forces and molecular trajectories, guiding the search for parameter sets that maximize the MOT capture velocity and the fraction of molecules trapped. The authors report a maximum MOT capture velocity of $v_c = 82.5$ m/s and a trapping fraction of 28.6% under optimal conditions, with transverse motion and spectral broadening playing critical roles in the slowing and trapping dynamics. Direct numerical validation confirms the optimization trends, albeit with a modest reduction in trapping efficiency due to recoil, establishing a practical, transferable framework for optimizing laser cooling of MgF and similar molecular systems.

Abstract

Diatomic molecules are promising systems for quantum science applications due to their complex energy structures and strong dipole-dipole interactions. Achieving ultracold temperatures is essential for these applications, but the complexity of molecular energy levels requires precise optimization of experimental parameters for laser slowing and magneto-optical trapping (MOT). Here, we simulate and optimize the complete process of slowing and trapping MgF molecules, from a buffer-gas beam source to MOT capture, using Bayesian optimization. By combining laser slowing and MOT simulations, we identify parameters that maximize the capture velocity and the ratio of trapped molecules. Our results demonstrate a maximum MOT capture velocity of 82.5 m/s, and 28.6% of the molecules that reach the MOT region are trapped under optimal conditions. These findings provide insights into experimental setups for MgF and similar molecules, offering a framework for advancing molecular laser cooling and quantum experiments.

Figures (10)

• Figure 1: MgF energy structure for (a) electro-vibrational states and (b) hyperfine states. (a) Main transition line is from $|\mathrm{X}^2\Sigma, v=0\rangle \rightarrow |\mathrm{A}^2\Pi_{1/2}, v'=0\rangle$ at 359 nm. $f_{nn}$ indicates the Franck-Condon factor(FCF) between two vibrational states. Two repump lasers($|X^2\Sigma,v=1\rangle\xrightarrow{} |B^2\Sigma,v'=0\rangle$ and $|X^2\Sigma, v=2\rangle \xrightarrow{} |A^2\Pi_{1/2},v'=1\rangle$) are required to increase the number of photon scattering up to $2\times 10^4$norrgard2023radiative. (b) Energy difference between $F'=0$ and $F'=1$ in $\textit{A}^2\Pi_{1/2}$ state are not resolved yet. Note that splitting between $F = 2$ and $F=1^+$ in $\textit{X}^2\Sigma^+$ state is smaller than $0.5\Gamma$.
• Figure 2: Schematic of the experimental setup for the simulation. After creation by ablation, MgF molecules are cooled down by He buffer-gas and emerge out from the buffer-gas cell as a MgF molecular beam (blue line), heading to an octagonal MOT chamber. The MOT stage is the region where six laser beams are crossed (inside the red square), and the slowing stage is the region from the exit of the buffer-gas cell to the entrance of MOT stage. Slowing lasers and MOT lasers are indicated as purple lines. Magnetic field is applied by anti-Helmholtz coils along the $z$ axis.
• Figure 3: (a) Acceleration on the MgF molecules and their calculated trajectories for the mean parameter set. Longitudinal axis has an angle of ${\pi}/{4}$ from the $x$ axis in the $xy$ plane. Acceleration is shown with red or blue color. Each trajectory line has different initial velocity from 7.5 m/s to 90 m/s with 3.75 m/s intervals. (b) State population vs time of molecules traveling in a MOT chamber with initial longitudinal velocity 82.5 m/s. Six colors indicate the sum of the populations in all states with the same $F$ number.
• Figure 4: Acceleration and motional trajectories of the molecules with a conventional parameter set. Global frequency detuning of $-0.5\ \Gamma$ and a magnetic field gradient of $1$ G/mm are applied. Laser power is equally divided to each frequency component. Polarizations are set as $(+, +, +,-)$.
• Figure 5: Capture velocity vs change each parameter from $\vec{X}_{\rm mean}$. (a) Frequency detuning, (b) Power ratio of each laser component. (c) Magnetic field gradient. (d) Total power.