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arXiv:2305.16576 · Physical Review A

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

S. Xu, R. X. Li, Yong Xia, M. Siercke, S. Ospelkaus

Published Sep 5, 2023• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.108.033102

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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 \textmuK\textmu{}\mathrm{K}\textmuK and 4.5\ifmmode×\else\texttimes\fi108cm\ensuremath−34.5\ifmmode\times\else\texttimes\fi{}{10}^{8} {\mathrm{cm}}^{\ensuremath{-}3}4.5\ifmmode×\else\texttimes\fi108cm\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.
A key method to produce trapped and laser-cooled molecules is the magneto-optical trap (MOT), which is conventionally created using light red detuned from an optical transition. In this work, we report a MOT for CaF molecules created using blue-detuned light. The blue-detuned MOT (BDM) achieves temperatures well below the Doppler limit and provides the highest densities and phase-space densities reported to date in CaF MOTs. Our results suggest that BDMs are likely achievable in many relatively light molecules including polyatomic ones, but our measurements suggest that BDMs will be challenging to realize in substantially heavier molecules due to sub-mK trap depths. In addition to record temperatures and densities, we find that the BDM substantially simplifies and enhances the loading of molecules into optical tweezer arrays, which are a promising platform for quantum simulation and quantum information processing. Notably, the BDM reduces molecular number requirements ninefold compared to a conventional red-detuned MOT, while not requiring additional hardware. Our work therefore substantially simplifies preparing large-scale molecular tweezer arrays, which are a novel platform for simulation of quantum many-body dynamics and quantum information processing with molecular qubits.
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.
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.
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.
Abstract Laser cooling is used to produce ultracold atoms and molecules for quantum science and precision measurement applications. Molecules are more challenging to cool than atoms due to their vibrational and rotational internal degrees of freedom. Molecular rotations lead to the use of type-II transitions ( F ⩾ F ′ ) for magneto-optical trapping (MOT). When typical red detuned light frequencies are applied to these transitions, sub-Doppler heating is induced, resulting in higher temperatures and larger molecular cloud sizes than realized with the type-I MOTs most often used with atoms. To improve type-II MOTs, Jarvis et al (2018 Phys. Rev. Lett. 120 083201) proposed a blue-detuned MOT to be applied after initial cooling and capture with a red-detuned MOT. This was successfully implemented (Burau et al 2023 Phys. Rev. Lett. 130 193401; Jorapur et al 2024 Phys. Rev. Lett. 132 163403; Li et al 2024 Phys. Rev. Lett. 132 233402), realizing colder and denser molecular samples. Very recently, Hallas et al (2024 arXiv:2404.03636) demonstrated a blue-detuned MOT with a ‘1+2’ configuration that resulted in even stronger compression of the molecular cloud. Here, we describe and characterize theoretically the conveyor-belt mechanism that underlies this observed enhanced compression. We perform numerical simulations of the conveyor-belt mechanism using both stochastic Schrödinger equation and optical Bloch equation approaches. We investigate the conveyor-belt MOT characteristics in relation to laser parameters, g-factors and the structure of the molecule, and find that conveyor-belt trapping should be applicable to a wide range of laser-coolable molecules.
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.