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Physical Review A

Radiative force from optical cycling on magnesium monofluoride

Ruoxi Gu, Kang Yan, Di Wu, Jin Wei, Yong Xia, Jianping Yin

Published Apr 13, 2022• 11 citations
Publisher

Abstract

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 ${f}_{00}=0.972$ and ${f}_{01}=0.028$, 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.

DOI
10.1103/physreva.105.042806

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We demonstrate radiative force deflection by using an optical cycling of the X2\ensuremathΣ1/2+\ensuremath−A2\ensuremathΠ1/2X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}\ensuremath{-}A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}X2\ensuremathΣ1/2+​\ensuremath−A2\ensuremathΠ1/2​ 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∼200\ensuremath{\sim}200\ensuremath∼200 photons per molecule. This work is encouraging toward laser cooling and magneto-optical trapping of MgF molecules.
We demonstrate a scheme for optical cycling in the polar, diatomic molecule strontium monofluoride (SrF) using the X2Sigma+ --> A2Pi(1/2) electronic transition. SrF's highly diagonal Franck-Condon factors suppress vibrational branching. We eliminate rotational branching by employing a quasicycling N = 1 --> N' = 0 type transition in conjunction with magnetic field remixing of dark Zeeman sublevels. We observe cycling fluorescence and deflection through radiative force of an SrF molecular beam using this scheme. With straightforward improvements our scheme promises to allow more than 10(5) photon scatters, possibly enabling the direct laser cooling of SrF.
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.
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 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.
We demonstrate a quasioptical cycling for the $X(v=0)\ensuremath{\rightarrow}A({v}^{\ensuremath{'}}=0)$ transition and a radiative force-induced deflection on the buffer-gas-cooled BaF molecular beam. The laser-induced fluorescence enhancement with additional sidebands and a polarization modulation scheme indicates that the hyperfine states and the Zeeman sublevels are closed. The quasioptical cycling by repumping the $X(v=1)\ensuremath{\rightarrow}A({v}^{\ensuremath{'}}=0)$ leads to an $\ensuremath{\sim}0.8\ensuremath{-}\mathrm{mm}$ deflection of the beam via scattering $\ensuremath{\sim}150$ photons per molecule, in good agreement with the predictions from our multilevel rate equation model. Further improvement by closing the leakage X(v=2)X(v=2)X(v=2) and $\mathrm{\ensuremath{\Delta}}$ state allows scattering of thousands of photons and laser cooling and slowing of BaF.
Achieving laser cooling of molecules necessitates the establishment of a closed optical cycling transition. In contrast to atoms, molecules exhibit additional vibrational and rotational structures, which must be carefully addressed-alongside hyperfine splittings-when designing the laser frequency scheme for efficient optical cycling. In this work, we investigated optical cycling in MgF molecules on the laser cooling transition, namely [Formula: see text] transition between the electronic ground state ([Formula: see text]) and the electronic excited state ([Formula: see text]). The ground state comprises four hyperfine levels, of which two are unresolved within the excited-state linewidth; the two hyperfine levels in the excited state are also unresolved. Consequently, three laser frequencies suffice to address all transitions. This was realized by generating three independently tunable frequency components using acousto-optic modulators (AOMs). With optimized detunings, power ratios, and total beam power, simultaneous application of all three frequency components increased the total number of scattered photons by up to [Formula: see text] relative to the sum of the individual single-frequency signals. Applying a tilted magnetic field to remix the dark Zeeman states increased the photon yield by an additional factor of [Formula: see text], leading to an overall enhancement of about sevenfold. These results provide quantitative benchmarks for MgF optical cycling and practical guidance for future molecular slowing and magneto-optical trapping experiments.