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arXiv:2305.10641 · Physical Review A

Deflection of barium monofluoride molecules using the bichromatic force: A density-matrix simulation

A. Marsman, Marko Horbatsch, Eric A. Hessels

Published Jul 17, 2023• 5 citations
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Abstract

A full density-matrix simulation is performed for optical deflection of a barium monofluoride ($^{138}\mathrm{Ba}^{19}\mathrm{F}$) beam using the bichromatic force, which employs pairs of counterpropagating laser beams that are offset in frequency. We show that the force is sufficient to separate BaF molecules from the other products generated in a helium-buffer-gas-cooled ablation source. For our simulations, the density-matrix and force equations are numerically integrated during the entire time that the molecules pass through a laser beam to ensure that effects of the evolution of the Doppler shift and of the optical intensity and phase at the position of the molecule are properly included. The results of this paper are compared to those of a deflection scheme [A. Marsman, D. Heinrich, M. Horbatsch, and E. A. Hessels, Phys. Rev. A 107, 032811 (2023)] which uses $\ensuremath{\pi}$ pulses to drive frequency-resolved transitions. This paper is part of an effort by the ${\mathrm{EDM}}^{3}$ collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Separation of BaF molecules will aid in producing a sufficiently pure solid.

DOI
10.1103/physreva.108.012811

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A full density-matrix simulation is performed for optical deflection of a barium monofluoride (138Ba19F^{138}\mathrm{Ba}^{19}\mathrm{F}138Ba19F) beam using the bichromatic force, which employs pairs of counterpropagating laser beams that are offset in frequency. We show that the force is sufficient to separate BaF molecules from the other products generated in a helium-buffer-gas-cooled ablation source. For our simulations, the density-matrix and force equations are numerically integrated during the entire time that the molecules pass through a laser beam to ensure that effects of the evolution of the Doppler shift and of the optical intensity and phase at the position of the molecule are properly included. The results of this paper are compared to those of a deflection scheme [A. Marsman, D. Heinrich, M. Horbatsch, and E. A. Hessels, Phys. Rev. A 107, 032811 (2023)] which uses \ensuremathπ\ensuremath{\pi}\ensuremathπ pulses to drive frequency-resolved transitions. This paper is part of an effort by the EDM3{\mathrm{EDM}}^{3}EDM3 collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Separation of BaF molecules will aid in producing a sufficiently pure solid.
A full density-matrix simulation is performed for optical deflection of a barium monofluoride (BaF) beam. Pairs of counterpropagating laser pulses are used for absorption followed by stimulated emission. The scheme produces a force which is nearly an order of magnitude larger than that obtainable using continuous-wave laser deflection, and yields a force-to-spontaneous-decay ratio which is more than an order of magnitude larger. The large reduction in spontaneous decay is key to optical deflection of molecules, where branching ratios to other vibrational states do not allow for cycling transitions. This paper is part of an effort by the EDM3{\mathrm{EDM}}^{3}EDM3 collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Deflection of BaF molecules will separate them from the other ablation products coming from a buffer-gas-cooled ablation source, before embedding them into the argon solid. Our simulations show that sufficiently large deflections for this separation are feasible.
A full density-matrix simulation is performed for optical deflection of a barium monofluoride (BaF) beam. Pairs of counter-propagating laser pulses are used for stimulated absorption followed by stimulated emission. The scheme produces a force which is nearly an order of magnitude larger than that obtainable using continuous-wave laser deflection, and yields a force-to-spontaneous-decay ratio which is more than an order of magnitude larger. The large reduction in spontaneous decay is key to optical deflection of molecules, where branching ratios to other vibrational states do not allow for cycling transitions. This work is part of an effort by the EDM3^33 collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Deflection of BaF molecules will separate them from the other ablation products coming from a buffer-gas-cooled ablation source, before embedding them into the argon solid. Our simulations show that sufficiently large deflections for this separation are feasible.
We reported a detailed experimental study of the cold collision of barium monofluoride (BaF) with buffer gas and the high-resolution spectroscopy relevant with direct laser cooling. BaF molecules are efficiently produced with laser ablation and buffer-gas cooled in a cryogenic apparatus. The laser cooling relevant transition $|X\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}},v=0,N=1\ensuremath{\rangle}$ to $|A\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Pi}},{v}^{\ensuremath{'}}=0,{J}^{\ensuremath{'}}=1/2\ensuremath{\rangle}$ is identified. The collision cross section with buffer gas is measured to be $1.4(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{4.pt}{0ex}}{\text{cm}}^{\ensuremath{-}2}$, which is very suitable for buffer-gas cooling. Both rotational and vibrational temperatures are effectively cooled, and a large amount of molecules are quenched into the desired states. Our study provides an important benchmark for further laser cooling of the BaF molecule.
We demonstrate the effect of the coherent optical bichromatic force on a molecule, the polar free radical strontium monohydroxide (SrOH). A dual-frequency retroreflected laser beam addressing the X[over ˜]^{2}Σ^{+}↔A[over ˜]^{2}Π_{1/2} electronic transition coherently imparts momentum onto a cryogenic beam of SrOH. This directional photon exchange creates a bichromatic force that transversely deflects the molecules. By adjusting the relative phase between the forward and counterpropagating laser beams we reverse the direction of the applied force. A momentum transfer of 70ℏk is achieved with minimal loss of molecules to dark states. Modeling of the bichromatic force is performed via direct numerical solution of the time-dependent density matrix and is compared with experimental observations. Our results open the door to further coherent manipulation of molecular motion, including the efficient optical deceleration of diatomic and polyatomic molecules with complex level structures.
Coherent optical bichromatic forces have been shown to be effective tools for rapidly slowing and cooling simple atomic systems. While previous estimates suggest that these forces may also be effective for rapidly decelerating molecules or complex atoms, a quantitative treatment for multilevel systems has been lacking. We describe detailed numerical modeling of bichromatic forces by direct numerical solution for the time-dependent density matrix in the rotating-wave approximation. We describe both the general phenomenology of an arbitrary few-level system and the specific requirements for slowing and cooling on a many-level transition in calcium monofluoride (CaF), one of the molecules of greatest current experimental interest. We show that it should be possible to decelerate a cryogenic buffer-gas-cooled beam of CaF nearly to rest without a repumping laser and within a longitudinal distance of about 1 cm. We also compare a full 16-level simulation for the CaF $B\ensuremath{\leftrightarrow}X$ system with a simplified numerical model and with a semiquantitative estimate based on two-level systems. The simplified model performs nearly as well as the complete version, whereas the two-level model is useful for making order-of-magnitude estimates, but nothing more.