Vibrational Branching Ratios Research Articles

Theoretical spin-orbit laser cooling for AlZn molecule.

A spin-orbit coupling electronic structure study of the AlZn molecule is conducted to investigate the molecular properties of the low-lying electronic states and their feasibility toward direct laser cooling. This study uses the complete active-space self-consistent field level of theory, followed by the multireference configuration interaction method with Davidson correction (+Q). The potential energy and dipole moment curves and the spectroscopic constants are computed for the low-lying doublet and quartet electronic states in the 2S+1Λ± and Ω(±) representations. The transition dipole moments, the Franck-Condon factors, the Einstein coefficient, the radiative lifetimes, the vibrational branching ratio, and the slowing distance are determined between the lowest spin-orbit bound electronic states. These results show that the molecule AlZn has a high potential for laser cooling through the X2Π1/2 → (2)2Π1/2 transition by utilizing four lasers at a wavelength in the ultraviolet region, reaching a sub-microkelvin temperature limit.

A theoretical study on excited-state dynamical properties and laser cooling of zinc monohydride including spin-orbit couplings.

By means of highly accurate ab initio and dynamical calculations, we identify a suitable laser cooling candidate that contains a transition metal element, namely zinc monohydride (ZnH). The internally contracted multireference configuration interaction method is employed to compute the five lowest-lying Λ-S states of ZnH with the spin-orbit coupling effects included, and very good agreement is obtained between our calculated and experimental spectroscopic data. Our findings show that the position of crossing point of the A2Π and B2Σ+ states of ZnH is above the v' = 2 vibrational level of the A2Π state indicating that the crossings with higher electronic states will have no effect on laser cooling. Hence, we construct a feasible laser-cooling scheme for ZnH using five lasers based on the A2Π1/2 → X2Σ+ 1/2 transition, which features a large vibrational branching ratio R 00 (0.8458), a large number of scattered photons (9.8 × 103) and an extremely short radiative lifetime (64ns). The present work demonstrates the importance of electronic state crossings and spin-orbit couplings in the study of molecular laser cooling.

Characterization of low-lying electronic states of diatomic sodium bismuthide cation including the spin-orbit coupling effect

We present a high-level ab initio investigation of the diatomic sodium bismuth (NaBi+), which is a hitherto experimentally unknown species. The explicitly correlated multireference configuration interaction method is used to calculate energy points of thirteen low-lying Λ-S electron states associated with five dissociation limits. Detailed information on structural features, electronic characters, and spectroscopic constants is acquired. Our calculated relative energies between each of the interested higher dissociation limits and the lowest one for NaBi+, as well as splittings of energy levels for Bi, agree well with experimental data. Besides, we have identified and discussed the transition properties of bands from excited Ω states to the ground one, including transition dipole moments, Einstein coefficients, Franck-Condon factors, vibrational branching ratios, and radiative lifetimes. The extent of perturbations originating from the spin-orbit coupling effect to the present species is quantified through discussions on term values of spin-orbit matrix elements, and the spin-orbit coupling effect is proved to have introduced a significant effect to the low-lying electronic states of NaBi+.

The laser‐cooling of low‐lying states of gold‐aluminum MRCI+Q study including spin‐orbit coupling

AbstractThe possible laser cooling of AuAl molecules was investigated using high‐level ab initio calculations and considering the spin‐orbit coupling effect. Multi‐reference configuration interaction and the Davidson correction were also employed. Six Λ‐S electronic states were obtained, which were divided into 14 Ω states via spin‐orbit coupling. The optical transition showed potential for laser‐cooling applications owing to its highly diagonal Franck‐Condon factors and larger vibrational branching ratios. A possible optical cycling scheme using four lasers at near‐resonance wavelengths to eliminate vibrational branching loss is proposed. This scheme can be experimentally tested in future laser‐cooling experiments.

A spin–orbit configuration interaction study of the low-lying electronic states of the diatomic lithium antimonide cation

High-level ab initio calculations were performed to determine the structural features, electronic characteristics and transitional properties of LiSb+, which is a hitherto experimentally unknown diatomic cation. We acquired and evaluated the potential energy curves, spectroscopic constants and vibrational energy levels for low-lying Λ-S electronic states and their related Ω states. The spin–orbit coupling effect has a slight impact on these states. Transitional properties, such as transition dipole moments, Einstein coefficients, Franck–Condon factors and vibrational branching ratios, as well as the radiative lifetimes of transitions from excited Ω states to the ground state, have been identified and discussed. We anticipate that these prognostic results will act as guidelines for future research.

Extensive theoretical studies of the highly excited electronic states with the experimental parameters calculation for the laser cooling of CaI molecule

By using the multireference configuration interaction method followed by Davidson correction, the electronic structure of the molecule CaI has been investigated. The potential energy curves, the permanent and transition dipole moment curves, and the spectroscopic parameters of 18 electronic states are investigated for these states, along with 111 vibrational levels of the four lowest electronic states. The Franck–Condon factors and the radiative lifetime are calculated for the X2Σ+–(1)2Π transition. For this transition, the vibrational branching ratio, the slowing distance L, and the number of cycles ( N) for photon absorption/emission are calculated along with the Doppler and the recoil temperatures. A pre-cooling temperature in a helium buffer gas is studied and a laser cooling scheme is presented. The calculation of these different experimental parameters is crucial to exploring the optimal conditions under which the laser cooling experiment of CaI molecule will be performed.

A computational study of the low-lying electronic states of diatomic beryllium bismuthide

We have performed high-level ab initio computations to provide information associated with potential energy curves, molecular structures, electronic structures and vibrational energy levels of BeBi, which is yet an experimentally unknown species. Spectroscopic constants for twelve Λ-S states of the first four Λ-S dissociation channels are obtained for the first time. The feature of seven low-lying excited Ω states of BeBi, corresponding to the first three Ω dissociation limits, has been reported. The spin-orbit coupling effect is proved to have caused a significant impact on the investigated electronic states and interactions among them. Moreover, transition probabilities, such as transition dipole moments, Franck-Condon factors, Einstein coefficients, vibrational branching ratios and radiative lifetimes, are calculated for selected transition bands. Accompany computations are also been carried out for other Be-VA group diatomics of BeN, BeP and BeAs. Relevant data correlated with BeSb are collected from our previous study [Spectrochim. Acta A 208 (2019) 124]. Regular tendencies associated with molecular structures and spectroscopic constants are demonstrated from BeN to BeBi. We expect this work will extend our knowledge of the Be-VA group species and satisfy demands for experimental detections on BeBi.

Vibronic branching ratios for nearly closed rapid photon cycling of SrOH

The vibrational branching ratios of SrOH for radiative decay to the ground electronic state, $X^{2}\Sigma^{+}$, from the first two electronically excited states, $A^{2}\Pi$ and $B^{2}\Sigma^{+}$, are determined experimentally at the $\sim10^{-5}$ level. The observed small branching ratios enable the design of a full, practical laser-cooling scheme, including magneto-optical trapping and sub-Doppler laser cooling, with $>10^4$ photon scatters per molecule. Ab initio calculations sensitive to weak vibronic transitions are performed to facilitate the experimental measurement and analysis, and show good agreement with experiment.

Direct laser cooling of calcium monohydride molecules

We demonstrate optical cycling and laser cooling of a cryogenic buffer-gas beam of calcium monohydride (CaH) molecules. We measure vibrational branching ratios for laser cooling transitions for both excited electronic states A and B. Furthermore, we measure that repeated photon scattering via the A ← X transition is achievable at a rate of photons s−1 and demonstrate interaction-time limited scattering of photons by repumping the largest vibrational decay channel. We also demonstrate a sub-Doppler cooling technique, namely the magnetically assisted Sisyphus effect, and use it to cool the transverse temperature of a molecular beam of CaH. Using a standing wave of light, we lower the transverse temperature from 12.2(1.2) mK to 5.7(1.1) mK. We compare these results to a model that uses optical Bloch equations and Monte Carlo simulations of the molecular beam trajectories. This work establishes a clear pathway for creating a magneto-optical trap (MOT) of CaH molecules. Such a MOT could serve as a starting point for production of ultracold hydrogen gas via dissociation of a trapped CaH cloud.

Laser cooling and electronic structure of Be halide anions BeX- (X = Cl, Br, F, and I).

The adiabatic potential energy curves of the low lying electronic states of the Be halide anions BeX- (Cl, Br, F, and I) have been investigated in the representation 2s+1Λ(+/-) by using the complete active space self-consistent field with a multireference configuration interaction method. The spectroscopic parameters Te, Re, ωe, and Be and the static and transition dipole moment μe were studied, and a rovibrational study of the investigated electronic states was performed. New electronic states were investigated here for the first time. The calculated highly diagonal Franck-Condon factor and the short radiative lifetime among the lowest vibrational levels of the X1Σ0+ - (1)3Π1 transitions of the molecular anion BeF- prove its candidacy for Doppler laser cooling. The experimental proof of the stability and the calculated experimental parameters, such as the vibrational branching ratio, the slowing distance, the recoil, and Doppler temperatures with the experimental conditions of the buffer gas cell of this anion, open the route for experimental work on the BeF- molecular ion.

Imaging the Mode-Specificity in Cl + CH3D(v1-I, v1-II, v4 = 1; |jK⟩ = |10⟩) → CH2D(41) + HCl(v).

We report a crossed-beam imaging experiment on the title reactions at two collisional energies (Ec) of 5.3 and 10 kcal mol-1. Both the integral cross sections relative to the ground-state reactivity and the differential cross sections were measured and compared. We found that one-quantum excitations of the CH3-stretching vibrations of the CH3D reagent exerted profound mode-specificity in forming the umbrella-mode-excited CH2D(41) products with the vibrational efficacy of v4 > v1-I > v1-II at both Ec values. The concomitantly formed HCl(v) coproducts were vibrationally cold. Interestingly, the branching ratios of (v = 1)/(v = 0) appeared invariant to the initial stretch-modes of excitation at Ec = 5.3 kcal mol-1, yet exhibited a pronounced mode-specific dependency in the order of v1-II > v1-I > v4 at Ec = 10.3 kcal mol-1. This large and Ec-dependent disparity between the two Fermi-coupled reagents, v1-I and v1-II, is particularly significant and could be another facet─in addition to that in the recently reported vibrational enhancement factors─of the Fermi-phase-induced interference effect manifested in the product vibrational branching ratio. The pair-correlated angular distributions (vCH2D, vHCl)s = (41, 0)s in the three stretch-excited reactions were globally alike and resembled that of the ground-state reaction pair (00, 0)g, suggestive of a direct abstraction mechanism of the peripheral type. This is in sharp contrast to all other vibrationally excited pairs of (11, 0)s, (31, 0)s, and (61, 0)s previously reported in the CH2D + HCl isotopic channel, for which both the direct abstraction and a time-delayed resonance pathway partake.

Investigation of the low-lying electronic states of sulfur monofluoride cation

High-level ab initio computations are performed for the low-lying Λ-S and Ω electronic states of SF+, with the icMRCI+Q methodology coupled with basis sets of quintuple-ζ quality. The manifolds of electronic states correlating with the first and second dissociation limits are well determined. Electronic structures of all excited states investigated are characterized for the first time. Dipole moments of all states are obtained, and trends of polarity variations are discussed. Transition probabilities, such as transition dipole moments, Franck-Condon factors, vibrational branching ratios and radiative lifetimes, are also calculated for selected transition bands. We have also performed a parallel calculation for the SF radical to verify our computational accuracy. From comparative studies on associated parameters derived in this work and those reported in literature, a mutually satisfactory agreement is noticed, indicating our data and results are trustworthy.

Theoretical study on spectroscopic properties of 8 Λ-S and 23 Ω states for BH molecule

In this work, the potential energy curves of eight low electronic states (X<sup>1</sup>Σ<sup>+</sup>, a<sup>3</sup>Π, A<sup>1</sup>Π, b<sup>3</sup>Σ<sup>-</sup>, 2<sup>3</sup>Π, 1<sup>3</sup>Σ<sup>+</sup>, 1<sup>5</sup>Σ<sup>-</sup>, and 1<sup>5</sup>Π) and twenty-three Ω states of BH molecule, and the transition dipole moments among the <inline-formula><tex-math id="M10">\begin{document}$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M10.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M11">\begin{document}$ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M11.png"/></alternatives></inline-formula>, a<sup>3</sup>Π<sub>1</sub>, a<sup>3</sup>Π<sub>2</sub>, and A<sup>1</sup>Π<sub>1</sub> states are calculated by using the internally contracted multireference configuration interaction (icMRCI) method. In order to obtain the accurate potential energy curve, the errors caused by single and double electron excitation, core-valence correlation effects, relativistic effects and basis set truncation are corrected. The spectral and transition data of BH molecule are in good agreement with the available theoretical and experimental data. The calculation results show that the A<sup>1</sup>Π<sub>1</sub>(<i>υ′</i> = 0-2, <i>J′</i> = 1, +) →<inline-formula><tex-math id="M12">\begin{document}$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M12.png"/></alternatives></inline-formula>(<i>υ′′</i> = 0-2, <i>J′′</i> = 1, –) transition has large Einstein <i>A</i>-coefficient, weighted absorption oscillator strength, and highly diagonal vibrational branching ratio<i> R</i><sub><i>υ′υ′′</i></sub>, and the excited state A<sup>1</sup>Π<sub>1</sub>(<i>υ′</i> = 0, 1) have short spontaneous radiation lifetimes. Moreover, the effects of <inline-formula><tex-math id="M13">\begin{document}$ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M13.png"/></alternatives></inline-formula>and a<sup>3</sup>Π<sub>1</sub> states on A<sup>1</sup>Π<sub>1</sub>(<i>υ′</i> = 0) ↔ <inline-formula><tex-math id="M14">\begin{document}$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M14.png"/></alternatives></inline-formula>(<i>υ′′</i> = 0) cycle transition can be ignored. Therefore, according to the A<sup>1</sup>Π<sub>1</sub>(<i>υ′</i><sub> </sub>= 0-1, <i>J′</i> = 1, +) ↔ <inline-formula><tex-math id="M15">\begin{document}$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220038_M15.png"/></alternatives></inline-formula>(<i>υ′′</i><sub> </sub>= 0-3, <i>J</i>′′ = 1, –) cycle transition, we propose to apply one main cooling laser (<i>λ</i><sub>00</sub> = 432.45 nm) and two repumping lasers (<i>λ</i><sub>10</sub> = 479.67 nm and <i>λ</i><sub>21</sub> = 481.40 nm) to laser cooling BH molecules, and evaluation of the cooling effect.

Excellent Ultracold Molecular Candidates From Group VA Hydrides: Whether Do Nearby Electronic States Interfere?

By means of highly accurate ab initio calculations, we identify two excellent ultracold molecular candidates from group VA hydrides. We find that NH and PH are suitable for the production of ultracold molecules, and the feasibility and advantage of two laser cooling schemes are demonstrated, which involve different spin-orbit states ( and ). The internally contracted multireference configuration interaction method is applied in calculations of the six low-lying Λ-S states of NH and PH with the spin-orbit coupling effects included, and excellent agreement is achieved between the computed and experimental spectroscopic data. We find that the locations of crossing point between the and states of NH and PH are higher than the corresponding v′ = 2 vibrational levels of the state indicating that the crossings with higher electronic states would not affect laser cooling. Meanwhile, the extremely small vibrational branching loss ratios of the → transition for NH and PH (NH: 1.81 × 10–8; PH: 1.08 × 10–6) indicate that the intermediate electronic state will not interfere with the laser cooling. Consequently, we construct feasible laser-cooling schemes for NH and PH using three lasers based on the → transition, which feature highly diagonal vibrational branching ratio (NH: 0.9952; PH: 0.9977), the large number of scattered photons (NH: 1.04×105; PH: 8.32×106) and very short radiative lifetimes (NH: 474 ns; PH: 526 ns). Our work suggests that feasible laser-cooling schemes could be established for a molecular system with extra electronic states close to those chosen for laser-cooling.

Theoretical investigation of the low lying electronic states of MgGa

In this work, we investigate the low-lying electronic states correlated to the first and the second dissociation channels of MgGa molecule, neglecting and including the spin–orbit coupling effect. High-level ab initio calculations have been performed by using the icMRCI + Q method. Potential energy curves, spectroscopic constants, electron configurations and dipole moments are derived and discussed. Molecular structures of several magnesium-group 13 diatomics have been probed and analyzed. Information associated with transition dipole moments, Franck-Condon factors, vibrational branching ratios and radiative lifetimes between the Ω states are also well characterized. It is anticipated this work will provide some inspiration for further studies on MgGa.

Observation and laser spectroscopy of ytterbium monomethoxide,YbOCH3

We describe a laser spectroscopic study of ytterbium monomethoxide, YbOCH$_3$, a species of interest to searches for time-reversal symmetry violation using laser-cooled molecules. We report measurements of vibrational structure in the $\tilde{X}$ and $\tilde{A}$ states, vibrational branching ratios for several components of the $\tilde{A}$ state, and radiative lifetimes of low-lying electronic states. $\textit{Ab initio}$ calculations are used to aid the assignment of vibronic emission bands and provide insight into the electronic and vibrational structure. Our results demonstrate that rapid optical cycling is feasible for YbOCH$_3$, opening a path to orders-of-magnitude increased sensitivity in future measurements of P- and/or T-violating physics.

Theoretical Investigation on the Laser Cooling of AlD Molecule

The potential energy curves for four Λ-S and eight Ω states of the AlD molecule are calculated by using the valence internally contracted multireference configuration interaction approach with the Davidson modification (icMRCI+Q). The core-valence correlation and relativistic corrections are included. The extrapolation of potential energies to the complete basis set limit is made. Transition dipole moments (TDMs) between the six bound Ω states are also calculated by the icMRCI approach. The calculated spectroscopic constants are in good agreement with the available experimental data and theoretical values. Based on the obtained potential energy curves and transition dipole moments, highly diagonal Franck-Condon factors and vibrational branching ratios are determined for the A1π1(υ'=0,1)→X1Σ+0+(υ'') transition, short spontaneous radiative lifetime and narrow radiative width for the excited state A1π1 (υ'=0, 1) are also predicted. On this account, the optical scheme of the laser cooling for AlD molecule is constructed with A1π1(υ')↔X1Σ+0+(υ'') as the close-loop transition. The proposed laser drives X1Σ+0+(υ'')→A1π1(υ') transition by using three wavelengths (main laser beam λ00=420.96 nm; two repumping laser beams λ10=443.00 nm and λ21=448.94 nm). The Doppler temperature (TDoppler=44.94 μK) and recoiltemperature(TRecoil=3.73 μK) for the A1π1 (υ'=0)X1Σ+0+ (υ''=0) transition are also calculated. These results can provide theoretical support for the experimental study of laser-cooled AlD molecules.

Theoretical investigation on the low-lying electronic states of diatomic magnesium bismuthide including the spin-orbit coupling effect

High-level ab initio computations have been performed to investigate molecular structures, potential energy curves, vibrational energy levels and spectroscopic constants for twelve Λ-S states of the first four dissociation limits of MgBi. Characterizations of seven Ω states, corresponding to the first and the second Λ-S dissociation limits, have been explored for the first time. The spin–orbit coupling effect is revealed to have introduced a significant impact on the pattern of these electronic states and interactions among them. Our predictions for molecular structures and spectroscopic constants of MgBi are compared with available data of other magnesium-group 18 family species. Regular tendencies of these parameters are clearly exhibited when the group 18 atom is replaced by another one in the group. Information associated with transition dipole moments, Franck-Condon factors, vibrational branching ratios and radiative lifetimes between the Ω states are obtained and their transitional properties are analyzed and discussed. The results and data determined in this work are expected to guide and assist laboratorial detections of MgBi and to extend our understanding for the magnesium-group 18 species.

Molecular Asymmetry and Optical Cycling: Laser Cooling Asymmetric Top Molecules

We present a practical roadmap to achieve optical cycling and laser cooling of asymmetric top molecules (ATMs). Our theoretical analysis describes how reduced molecular symmetry, as compared to diatomic and symmetric non-linear molecules, plays a role in photon scattering. We present methods to circumvent limitations on rapid photon cycling in these systems. We calculate vibrational branching ratios for a diverse set of asymmetric top molecules and find that many species within a broad class of molecules can be effectively cooled with a manageable number of lasers. We also describe methods to achieve rotationally closed optical cycles in ATMs. Despite significant structural complexity, laser cooling can be made effective using extensions of the current techniques used for linear molecules. Potential scientific impacts of laser-cooled ATMs span frontiers in controlled chemistry, quantum simulation, and searches for physics beyond the Standard Model.

A Theoretical Study on Laser Cooling Feasibility of Group IVA Hydrides XH (X = Si, Ge, Sn, and Pb): The Role of Electronic State Crossing.

The feasibility of direct laser cooling of SiH, GeH, SnH, and PbH is investigated and assessed based upon first principles. The internally contracted multi-reference configuration interaction method with the Davidson correction is applied. Very good agreement is obtained between our computed spectroscopic constants and the available experimental data. We find that the locations of crossing point between the B2Σ− and A2Δ states have the tendency of moving downwards from CH to SnH relative to the bottom of the corresponding A2Δ potential, which precludes the laser cooling of GeH, SnH, and PbH. By including the spin-orbit coupling effects and on the basis of the transition, we propose a feasible laser cooling scheme for SiH using three lasers with wavelengths varying from 400 to 500 nm, which features a very large vibrational branching ratio (0.9954) and a very short radiative lifetime (575 ns). Moreover, similar studies are extended to carbon monosulfide (CS) with a feasible laser cooling scheme proposed. The importance of electronic state crossing in molecular laser cooling is underscored, and our work suggests useful caveats to the choice of promising candidates for producing ultracold molecules.