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

Chinese Physics B

Sub-Doppler cooling of magnesium fluoride molecules

Jin 晋 Wei 魏, Di 迪 Wu 吴, T. V. Dong, Caizhen Zu, Yong 勇 Xia 夏, Jianping Yin

Published Mar 24, 2025• 0 citations
Publisher

Abstract

Abstract We present a theoretical approach to achieve sub-Doppler cooling of magnesium fluoride (MgF) molecules by tuning the AC Stark shift with a blue-detuned laser. We study three blue-detuned magneto–optical trapping (MOT) schemes by using the Bayesian optimization method with the optical Bloch equations. We perform a comprehensive analysis of the relationship between the force in the MOT and the velocities and positions of the MgF molecules. Monte–Carlo simulations show that our MOT schemes can achieve a temperature as low as 28 μK and a density as high as 4.0 × 108 cm−3 at the conditions of a ratio of two laser intensities of 2:7, a detuning of 3Γ and a polarization configuration of σ −–σ +. These results provide a clear way for transferring a large number of MgF molecules into a conservative trap to enhance the subsequent cooling such as evaporative or sympathetic cooling.

DOI
10.1088/1674-1056/adc408

Related papers

Blue-detuned molecular magneto-optical trap schemes based on Bayesian optimization

S. Xu, R. X. Li, Yong Xia +2 more

Direct laser cooling and trapping of molecules to temperature below the Doppler limit and density exceeding ${10}^{8}$ are challenging due to the sub-Doppler heating effects of a molecular magneto-optical trap (MOT). In our previous paper [S. Xu et al., Phys. Rev. Res. 4, L042036 (2022)], we presented a general approach to engineering the sub-Doppler force by tuning the AC Stark shift with the addition of a blue-detuned laser. Here, by employing the Bayesian optimization method to optical Bloch equations, we have identified multiple blue-detuned MOT schemes for the CaF molecule. From the three-dimensional Monte Carlo simulation, we obtained a MOT temperature and density of 14 $\textmu{}\mathrm{K}$ and $4.5\ifmmode\times\else\texttimes\fi{}{10}^{8} {\mathrm{cm}}^{\ensuremath{-}3}$, respectively. Our findings present a potential avenue for directly loading molecular MOTs into conservative traps, which can capitalize on the high density and low temperature of the MOTs.

arXiv:2305.16576•Physical Review A•Sep 5, 2023•4 citations

Blue-Detuned Magneto-optical Trap of Molecules

Justin J. Burau, Parul Aggarwal, Kameron Mehling +1 more

Direct laser cooling of molecules has reached a phase-space density exceeding 10^{-6} in optical traps but with rather small molecular numbers. To progress toward quantum degeneracy, a mechanism that combines sub-Doppler cooling and magneto-optical trapping would facilitate near unity transfer of ultracold molecules from the magneto-optical trap (MOT) to a conservative optical trap. Using the unique energy level structure of YO molecules, we demonstrate the first blue-detuned MOT for molecules that is optimized for both gray-molasses sub-Doppler cooling and relatively strong trapping forces. This first sub-Doppler molecular MOT provides an increase of phase-space density by 2 orders of magnitude over any previously reported molecular MOT.

arXiv:2212.07472•Physical Review Letters•May 10, 2023•44 citations

Engineering the sub-Doppler force in molecular magneto-optical traps

S. Xu, P. Kaebert, M. Stepanova +3 more

Current dual-frequency magneto-optical traps for ultracold molecules are plagued by sub-Doppler heating effects, making them vastly inferior to standard atomic MOTs. Here we demonstrate theoretically that the sub-Doppler effects in such a MOT can be engineered to provide cooling instead of heating. We give an intuitive picture how to achieve such cooling and show the cooling and trapping force results of the 16 level optical Bloch equations for the case of CaF molecules. From three-dimensional Monte Carlo simulations we estimate the temperature and density of our MOT to be $40 μK$ and $4 \times 10^8 cm^{-3}$ respectively for a molecule number of $10^5$.

arXiv:2203.07754•Mar 15, 2022•1 citation

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

Lim, Dongkyu, Eunmi Chae

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.

arXiv:2511.16022•Nov 20, 2025•0 citations

Trapping and cooling mechanisms in blue-detuned magneto-optical traps of molecules

Qinshu Lyu, Michael R. Tarbutt

In red-detuned magneto-optical traps (MOTs) of molecules, sub-Doppler heating competes with Doppler cooling, resulting in high temperature and low density. A solution is offered by the blue-detuned MOT where sub- Doppler cooling dominates and the cloud is compressed. Several blue-detuned molecular MOTs have been implemented. A recent implementation relies on a pair of orthogonally polarized components whose frequency separation is smaller than the transition linewidth. We identify the trapping force in these MOTs. At a certain magnetic field, there is a state that is dark to the laser propagating in one direction, but not to the counterpropagating one. This Zeeman-induced dark state (ZIDS) sets up an imbalance in the photon scattering rate, leading to a restoring force. We also study the role of the moving lattices generated by the closely spaced frequency components of the light. We show that there is a velocity-dependent force that drives the molecules toward the speeds of these moving lattices, and that over a relevant range of magnetic fields this combines with the ZIDS force to transport molecules toward the center of the MOT. Here, gray molasses cooling, assisted by nonadiabatic transitions driven by the time-varying polarization of the light field, cools the molecules toward zero velocity. We study these mechanisms for model systems with simple level structures and then extend them to molecules with ground-state hyperfine structure.

arXiv:2601.21097•Physical Review Research•May 3, 2026•0 citations

Dual-species stimulated deceleration of MgF molecules with Rb atoms

Wei Jin, Di Wu, Caizhen Zu +2 more

Abstract We propose a scheme for dual-species deceleration and trapping of a cold atom–molecule mixture by a frequency chirping stimulated force. We study the stimulated force exerted on MgF and Rb using optical Bloch equations based on a direct numerical solution for the time-dependent density matrix. We analyze the relationship between the frequency chirping rate and the number of MgF molecules and Rb atoms. In addition, we study the dynamical process of molecular deceleration and the effect of transverse diffusion. Monte–Carlo simulations show that buffer-gas-cooled MgF and Rb beams, with initial velocities of 200 m/s and 130 m/s respectively, can be decelerated to less than 10 m/s. This is achieved with laser powers of as low as 357 mW for MgF and 10 mW for Rb per traveling wave. The rapid deceleration minimizes molecular loss due to transverse diffusion during the deceleration process. The estimated number of molecules that can be trapped in a magneto-optical trap (MOT) is about 9.0 × 106, which is an order of magnitude larger than the number of MgF molecules decelerated by the spontaneous radiation force. The results offer a promising starting point for further studies of sympathetic cooling.

Chinese Physics B•Apr 10, 2025•0 citations
Abstract We present a theoretical approach to achieve sub-Doppler cooling of magnesium fluoride (MgF) molecules by tuning the AC Stark shift with a blue-detuned laser. We study three blue-detuned magneto–optical trapping (MOT) schemes by using the Bayesian optimization method with the optical Bloch equations. We perform a comprehensive analysis of the relationship between the force in the MOT and the velocities and positions of the MgF molecules. Monte–Carlo simulations show that our MOT schemes can achieve a temperature as low as 28 μK and a density as high as 4.0 × 108 cm−3 at the conditions of a ratio of two laser intensities of 2:7, a detuning of 3Γ and a polarization configuration of σ −–σ +. These results provide a clear way for transferring a large number of MgF molecules into a conservative trap to enhance the subsequent cooling such as evaporative or sympathetic cooling.
Direct laser cooling and trapping of molecules to temperature below the Doppler limit and density exceeding 108{10}^{8}108 are challenging due to the sub-Doppler heating effects of a molecular magneto-optical trap (MOT). In our previous paper [S. Xu et al., Phys. Rev. Res. 4, L042036 (2022)], we presented a general approach to engineering the sub-Doppler force by tuning the AC Stark shift with the addition of a blue-detuned laser. Here, by employing the Bayesian optimization method to optical Bloch equations, we have identified multiple blue-detuned MOT schemes for the CaF molecule. From the three-dimensional Monte Carlo simulation, we obtained a MOT temperature and density of 14 $\textmu{}\mathrm{K}$ and $4.5\ifmmode\times\else\texttimes\fi{}{10}^{8} {\mathrm{cm}}^{\ensuremath{-}3}$, respectively. Our findings present a potential avenue for directly loading molecular MOTs into conservative traps, which can capitalize on the high density and low temperature of the MOTs.
Direct laser cooling of molecules has reached a phase-space density exceeding 10^{-6} in optical traps but with rather small molecular numbers. To progress toward quantum degeneracy, a mechanism that combines sub-Doppler cooling and magneto-optical trapping would facilitate near unity transfer of ultracold molecules from the magneto-optical trap (MOT) to a conservative optical trap. Using the unique energy level structure of YO molecules, we demonstrate the first blue-detuned MOT for molecules that is optimized for both gray-molasses sub-Doppler cooling and relatively strong trapping forces. This first sub-Doppler molecular MOT provides an increase of phase-space density by 2 orders of magnitude over any previously reported molecular MOT.
Current dual-frequency magneto-optical traps for ultracold molecules are plagued by sub-Doppler heating effects, making them vastly inferior to standard atomic MOTs. Here we demonstrate theoretically that the sub-Doppler effects in such a MOT can be engineered to provide cooling instead of heating. We give an intuitive picture how to achieve such cooling and show the cooling and trapping force results of the 16 level optical Bloch equations for the case of CaF molecules. From three-dimensional Monte Carlo simulations we estimate the temperature and density of our MOT to be 40μK40 μK40μK and 4×108cm−34 \times 10^8 cm^{-3}4×108cm−3 respectively for a molecule number of 10510^5105.
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.
In red-detuned magneto-optical traps (MOTs) of molecules, sub-Doppler heating competes with Doppler cooling, resulting in high temperature and low density. A solution is offered by the blue-detuned MOT where sub- Doppler cooling dominates and the cloud is compressed. Several blue-detuned molecular MOTs have been implemented. A recent implementation relies on a pair of orthogonally polarized components whose frequency separation is smaller than the transition linewidth. We identify the trapping force in these MOTs. At a certain magnetic field, there is a state that is dark to the laser propagating in one direction, but not to the counterpropagating one. This Zeeman-induced dark state (ZIDS) sets up an imbalance in the photon scattering rate, leading to a restoring force. We also study the role of the moving lattices generated by the closely spaced frequency components of the light. We show that there is a velocity-dependent force that drives the molecules toward the speeds of these moving lattices, and that over a relevant range of magnetic fields this combines with the ZIDS force to transport molecules toward the center of the MOT. Here, gray molasses cooling, assisted by nonadiabatic transitions driven by the time-varying polarization of the light field, cools the molecules toward zero velocity. We study these mechanisms for model systems with simple level structures and then extend them to molecules with ground-state hyperfine structure.
Abstract We propose a scheme for dual-species deceleration and trapping of a cold atom–molecule mixture by a frequency chirping stimulated force. We study the stimulated force exerted on MgF and Rb using optical Bloch equations based on a direct numerical solution for the time-dependent density matrix. We analyze the relationship between the frequency chirping rate and the number of MgF molecules and Rb atoms. In addition, we study the dynamical process of molecular deceleration and the effect of transverse diffusion. Monte–Carlo simulations show that buffer-gas-cooled MgF and Rb beams, with initial velocities of 200 m/s and 130 m/s respectively, can be decelerated to less than 10 m/s. This is achieved with laser powers of as low as 357 mW for MgF and 10 mW for Rb per traveling wave. The rapid deceleration minimizes molecular loss due to transverse diffusion during the deceleration process. The estimated number of molecules that can be trapped in a magneto-optical trap (MOT) is about 9.0 × 106, which is an order of magnitude larger than the number of MgF molecules decelerated by the spontaneous radiation force. The results offer a promising starting point for further studies of sympathetic cooling.