Spectroscopy of the $\mathbf{X^2Σ^+(v=2) \rightarrow A^2Π_{1/2}(v=1)}$ Transition in MgF: Hyperfine Structures and Spectroscopic Constants

Abstract

We report spectroscopic results of the \(X^2Σ^+(v=2) \rightarrow A^2Π_{1/2}(v=1)\) transition in magnesium monofluoride (MgF). Using Doppler-free Laser-Induced Fluorescence (LIF) spectroscopy on the \(X^2Σ^+(v=2) \rightarrow A^2Π_{1/2}(v=1)\) transition, we resolved 47 hyperfine components distributed over 11 transition lines in X and A states. An effective Hamiltonian -- comprising contributions from vibrational, rotational, \(Λ\)-doubling, and hyperfine interactions -- was presented to model the energy structure of the \(A^2Π_{1/2}(v=1)\) state. The spectroscopic parameters, including the rotational constant, the \(Λ\)-doubling parameter, and the hyperfine interaction constants, were extracted using a least-square fitting and Markov Chain Monte Carlo (MCMC) procedure. Our study reveals that the spectroscopic constants show subtle changes compared to the \(A^2Π_{1/2}(v=0)\) state. These results provide critical spectroscopic benchmarks for optimizing optical cycling schemes in MgF, thereby advancing optical cycling efficiency in the magneto-optical trapping of MgF.

Figures (4)

• Figure 1: Schematic diagram of the electronic-rovibrational states and transitions for laser cooling of MgF molecules. The $X^2\Sigma^+(v=0) \rightarrow A^2\Pi_{1/2}(v=0)$ transition provides the main optical cycling path, while additional lasers at 274.2 nm and 368.4 nm repump population leaked into vibrationally excited states. The relative branching ratios $b_{v^{\prime\prime} v^{\prime}}$ and rotational quantum number $N$ are also indicated.MgFcoolingMgFcooling6
• Figure 2: A diagram of the transition lines is provided. All possible transition lines within these energy levels are illustrated, with the $O_1,\, P_1,\, Q_1,\, R_1,\, S_1$ drawn as a solid line and the $P_{12},\, Q_{12},\, R_{12},\, S_{12}$ as a dashed line. The energy level’s parity is indicated by color. Red denotes the ($+$) parity state, while blue denotes the ($-$) parity state. On the right side of the figure, the hyperfine structures of the $X^2\Sigma^+(v=2, N=1)$ and $A^2\Pi_{1/2}(v=1, J=1/2)$ states are given and $P_1(1)/Q_{12}(1)$ the transition lines used as the 2nd repump transition for laser cooling are drawn. Energies are not to scale for clarity.
• Figure 3: Schematic of the experimental setup. The direction of the excitation laser is perpendicular to the MgF molecular beam propagation, and the laser-induced fluorescence (LIF) is collected by a photomultiplier tube (PMT) with an optical filter and imaging lens setup. The coordinate axes indicate that the excitation laser propagates along the $x$-axis while the MgF beam travels along the $z$-axis.
• Figure 4: The total LIF spectra obtained in the experiment. The red lines indicate the fitting lines, and the blue vertical lines denote frequency and relative strength of each transition determined by fitting the data. The FWHM of the spectra was approximately 30-40 MHz. The reference point of the horizontal axis is at 814044 GHz. As the rotational quantum number $N$ increases, the LIF signal tends to gradually decrease, resulting in a low signal-to-noise ratio. This can be explained by the fact that our molecular beam has a rotational temperature of a few Kelvin so that more molecules are populated in the low rotational states.