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Journal of Physics B Atomic Molecular and Optical Physics

Bichromatic slowing of MgF molecules in multilevel systems

Xiuxiu Yang, Chuanliang Li, Yanning Yin, Supeng Xu, Xingjia Li, Yong Xia, Jianping Yin

Published Dec 6, 2016• 18 citations
Publisher

Abstract

Abstract We present a theoretical study of the bichromatic force exerted on magnesium monofluoride (MgF), in which we have considered the complex vibrational and rotational levels and the effects of small internal splittings and degeneracies, including fine and hyperfine structures and the magnetic quantum numbers. We calculate some parameters used in the MgF molecular transitions between X 2 Σ + , A 2 Π and B 2 Σ + states. It is the first time that the radiative lifetimes of B 2 Σ + → X 2 Σ + and B 2 Σ + → A 2 Π have been derived by ab initio calculations. The detailed numerical modeling of bichromatic forces by direct numerical solution for the time-dependent density matrix is presented. Here, we propose a simplified numerical model to study the dynamic process of MgF slowing by neglecting the effect of the high vibrational levels, in which a skewed magnetic field is applied to destabilize the dark state. We deduce the relation between per-bichromatic-component irradiance I and the total Rabi frequency amplitude. We also compare our proposed simplified model with two other theoretical ones (Aldridge et al 2016 Phys. Rev. A 93 013419 ). Monte Carlo simulations show that a buffer-gas-cooled MgF beam with a forward velocity of 120 m s −1 can be decelerated nearly to several m/s within a distance of ∼0.5 cm. Comparing with the B → X transition, we find that the A → X transition in MgF is more suitable for the bichromatic force cooling and slowing.

DOI
10.1088/1361-6455/50/1/015001

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Journal of Physics B Atomic Molecular and Optical Physics•Mar 31, 2015•8 citations
Abstract We present a theoretical study of the bichromatic force exerted on magnesium monofluoride (MgF), in which we have considered the complex vibrational and rotational levels and the effects of small internal splittings and degeneracies, including fine and hyperfine structures and the magnetic quantum numbers. We calculate some parameters used in the MgF molecular transitions between X 2 Σ + , A 2 Π and B 2 Σ + states. It is the first time that the radiative lifetimes of B 2 Σ + → X 2 Σ + and B 2 Σ + → A 2 Π have been derived by ab initio calculations. The detailed numerical modeling of bichromatic forces by direct numerical solution for the time-dependent density matrix is presented. Here, we propose a simplified numerical model to study the dynamic process of MgF slowing by neglecting the effect of the high vibrational levels, in which a skewed magnetic field is applied to destabilize the dark state. We deduce the relation between per-bichromatic-component irradiance I and the total Rabi frequency amplitude. We also compare our proposed simplified model with two other theoretical ones (Aldridge et al 2016 Phys. Rev. A 93 013419 ). Monte Carlo simulations show that a buffer-gas-cooled MgF beam with a forward velocity of 120 m s −1 can be decelerated nearly to several m/s within a distance of ∼0.5 cm. Comparing with the B → X transition, we find that the A → X transition in MgF is more suitable for the bichromatic force cooling and slowing.
We present a theoretical study of magneto-optical trapping (MOT) force exerted on magnesium monofluoride (MgF) with three-dimensional rate equations, in which we have considered the complex vibrational and rotational levels and the effects of small internal splittings and degeneracies, including fine and hyperfine structures and the magnetic quantum numbers. We investigate the feasibility of MOT for MgF with a very small excited-state ggg factor $(\phantom{\rule{4pt}{0ex}}{g}_{e}=\ensuremath{-}0.0002)$ and a large radiative decay rate $(\mathrm{\ensuremath{\Gamma}}=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}22\phantom{\rule{0.16em}{0ex}}\mathrm{MHz})$ for the electronic transition of $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ to $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}$ states. We also optimize the MOT with reference to the three-, four-, and more-frequency component models with various polarization configurations and detunings. By applying the dual-frequency arrangement to more than one hyperfine level, we suggest a configuration of the (3+1)(3+1)(3+1)-frequency components for achieving the MOT of MgF.
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.
A significant problem in laser cooling of molecules is the presence of the dark Zeeman sublevels. Herein, a detailed theoretical and experimental study of destabilizing the dark states is reported in magnesium monofluoride molecules. By applying an external magnetic field, the Zeeman sublevels are made to be time dependent and nondegenerate, forcing the dark states to Larmor precess into the bright states. It is found that the laser induced fluorescence signal depends on the angle and the magnitude of the magnetic field. Theoretical calculations are performed by solving the density matrix equations for the multiple-level system, which shows good agreement with experimental data. This study may provide a useful perspective for continuous efforts toward laser cooling of MgF molecules.
We demonstrate radiative force deflection by using an optical cycling of the $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}\ensuremath{-}A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}$ electronic transition in diatomic molecule magnesium monofluoride (MgF). For the (0,0) and (0,1) bands of the electronic transition, the Franck-Condon factors---obtained by the dispersed laser-induced fluorescence spectrum---are f00=0.972{f}_{00}=0.972f00​=0.972 and f01=0.028{f}_{01}=0.028f01​=0.028, which suggests that the vibrational branching is quasiclosed. Furthermore, the dark Zeeman sublevels are destabilized by applying an external magnetic field. The cycling fluorescence is clearly observed to reveal that the molecular beam is deflected by 4.9 mm via scattering $\ensuremath{\sim}200$ photons per molecule. This work is encouraging toward laser cooling and magneto-optical trapping of MgF molecules.
We report on hyperfine-resolved laser spectroscopy of the A2Π ← X2Σ+ transition of magnesium monofluoride (MgF), relevant for laser cooling. We recorded 25 rotational transitions with an absolute accuracy of better than 20 MHz, assigned 56 hyperfine lines, and determined precise rotational, fine, and hyperfine structure parameters for the A2Π state. The radiative lifetime of the A2Π state was determined to be 7.2(3) ns, in good agreement with ab initio calculations. The transition isotope shift between bosonic isotopologues of the molecule is recorded and compared to predicted values within the Born–Oppenheimer approximation. We measured the Stark effect of selected rotational lines of the A2Π ← X2Σ+ transition by applying electric fields of up to 10.6 kV cm−1 and determined the permanent electric dipole moments of 24MgF in its ground X2Σ+ and first excited A2Π states to be μX = 2.88(20) D and μA = 3.20(22) D, respectively. Based on these measurements, we caution for potential losses from the optical cycling transition due to electric field induced parity mixing in the excited state. In order to scatter 104 photons, the electric field must be controlled to below 1 V cm−1.
Abstract We theoretically investigate the possibility of stimulated light force deceleration and cooling of the diatomic magnesium fluoride molecular beam with near-cycling transitions in the bichromatic standing light wave of high intensity. The weighted degeneracy and force reduction factor are considered due to the behavior of the optical bichromatic force (BCF) in near-cycling transitions with internal degeneracies, and the two-level optical Bloch equations can estimate the actual behavior of the BCF. Our simulation shows that the stimulated force exceeding the spontaneous force by a factor of 2.8 can slow down the molecular beam to several m s −1 within centimeter-scale distance, and this slowing mechanism can eliminate the need of compensation of Doppler shift during the longitudinal deceleration of the molecular beam.