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 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 and
f01=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 high resolution electronic spectroscopy of cold magnesium monofluoride (MgF) molecules in the gas phase, which are created by a combination of laser ablation, chemical reaction, and 6 K helium buffer-gas cooling. Thanks to the sufficient population in the low-lying rotational states, the P, Q, and R branches in the electronic transition of the X2Σ+ to A2Π state are able to be measured unambiguously by in-cell absorption spectra. For the first time, we show that the A2Π state of MgF is actually a normal state, not an inverted one. The laser cooling relevant transitions X2Σ+v=0,1,N=1→A2Π1/2(v=0,J′=1/2) are also identified, along with the hyperfine structure of the X2Σ+(v = 0, N = 1) state. This study provides an important step for ongoing laser cooling experiments 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
g 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)-frequency components for achieving the MOT of MgF.
More recently, laser cooling of the diatomic radical magnesium monofluoride (
24Mg19F) is being experimentally preformed [Appl. Phys. Express 8, 092701 (2015) and Opt. Express 22, 28645 (2014)] and was also studied theoretically [Phys. Rev. A 91, 042511 (2015)]. However, some important problems still remain unsolved, so, in our paper, we perform further theoretical study for the feasibility of laser cooling and trapping the
24Mg19F molecule. At first, the highly diagonal Franck-Condon factors of the main transitions are verified by the closed-form approximation, Morse approximation, and Rydberg-Klein-Rees inversion methods, respectively. Afterwards, we investigate the lower $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}$ hyperfine manifolds using a quantum effective Hamiltonian approach and obtain the zero-field hyperfine spectrum with an accuracy of less than 30 $\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{K}$ compared with the experimental results, and then find out that one cooling beam and one or two repumping beams with their first-order sidebands are enough to implement an efficient laser slowing and cooling of
24Mg19F. Meanwhile, we also calculate the accurate hyperfine structure magnetic
g factors of the rotational state ($X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+},N=1$) and briefly discuss the influence of the external fields on the hyperfine structure of
24Mg19F as well as its possibility of preparing three-dimensional magneto-optical trapping. Finally we give an explanation for the difference between the Stark and Zeeman effects from the perspective of parity and time reversal symmetry. Our study shows that, besides appropriate excitation wavelengths, the short lifetime for the first excited state $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}$, and lighter mass, the
24Mg19F radical could be a good candidate molecule amenable to laser cooling and magneto-optical trapping.
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.