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.
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.
Abstract Alkaline-earth and alkali-metal mixtures have an electronic structure that is perfect for laser cooling. This makes them highly attractive for trapping and laser cooling experiments, allowing the formation of cold molecules. For this object, potential-energy curves and relevant spectroscopic parameters of the low-lying electronic excited states of 1,3Σ+, 1,3Π, and 1,3Δ symmetries of molecular-ion systems composed of alkaline-earth-ion and Francium alkali-metal-atom: ALKE-Fr+ (ALKE = Be, Mg, Ca and Sr), are determined using advanced theoretical technique in quantum chemistry, including a non-empirical pseudopotential, core-valence correlation, large Gaussian basis sets and Full Configuration Interaction (FCI). In order to obtain a more accurate understanding of the electronic structure of these systems, we also determined transition and permanent dipole moments and vibrational properties. Thereafter, the spontaneous and the black-body stimulated transition rates were determined and were employed to calculate lifetimes for all vibrational states of the ground electronic states 11Σ+ of molecular-ions under consideration. For the first and the second excited states, radiative lifetimes were investigated via the Franck–Condon approximation including bound-bound and bound-free transitions. High diagonal structure and large Franck Condon Factor (FCF) values f 00 = 0.987, f 11 = 0.959 and f 22 = 0.919 were obtained for the 11Π (v′ = 0, 1, 2)→ 11Σ+ (v = 0, 1, 2) transition making the BeFr+ system a good candidate for laser cooling. Furthermore, the current results could be used to investigate elastic scattering properties in cold-ion-atom collisions for the first excited states and may help the experimentalists for possible formation, spectroscopy, and photoassociation of cold ion-atom mixtures.
The feasibility of laser cooling MH (M=Be,Mg,Ca,Sr,andBa) is investigated using ab initio quantum chemistry. The ground state $X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}$ and first excited state $A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}$ of MH species are calculated using the multireference configuration interaction (MRCI) level of theory. For CaH, SrH, and BaH, the spin-orbit coupling effects are also taken into account in electronic structure calculations at the MRCI level. Calculated spectroscopic constants for 9BeH, 24MgH, 40CaH, 86SrH, and 138BaH show good agreement with available theoretical and experimental results. The permanent dipole moments and transition dipole moments (TDMs) of the $X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}$ and $A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}$ states of MH species are also calculated at the MRCI level of theory, and they are in good agreement with previous theoretical results. With the potential energy curves and TDMs obtained, the highly diagonally distributed Franck-Condon factors f00(9BeH:0.998,24MgH:0.954,40CaH:0.961,86SrH:0.978,and138BaH:0.971) for the $A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}\left({v}^{\ensuremath{'}}=0\right)\ensuremath{\rightarrow}X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}\left(v=0\right)$ transition are determined. Radiative lifetime calculations of the $A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}\left({v}^{\ensuremath{'}}=0\right)$ state (9BeH:82.0ns, 24MgH:48.6ns, 40CaH:33.3ns, 86SrH:33.2ns, and 138BaH: 68.6 ns) are found to be short enough for rapid laser cooling. The proposed main cycling laser drives the $X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}\left(v=0\right)\ensuremath{\rightarrow}A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}\left({v}^{\ensuremath{'}}=0\right)$ transition at wavelength ${\ensuremath{\lambda}}_{00}\left({}^{9}\mathrm{BeH}:497.2\phantom{\rule{0.16em}{0ex}}\mathrm{nm}{,}^{24}\mathrm{MgH}:525.5\phantom{\rule{0.16em}{0ex}}\mathrm{nm}{,}^{40}\mathrm{CaH}:675.4\phantom{\rule{0.16em}{0ex}}\mathrm{nm}{,}^{86}\mathrm{SrH}:740.3\phantom{\rule{0.16em}{0ex}}\mathrm{nm},\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.28em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{138}\mathrm{BaH}:952.6\phantom{\rule{0.16em}{0ex}}\mathrm{nm}\right)$. The results demonstrate the possibility of laser cooling MH species, and provide a promising theoretical reference for further theoretical and experimental research on alkaline-earth-metal monohydrides.
The main electronic properties, namely potential energy curves, permanent and transition dipole moments, static dipole polarizabilities, of the alkaline-earth hydride ion SrH + , as well as of CaH + and BaH + are computed through a full configuration interaction performed in a two-valence electronic configuration space build from a large Gaussian basis set. The doubly charged ionic core of the alkaline-earth atoms is modelled by an effective core potential including core polarization effects. Our study confirms that the properties of these series of molecular ions have very similar patterns, while it is predicted that the major electronic transition between the electronic ground state and the lowest excited state in BaH + is significantly weaker than the one in CaH + and SrH + . Such a study represents a first step towards the modelling of reactive collisions between cold and trapped alkaline-earth ions and H 2 , as well as for precision measurements based on overtone transitions using cold molecular ions.
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 this work, we present a thorough theoretical structure and spectroscopic study of the ground and low lying excited states of RbBa molecule. High-level ab-initio calculations are performed, using MCSCF/MRCI+Q level of method, based on the effective core potential (ECP) and core-polarization potential (CPP) approach. The potential energy curves, spectroscopic parameters, vibrationnel energy levels of the 16( 2,4 Σ + , 2,4 Π, 2,4 Δ) first electronic states, with respect to the lowest five dissociation limits were calculated. The comparison of the spectroscopic constants of the ground state X 2 Σ + with the available theoretical work, are in good agreement. The study of all the excited states is performed in this work for the first time. Afterwards, the spin-orbit operator is incorporated in valence MRCI calculation using optimized relativistic spin-orbit pseudo-potentials and 33 Ω states are generated and split into Λ-S states. In addition, both relativistic and non relativistic calculations of permanent and transition dipole moments are presented and discussed. Stimulated black body ( T = 300 K) and spontaneous transition rates of vibrational states of X 2 Σ + state were evaluated. The related vibrational lifetimes for RbBa are found to be in order of 10 3 s which is sufficiently large for ultracold experiments. Moreover, the vibrational life-time for the A 2 Σ + ( v’ ) and A 2 П ( v” ) states are measured and the possibility of Laser Cooling for the RbBa molecule is discussed based on Franck–Condon factors calculation of A 2 Σ + ( v’ )→ X 2 Σ + ( v ) and A 2 П( v” ) → X 2 Σ + ( v ) transition. This work represents a significant contribution for experimentalists as it provides efficient information in order to form cold alkali and alkaline-earth RbBa molecules.
Abstract In this theoretical work, we calculate molecular potential energy curves, spectroscopic constants and transition dipole moments for the ground ( X 2 Σ + u , B 2 Σ + g ) and first excited electronic states (A 2 Π u ) of alkaline-earth molecular ion Mg 2 + . We consider an ab initio multi-reference configuration interaction method using an aug-cc-pv5z Gaussian basis set and compare our results with those obtained by others. The comparison shows a very good agreement. In addition, we investigate the ion-atom elastic collisions for a wide range of energies including the isotopic effect. In close connections, we determine the scattering T-matrix elements for ground-state electronic potentials, which show divergent behavior at a particular energy, indicating the occurrence of scattering resonances. We find that the s -wave scattering length is positive for both ground-state potentials. We also study possible free-bound transitions and Franck–Condon overlap for our system.