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Physical Review A

Large optical forces on a barium monofluoride molecule using laser pulses for absorption and stimulated emission: A full density-matrix simulation

A. Marsman, D. Heinrich, Marko Horbatsch, Eric A. Hessels

Published Mar 10, 2023• 2 citations
Publisher

Abstract

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 ${\mathrm{EDM}}^{3}$ 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.

DOI
10.1103/physreva.107.032811

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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.
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 $\ensuremath{\pi}$ 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.
As a heavy molecule, barium monofluoride (BaF) presents itself as a promising candidate for measuring permanent electric dipole moment. Here we report the realization of three-dimensional magneto-optical trapping (MOT) of BaF molecules. Through the repumping of all the vibrational states up to v=3, and rotational states up to N=3, we effectively close the transition to a leakage level lower than 10^{-5}. This approach enables molecules to scatter a sufficient number of photons required for laser cooling and trapping. By employing a technique that involves chirping the slowing laser frequency, BaF molecules are decelerated to near-zero velocity, resulting in the capture of approximately 3×10^{3} molecules in a MOT. Our findings represent a significant step towards the realization of ultracold BaF molecules and the conduct of precision measurements with cold molecules.
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 that a bichromatic standing-wave laser field can exert a significantly larger force on a molecule than ordinary radiation pressure. Our experiment measures the deflection of a pulsed supersonic beam of CaF molecules by a two-frequency laser field detuned symmetrically about resonance with the nearly closed $X(v=0)\ensuremath{\rightarrow}B({v}^{\ensuremath{'}}=0)$ transition. The inferred force as a function of relative phase between the two counterpropagating beams is in reasonable agreement with numerical simulations of the bichromatic force in this multilevel system. The large magnitude of the force, coupled with the reduced rate of spontaneous emission, indicates its potential utility in the production and manipulation of ultracold molecules.