The feasibility of direct laser cooling of SiH, GeH, SnH and PbH is investigated and assessed based upon first principles. The internally contracted multireference 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 B2Sigma- and A2Delta states have the tendency of moving downwards from CH to SnH relative to the bottom of the corresponding A2Delta potential, which precludes the laser cooling of GeH, SnH and PbH. By including the spin-orbit coupling effects and on the basis of the A2Delta5/2-> X2Pi3/2 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). 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.
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 ( A3Π2 and X3Σ1− ). 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 A3Π and Σ−5 states of NH and PH are higher than the corresponding v′ = 2 vibrational levels of the A3Π state indicating that the crossings with higher electronic states would not affect laser cooling. Meanwhile, the extremely small vibrational branching loss ratios of the A3Π2 → a1Δ2 transition for NH and PH (NH: 1.81 × 10–8; PH: 1.08 × 10–6) indicate that the a1Δ2 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 A3Π2 → X3Σ1− transition, which feature highly diagonal vibrational branching ratio R00 (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.
Laser cooling of polyatomic molecules to the ultracold regime may enable some new science and technology applications; however, the related study is still at its very early stage. Here, by means of accurate ab initio and dynamical calculations, we identify two new candidate tetratomic molecules that are suitable for laser cooling and demonstrate the feasibility and advantage of two laser cooling schemes that are able to produce ultracold CaCCH and SrCCH molecules. The internally contracted multiconfiguration reference configuration interaction method is applied, and excellent agreement is achieved between the computed and experimental spectroscopic data. We find that the X2Σ1/2+→A2Π1/2 transitions for both candidates feature diagonal Franck–Condon factors, short radiative lifetimes, and no interference from intermediate electronic states. In addition, the crossings with higher electronic states do not interfere. We further construct feasible laser cooling schemes for CaCCH and SrCCH, each of which allows scattering 104 photons for direct laser cooling. The estimated Doppler temperatures for both CaCCH and SrCCH are on the order of μK.
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.
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.
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.
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.