Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Electronic and hyperfine structures of MgH24 with relevance to laser cooling

Yufeng Gao

Published Oct 28, 2020• 2 citations
Publisher

Abstract

We study the electronic and hyperfine structures of $^{24}\mathrm{MgH}$ molecule, which are of crucial importance for the laser cooling of the molecule. The accurate spectroscopic constants and hyperfine levels are presented for $X^{2}\mathrm{\ensuremath{\Sigma}}^{+}$ and $A^{2}\mathrm{\ensuremath{\Pi}}$ symmetries. The theoretical results are in good agreement with the experimental data. We then provide a scheme for the laser-driven cycling transitions of $A^{2}\mathrm{\ensuremath{\Pi}}_{1/2}\ensuremath{\leftarrow}X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2}$. In addition, we calculate the hyperfine branching ratios for the rate of decay from $|A^{2}\mathrm{\ensuremath{\Pi}}_{1/2},{J}^{\ensuremath{'}}=1/2,+\ensuremath{\rangle}$ to $|X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2},N=1,\ensuremath{-}\ensuremath{\rangle}$ transition. We also provide a sideband modulation scheme to the pumping lasers to match all four hyperfine levels of the $X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2}$ ($v=0$, $N=1$). Finally, we calculate the Zeeman shift of the ($X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2}$, $v=0$, $N=1$) ground state, and the typical hyperfine structure magnetic $g$ factor ${g}_{F}$ and mixed $g$ factors ${g}_{F}^{\mathrm{eff}}$ are also calculated. Our study is expected to be useful for the laser-cooling $^{24}\mathrm{MgH}$ molecule and the interpretation of astronomical spectra involving MgH molecule.

DOI
10.1103/physreva.102.042821

Related papers

Structure, branching ratios, and a laser-cooling scheme for the BaF138 molecule

Tao Chen, Wenhao Bu, Bo Yan

For laser-cooling considerations, we have theoretically investigated the electronic, rovibrational, and hyperfine structures of the BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between the metastable ${A}^{{\ensuremath{'}}^{2}}\mathrm{\ensuremath{\Delta}}$ and ${A}^{2}\mathrm{\ensuremath{\Pi}}$ states and, further, the lifetime of the $\mathrm{\ensuremath{\Delta}}$ state have been estimated since the loss procedure via the $\mathrm{\ensuremath{\Delta}}$ state might fatally break the main quasicycling $\mathrm{\ensuremath{\Sigma}}\ensuremath{-}\mathrm{\ensuremath{\Pi}}$ transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational state in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state provide benchmarks for sideband modulations of the cooling and repumping lasers and the remixing microwaves to address all necessary levels. The calculated Zeeman shift and $g$ factors for both $X$ and $A$ states serve as benchmarks for selection of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.

arXiv:1609.07707•Physical Review A•Dec 19, 2016•54 citations

Calculation of vibrational branching ratios and hyperfine structure of 24Mg19F and its suitability for laser cooling and magneto-optical trapping

Liang Xu, Yanning Yin, Bin Wei +2 more

More recently, laser cooling of the diatomic radical magnesium monofluoride (${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$) is being experimentally preformed [Appl. Phys. Express 8, 092701 (2015) and Opt. Express 22, 28645 (2014)] and was also studied theoretically [Phys. Rev. A 91, 042511 (2015)]. However, some important problems still remain unsolved, so, in our paper, we perform further theoretical study for the feasibility of laser cooling and trapping the ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$ molecule. At first, the highly diagonal Franck-Condon factors of the main transitions are verified by the closed-form approximation, Morse approximation, and Rydberg-Klein-Rees inversion methods, respectively. Afterwards, we investigate the lower $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}$ hyperfine manifolds using a quantum effective Hamiltonian approach and obtain the zero-field hyperfine spectrum with an accuracy of less than 30 $\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{K}$ compared with the experimental results, and then find out that one cooling beam and one or two repumping beams with their first-order sidebands are enough to implement an efficient laser slowing and cooling of ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$. Meanwhile, we also calculate the accurate hyperfine structure magnetic $g$ factors of the rotational state ($X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+},N=1$) and briefly discuss the influence of the external fields on the hyperfine structure of ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$ as well as its possibility of preparing three-dimensional magneto-optical trapping. Finally we give an explanation for the difference between the Stark and Zeeman effects from the perspective of parity and time reversal symmetry. Our study shows that, besides appropriate excitation wavelengths, the short lifetime for the first excited state $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}$, and lighter mass, the ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$ radical could be a good candidate molecule amenable to laser cooling and magneto-optical trapping.

Physical Review A•Jan 12, 2016•46 citations

Vibrational branching ratios and hyperfine structure of 11BH and its suitability for laser cooling

Richard Hendricks, Darren Holland, Stefan Truppe +2 more

The simple structure of the BH molecule makes it an excellent candidate for direct laser cooling. We measure the branching ratios for the decay of the A^{1}Pi (v'=0) state to vibrational levels of the ground state, X^{1}Sigma^{+}, and find that they are exceedingly favourable for laser cooling. We verify that the branching ratio for the spin-forbidden transition to the intermediate a^{3}Pi state is inconsequentially small. We measure the frequency of the lowest rotational transition of the X state, and the hyperfine structure in the relevant levels of both the X and A states, and determine the nuclear electric quadrupole and magnetic dipole coupling constants. Our results show that, with a relatively simple laser cooling scheme, a Zeeman slower and magneto-optical trap can be used to cool, slow and trap BH molecules.

arXiv:1404.6174•Frontiers in Physics•Aug 19, 2014•33 citations

Progress towards laser cooling of BH molecules

Darren Holland

This thesis investigates the suitability of BH molecules for laser cooling and describes progress towards the laser cooling of this molecule. We produce a molecular beam of BH and measure the branching ratios for the excited electronic state, A^{1}\Pi(v_{0}=0), to decay to the various vibrational states of the ground electronic state, X^{1}\Sigma. We verify that the branching ratio for the spin-forbidden transition to an intermediate triplet state is inconsequentially small. We measure the frequency of the lowest rotational transition of the X state, and the hyper fine structure in the relevant levels of both the X and A states, and determine the nuclear electric quadrupole and magnetic dipole coupling constants. We use a semiclassical model of the molecule-light interaction to investigate the expected cycling behaviour on the main cooling transition using light with modulated polarisation. The results of the model are compared with the effect of modulating the polarisation experimentally using an electro-optic modulator. In order to repump the population that leaks into the first vibrationally excited state, we have designed, built and tested a suitable repump laser and have demonstrated that we can drive the repump transition. We have also designed a Zeeman slower for slowing molecules to low velocity so that they can be trapped. Our results show that a relatively simple laser cooling scheme can be used to cool, slow and trap BH molecules.

•Aug 1, 2016•0 citations

Theoretical Investigation of Spectroscopic Properties of the Alkaline-Earth-Metal Monohydrides toward Laser Cooling and Magneto-Optical Trapping

Renjun Pang, J. H. Yin, Yueyang Wang +7 more

High Resolution Image Download MS PowerPoint Slide Alkaline-earth-metal monohydrides M H ( M = Be, Mg, Ca, Sr, Ba) have long been regarded as promising candidates toward laser cooling and trapping; however, their rich internal level structures that are amenable to magneto-optical trapping have not been completely explored. Here, we first systematically evaluated Franck–Condon factors of these alkaline-earth-metal monohydrides in the A 2 Π 1/2 ← X 2 Σ + transition, exploiting three respective methods (the Morse potential, the closed-form approximation, and the Rydberg–Klein–Rees method). The effective Hamiltonian matrix was introduced for MgH, CaH, SrH, and BaH individually in order to figure out their molecular hyperfine structures of X 2 Σ +, the transition wavelengths in the vacuum, and hyperfine branching ratios of A 2 Π 1/2 ( J ′ = 1/2,+) ← X 2 Σ + ( N = 1,−), followed by possible sideband modulation proposals to address all hyperfine manifolds. Lastly, the Zeeman energy level structures and associated magnetic g factors of the ground state X 2 Σ + ( N = 1,−) were also presented. Our theoretical results here not only shed more light on the molecular spectroscopy of alkaline-earth-metal monohydrides toward laser cooling and magneto-optical trapping but also can contribute to research in molecular collisions involving few-atom molecular systems, spectral analysis in astrophysics and astrochemistry, and even precision measurement of fundamental constants such as the quest for nonzero detection of electron’s electric dipole moment.

ACS Omega•May 24, 2023•5 citations

Optical cycling of MgF molecules within the hyperfine states in X(N=1) state

Kikyeong Kwon, Seunghwan Roh, Youngju Cho +2 more

Achieving laser cooling of molecules necessitates the establishment of a closed optical cycling transition. In contrast to atoms, molecules exhibit additional vibrational and rotational structures, which must be carefully addressed-alongside hyperfine splittings-when designing the laser frequency scheme for efficient optical cycling. In this work, we investigated optical cycling in MgF molecules on the laser cooling transition, namely [Formula: see text] transition between the electronic ground state ([Formula: see text]) and the electronic excited state ([Formula: see text]). The ground state comprises four hyperfine levels, of which two are unresolved within the excited-state linewidth; the two hyperfine levels in the excited state are also unresolved. Consequently, three laser frequencies suffice to address all transitions. This was realized by generating three independently tunable frequency components using acousto-optic modulators (AOMs). With optimized detunings, power ratios, and total beam power, simultaneous application of all three frequency components increased the total number of scattered photons by up to [Formula: see text] relative to the sum of the individual single-frequency signals. Applying a tilted magnetic field to remix the dark Zeeman states increased the photon yield by an additional factor of [Formula: see text], leading to an overall enhancement of about sevenfold. These results provide quantitative benchmarks for MgF optical cycling and practical guidance for future molecular slowing and magneto-optical trapping experiments.

arXiv:2506.23507•Scientific Reports•Dec 4, 2025•0 citations
We study the electronic and hyperfine structures of 24MgH^{24}\mathrm{MgH}24MgH molecule, which are of crucial importance for the laser cooling of the molecule. The accurate spectroscopic constants and hyperfine levels are presented for X2\ensuremathΣ+X^{2}\mathrm{\ensuremath{\Sigma}}^{+}X2\ensuremathΣ+ and A2\ensuremathΠA^{2}\mathrm{\ensuremath{\Pi}}A2\ensuremathΠ symmetries. The theoretical results are in good agreement with the experimental data. We then provide a scheme for the laser-driven cycling transitions of A2\ensuremathΠ1/2\ensuremath←X2\ensuremathΣ1/2A^{2}\mathrm{\ensuremath{\Pi}}_{1/2}\ensuremath{\leftarrow}X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2}A2\ensuremathΠ1/2​\ensuremath←X2\ensuremathΣ1/2​. In addition, we calculate the hyperfine branching ratios for the rate of decay from ∣A2\ensuremathΠ1/2,J\ensuremath′=1/2,+\ensuremath⟩|A^{2}\mathrm{\ensuremath{\Pi}}_{1/2},{J}^{\ensuremath{'}}=1/2,+\ensuremath{\rangle}∣A2\ensuremathΠ1/2​,J\ensuremath′=1/2,+\ensuremath⟩ to ∣X2\ensuremathΣ1/2,N=1,\ensuremath−\ensuremath⟩|X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2},N=1,\ensuremath{-}\ensuremath{\rangle}∣X2\ensuremathΣ1/2​,N=1,\ensuremath−\ensuremath⟩ transition. We also provide a sideband modulation scheme to the pumping lasers to match all four hyperfine levels of the X2\ensuremathΣ1/2X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2}X2\ensuremathΣ1/2​ (v=0v=0v=0, N=1N=1N=1). Finally, we calculate the Zeeman shift of the (X2\ensuremathΣ1/2X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2}X2\ensuremathΣ1/2​, v=0v=0v=0, N=1N=1N=1) ground state, and the typical hyperfine structure magnetic ggg factor gF{g}_{F}gF​ and mixed ggg factors gFeff{g}_{F}^{\mathrm{eff}}gFeff​ are also calculated. Our study is expected to be useful for the laser-cooling 24MgH^{24}\mathrm{MgH}24MgH molecule and the interpretation of astronomical spectra involving MgH molecule.
For laser-cooling considerations, we have theoretically investigated the electronic, rovibrational, and hyperfine structures of the BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between the metastable ${A}^{{\ensuremath{'}}^{2}}\mathrm{\ensuremath{\Delta}}$ and ${A}^{2}\mathrm{\ensuremath{\Pi}}$ states and, further, the lifetime of the $\mathrm{\ensuremath{\Delta}}$ state have been estimated since the loss procedure via the $\mathrm{\ensuremath{\Delta}}$ state might fatally break the main quasicycling $\mathrm{\ensuremath{\Sigma}}\ensuremath{-}\mathrm{\ensuremath{\Pi}}$ transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational state in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state provide benchmarks for sideband modulations of the cooling and repumping lasers and the remixing microwaves to address all necessary levels. The calculated Zeeman shift and ggg factors for both XXX and AAA states serve as benchmarks for selection of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.
More recently, laser cooling of the diatomic radical magnesium monofluoride (24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F) is being experimentally preformed [Appl. Phys. Express 8, 092701 (2015) and Opt. Express 22, 28645 (2014)] and was also studied theoretically [Phys. Rev. A 91, 042511 (2015)]. However, some important problems still remain unsolved, so, in our paper, we perform further theoretical study for the feasibility of laser cooling and trapping the 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F molecule. At first, the highly diagonal Franck-Condon factors of the main transitions are verified by the closed-form approximation, Morse approximation, and Rydberg-Klein-Rees inversion methods, respectively. Afterwards, we investigate the lower $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}$ hyperfine manifolds using a quantum effective Hamiltonian approach and obtain the zero-field hyperfine spectrum with an accuracy of less than 30 $\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{K}$ compared with the experimental results, and then find out that one cooling beam and one or two repumping beams with their first-order sidebands are enough to implement an efficient laser slowing and cooling of 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F. Meanwhile, we also calculate the accurate hyperfine structure magnetic ggg factors of the rotational state ($X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+},N=1$) and briefly discuss the influence of the external fields on the hyperfine structure of 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F as well as its possibility of preparing three-dimensional magneto-optical trapping. Finally we give an explanation for the difference between the Stark and Zeeman effects from the perspective of parity and time reversal symmetry. Our study shows that, besides appropriate excitation wavelengths, the short lifetime for the first excited state $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}$, and lighter mass, the 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F radical could be a good candidate molecule amenable to laser cooling and magneto-optical trapping.
The simple structure of the BH molecule makes it an excellent candidate for direct laser cooling. We measure the branching ratios for the decay of the A^{1}Pi (v'=0) state to vibrational levels of the ground state, X^{1}Sigma^{+}, and find that they are exceedingly favourable for laser cooling. We verify that the branching ratio for the spin-forbidden transition to the intermediate a^{3}Pi state is inconsequentially small. We measure the frequency of the lowest rotational transition of the X state, and the hyperfine structure in the relevant levels of both the X and A states, and determine the nuclear electric quadrupole and magnetic dipole coupling constants. Our results show that, with a relatively simple laser cooling scheme, a Zeeman slower and magneto-optical trap can be used to cool, slow and trap BH molecules.
This thesis investigates the suitability of BH molecules for laser cooling and describes progress towards the laser cooling of this molecule. We produce a molecular beam of BH and measure the branching ratios for the excited electronic state, A^{1}\Pi(v_{0}=0), to decay to the various vibrational states of the ground electronic state, X^{1}\Sigma. We verify that the branching ratio for the spin-forbidden transition to an intermediate triplet state is inconsequentially small. We measure the frequency of the lowest rotational transition of the X state, and the hyper fine structure in the relevant levels of both the X and A states, and determine the nuclear electric quadrupole and magnetic dipole coupling constants. We use a semiclassical model of the molecule-light interaction to investigate the expected cycling behaviour on the main cooling transition using light with modulated polarisation. The results of the model are compared with the effect of modulating the polarisation experimentally using an electro-optic modulator. In order to repump the population that leaks into the first vibrationally excited state, we have designed, built and tested a suitable repump laser and have demonstrated that we can drive the repump transition. We have also designed a Zeeman slower for slowing molecules to low velocity so that they can be trapped. Our results show that a relatively simple laser cooling scheme can be used to cool, slow and trap BH molecules.
High Resolution Image Download MS PowerPoint Slide Alkaline-earth-metal monohydrides M H ( M = Be, Mg, Ca, Sr, Ba) have long been regarded as promising candidates toward laser cooling and trapping; however, their rich internal level structures that are amenable to magneto-optical trapping have not been completely explored. Here, we first systematically evaluated Franck–Condon factors of these alkaline-earth-metal monohydrides in the A 2 Π 1/2 ← X 2 Σ + transition, exploiting three respective methods (the Morse potential, the closed-form approximation, and the Rydberg–Klein–Rees method). The effective Hamiltonian matrix was introduced for MgH, CaH, SrH, and BaH individually in order to figure out their molecular hyperfine structures of X 2 Σ +, the transition wavelengths in the vacuum, and hyperfine branching ratios of A 2 Π 1/2 ( J ′ = 1/2,+) ← X 2 Σ + ( N = 1,−), followed by possible sideband modulation proposals to address all hyperfine manifolds. Lastly, the Zeeman energy level structures and associated magnetic g factors of the ground state X 2 Σ + ( N = 1,−) were also presented. Our theoretical results here not only shed more light on the molecular spectroscopy of alkaline-earth-metal monohydrides toward laser cooling and magneto-optical trapping but also can contribute to research in molecular collisions involving few-atom molecular systems, spectral analysis in astrophysics and astrochemistry, and even precision measurement of fundamental constants such as the quest for nonzero detection of electron’s electric dipole moment.
Achieving laser cooling of molecules necessitates the establishment of a closed optical cycling transition. In contrast to atoms, molecules exhibit additional vibrational and rotational structures, which must be carefully addressed-alongside hyperfine splittings-when designing the laser frequency scheme for efficient optical cycling. In this work, we investigated optical cycling in MgF molecules on the laser cooling transition, namely [Formula: see text] transition between the electronic ground state ([Formula: see text]) and the electronic excited state ([Formula: see text]). The ground state comprises four hyperfine levels, of which two are unresolved within the excited-state linewidth; the two hyperfine levels in the excited state are also unresolved. Consequently, three laser frequencies suffice to address all transitions. This was realized by generating three independently tunable frequency components using acousto-optic modulators (AOMs). With optimized detunings, power ratios, and total beam power, simultaneous application of all three frequency components increased the total number of scattered photons by up to [Formula: see text] relative to the sum of the individual single-frequency signals. Applying a tilted magnetic field to remix the dark Zeeman states increased the photon yield by an additional factor of [Formula: see text], leading to an overall enhancement of about sevenfold. These results provide quantitative benchmarks for MgF optical cycling and practical guidance for future molecular slowing and magneto-optical trapping experiments.