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arXiv:2203.07754

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

S. Xu, P. Kaebert, M. Stepanova, T. Poll, M. Siercke, S. Ospelkaus

Published Mar 15, 2022• 1 citation
arXivHTMLPDF

Abstract

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 $10^5$.

DOI
10.48550/arxiv.2203.07754

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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 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.
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 Recent experiments have demonstrated direct cooling and trapping of diatomic and triatomic molecules in magneto-optical traps (MOTs). However, even the best molecular MOTs to date still have density 10−5 times smaller than in typical atomic MOTs. The main limiting factors are: (i) inefficiencies in slowing molecules to velocities low enough to be captured by the MOT, (ii) low MOT capture velocities, and (iii) limits on density within the MOT resulting from sub-Doppler heating (Devlin and Tarbutt 2018 Phys. Rev. A 90 063415). All of these are consequences of the need to drive ‘Type-II’ optical cycling transitions, where dark states appear in Zeeman sublevels, in order to avoid rotational branching. We present simulations demonstrating ways to mitigate each of these limitations. This should pave the way toward loading molecules into conservative traps with sufficiently high density and number to evaporatively cool them to quantum degeneracy.
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.