Abstract Aiming at a laser cooling investigation, we have used ab initio complete active space self consistent field (CASSCF)/(MRCI +Q) calculations to study the electronic structure of the diatomic molecule CaK and its molecular ions CaK+ and CaK−. The potential energy curves and the static dipole moment curves have been investigated for the considered molecules along with the spectroscopic constants T e, ω e, B e, and R e, in addition to the values of dipole moment μ e and dissociation energy D e. Overall, 19 and 14 electronic states have been studied respectively for CaK, CaK+, from which 12 for CaK and six for CaK+ have been investigated here for the first time. Our obtained results agree well with data related to states that have been previously examined. Nineteen electronic states have been explored for CaK−, which up to our knowledge have not been previously calculated. The transition dipole moments have been calculated for the lowest Σ+–Σ+ and Σ+–Π transitions along with the Franck–Condon factor, Einstein coefficient, the spontaneous radiative lifetime, and the emission oscillator strength corresponding to the investigated transitions. A ro-vibrational analysis has been done via the canonical function approach, where the vibrational parameters E v, B v, D v, and the turning points R min and R max have been determined. These calculations showed that the molecule CaK is a suitable candidate for Doppler laser cooling, and we propose a laser cooling scheme to this end. The Doppler limit temperature T D and recoil temperature T r have values as low as T D = 51 μK and T r = 156 nK. The results should provide a useful reference for experimental spectroscopic and ultra-cold molecular physics studies.
Abstract Aiming at a laser cooling investigation, we have used ab initio complete active space self consistent field (CASSCF)/(MRCI +Q) calculations to study the electronic structure of the diatomic molecule CaK and its molecular ions CaK+ and CaK−. The potential energy curves and the static dipole moment curves have been investigated for the considered molecules along with the spectroscopic constants T e, ω e, B e, and R e, in addition to the values of dipole moment μ e and dissociation energy D e. Overall, 19 and 14 electronic states have been studied respectively for CaK, CaK+, from which 12 for CaK and six for CaK+ have been investigated here for the first time. Our obtained results agree well with data related to states that have been previously examined. Nineteen electronic states have been explored for CaK−, which up to our knowledge have not been previously calculated. The transition dipole moments have been calculated for the lowest Σ+–Σ+ and Σ+–Π transitions along with the Franck–Condon factor, Einstein coefficient, the spontaneous radiative lifetime, and the emission oscillator strength corresponding to the investigated transitions. A ro-vibrational analysis has been done via the canonical function approach, where the vibrational parameters E v, B v, D v, and the turning points R min and R max have been determined. These calculations showed that the molecule CaK is a suitable candidate for Doppler laser cooling, and we propose a laser cooling scheme to this end. The Doppler limit temperature T D and recoil temperature T r have values as low as T D = 51 μK and T r = 156 nK. The results should provide a useful reference for experimental spectroscopic and ultra-cold molecular physics studies.
Abstract The ground and excited electronic states of the diatomic molecules CaCs and CaNa have been investigated by implementing the ab initio CASSCF/(MRCI + Q) calculation. The potential energy curves of the doublet and quartet electronic low energy states in the representation 2s+1Λ(±) have been determined for the two considered molecules, in addition to the spectroscopic constants Te, ωe, Be, Re, and the values of the dipole moment μe and the dissociation energy De. The determination of vibrational constants Ev, Bv, Dv, and the turning points Rmin and Rmax up to the vibrational level v = 100 was possible with the use of the canonical functions schemes. Additionally, the transition and the static dipole moments curves, Einstein coefficients, the spontaneous radiative lifetime, the emission oscillator strength, and the Franck–Condon factors are computed. These calculations showed that the molecule CaCs is a good candidate for Doppler laser cooling with an intermediate state. A “four laser” cooling scheme is presented, along with the values of Doppler limit temperature TD = 55.9 μK and the recoil temperature Tr = 132 nK. These results should provide a good reference for experimental spectroscopic and ultra-cold molecular physics studies.
The electronic structure, including the spin–orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω(±) and 2s+1Ʌ(+/-) representation. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energies De agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ -Π, Π - ∑+ and Δ - Φ transitions among specific Ω(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission Aν′ν, and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character fionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.
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 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.
Abstract This work presents a theoretical study of the laser cooling feasibility of the molecule LuF, in the fine structure level of approximation. An ab-initio complete active space self-consistent field (CASSCF)/MRCI with Davidson correction calculation has been done in the Λ(±) and Ω(±) representations. The corresponding adiabatic potential energy curves and spectroscopic parameters have been investigated for the low-lying electronic states. The calculated values of the internuclear distances of the X3Σ0+ and (1)3Π0+ states show the candidacy of the molecule LuF for direct laser cooling. Since the existence of the intermediate (1)3Δ1 state cannot be ignored, the investigation has been done by taking into consideration the two transitions (1)3Π0+−(1)3Δ1 and (1)3Π0+ −X3Σ0+. The calculation of the Franck–Condon factors, the radiative lifetimes, the total branching ratio, the slowing distance, and the laser cooling scheme study prove that the molecule LuF is a good candidate for Doppler laser cooling.
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.