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Physical Review A

Calculation of vibrational branching ratios and hyperfine structure of 24Mg19F and its suitability for laser cooling and magneto-optical trapping

Liang Xu, Yanning Yin, Bin Wei, Yong Xia, Jianping Yin

Published Jan 12, 2016• 46 citations
Publisher

Abstract

More recently, laser cooling of the diatomic radical magnesium monofluoride (${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$) 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 ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$ 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 ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$. 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 ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$ 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 ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$ radical could be a good candidate molecule amenable to laser cooling and magneto-optical trapping.

DOI
10.1103/physreva.93.013408

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More recently, laser cooling of the diatomic radical magnesium monofluoride (24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}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{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}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 X2\ensuremathΣ1/2+X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}X2\ensuremathΣ1/2+​ hyperfine manifolds using a quantum effective Hamiltonian approach and obtain the zero-field hyperfine spectrum with an accuracy of less than 30 kHz\ensuremath∼5\ensuremathμK\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{K}kHz\ensuremath∼5\ensuremathμK 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{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F. Meanwhile, we also calculate the accurate hyperfine structure magnetic ggg factors of the rotational state (X2\ensuremathΣ1/2+,N=1X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+},N=1X2\ensuremathΣ1/2+​,N=1) and briefly discuss the influence of the external fields on the hyperfine structure of 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}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 A2\ensuremathΠ1/2A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}A2\ensuremathΠ1/2​, and lighter mass, the 24Mg19F{}^{24}{\mathrm{Mg}}^{19}\mathrm{F}24Mg19F radical could be a good candidate molecule amenable to laser cooling and magneto-optical trapping.
For laser-cooling considerations, we have theoretically investigated the electronic, rovibrational, and hyperfine structures of the BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between the metastable ${A}^{{\ensuremath{'}}^{2}}\mathrm{\ensuremath{\Delta}}$ and ${A}^{2}\mathrm{\ensuremath{\Pi}}$ states and, further, the lifetime of the $\mathrm{\ensuremath{\Delta}}$ state have been estimated since the loss procedure via the $\mathrm{\ensuremath{\Delta}}$ state might fatally break the main quasicycling $\mathrm{\ensuremath{\Sigma}}\ensuremath{-}\mathrm{\ensuremath{\Pi}}$ transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational state in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state provide benchmarks for sideband modulations of the cooling and repumping lasers and the remixing microwaves to address all necessary levels. The calculated Zeeman shift and ggg factors for both XXX and AAA states serve as benchmarks for selection of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.
Recently, there have been great interest and advancement in the field of laser cooling and magneto-optical trapping of molecules. The rich internal structure of molecules naturally lends themselves to extensive and exciting applications. In this paper, the radical , as a promising candidate for laser cooling and magneto-optical trapping, is discussed in detail. The highly diagonal Franck–Condon factors between the and states are first confirmed with three different methods. Afterwards, with the effective Hamiltonian approach and irreducible tensor theory, the hyperfine structure of the state is calculated accurately. A scheme for laser cooling is given clearly. Besides, the Zeeman effects of the upper ( ) and lower ( ) levels are also studied, and their respective g factors are obtained under a weak magnetic field. Its large g factor of the upper state is advantageous for magneto-optical trapping. Finally, by studying Stark effect of BaF in the , we investigate the dependence of the internal effective electric field on the applied electric field. It is suggested that such a laser-cooled BaF is also a promising candidate for precision measurement of electron electric dipole moment.
High Resolution Image Download MS PowerPoint Slide Alkaline-earth-metal monohydrides M H ( M = Be, Mg, Ca, Sr, Ba) have long been regarded as promising candidates toward laser cooling and trapping; however, their rich internal level structures that are amenable to magneto-optical trapping have not been completely explored. Here, we first systematically evaluated Franck–Condon factors of these alkaline-earth-metal monohydrides in the A 2 Π 1/2 ← X 2 Σ + transition, exploiting three respective methods (the Morse potential, the closed-form approximation, and the Rydberg–Klein–Rees method). The effective Hamiltonian matrix was introduced for MgH, CaH, SrH, and BaH individually in order to figure out their molecular hyperfine structures of X 2 Σ +, the transition wavelengths in the vacuum, and hyperfine branching ratios of A 2 Π 1/2 ( J ′ = 1/2,+) ← X 2 Σ + ( N = 1,−), followed by possible sideband modulation proposals to address all hyperfine manifolds. Lastly, the Zeeman energy level structures and associated magnetic g factors of the ground state X 2 Σ + ( N = 1,−) were also presented. Our theoretical results here not only shed more light on the molecular spectroscopy of alkaline-earth-metal monohydrides toward laser cooling and magneto-optical trapping but also can contribute to research in molecular collisions involving few-atom molecular systems, spectral analysis in astrophysics and astrochemistry, and even precision measurement of fundamental constants such as the quest for nonzero detection of electron’s electric dipole moment.
We study the electronic and hyperfine structures of 24MgH^{24}\mathrm{MgH}24MgH molecule, which are of crucial importance for the laser cooling of the molecule. The accurate spectroscopic constants and hyperfine levels are presented for $X^{2}\mathrm{\ensuremath{\Sigma}}^{+}$ and $A^{2}\mathrm{\ensuremath{\Pi}}$ symmetries. The theoretical results are in good agreement with the experimental data. We then provide a scheme for the laser-driven cycling transitions of $A^{2}\mathrm{\ensuremath{\Pi}}_{1/2}\ensuremath{\leftarrow}X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2}$. In addition, we calculate the hyperfine branching ratios for the rate of decay from $|A^{2}\mathrm{\ensuremath{\Pi}}_{1/2},{J}^{\ensuremath{'}}=1/2,+\ensuremath{\rangle}$ to $|X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2},N=1,\ensuremath{-}\ensuremath{\rangle}$ transition. We also provide a sideband modulation scheme to the pumping lasers to match all four hyperfine levels of the $X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2}$ (v=0v=0v=0, N=1N=1N=1). Finally, we calculate the Zeeman shift of the ($X^{2}\mathrm{\ensuremath{\Sigma}}_{1/2}$, v=0v=0v=0, N=1N=1N=1) ground state, and the typical hyperfine structure magnetic ggg factor gF{g}_{F}gF​ and mixed ggg factors gFeff{g}_{F}^{\mathrm{eff}}gFeff​ are also calculated. Our study is expected to be useful for the laser-cooling 24MgH^{24}\mathrm{MgH}24MgH molecule and the interpretation of astronomical spectra involving MgH molecule.
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 measure the upper-state lifetime and two ratios of vibrational branching fractions ${f}_{{v}^{\ensuremath{'}}v}$ on the $B{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Pi}}_{1}({v}^{\ensuremath{'}})\ensuremath{-}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}(v)$ transition of TlF. We find the BBB-state lifetime to be 99(9) ns. We also determine that the off-diagonal vibrational decays are highly suppressed: ${f}_{01}/{f}_{00}<2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and f02/f00=1.10(6){f}_{02}/{f}_{00}=1.10(6)f02​/f00​=1.10(6)%, in excellent agreement with their predicted values of ${f}_{01}/{f}_{00}<8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and f02/f00=1.0(2){f}_{02}/{f}_{00}=1.0(2)f02​/f00​=1.0(2)% based on Franck-Condon factors calculated using Morse and Rydberg-Klein-Rees (RKR) potentials. The implications of these results for the possible laser cooling of TlF and fundamental symmetries experiments are discussed.