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Physical Review A

Theoretical investigation of the laser cooling of a LiBe molecule

Yang You, Chuan‐Lu Yang, Meishan Wang, Xiao‐Guang Ma, Wen-Wang Liu

Published Sep 8, 2015• 37 citations
Publisher

Abstract

An optical scheme to create the simplest heteronuclear metal ultracold LiBe molecule is proposed based on ab initio quantum chemistry calculations. The potential energy curves, dipole moments, and transition dipole moments of $1\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}, 2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}, 1\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Pi}}$, and $2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Pi}}$ states are calculated using the multireference configuration interaction and large basis sets. The analytical functions deduced from the obtained curves are used to determine the rovibrational energy levels, the Franck-Condon factors, and the Einstein coefficients of the states through solving the Schr\"odinger equation of nuclear movement. The spectroscopic parameters are deduced with the obtained rovibrational energy levels. The Franck-Condon factors $({f}_{00}:0.998, {f}_{11}:0.986, {f}_{22}:0.920)$ for the $2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}\phantom{\rule{0.28em}{0ex}}(v=0)\ensuremath{\leftrightarrow}1\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}\phantom{\rule{0.28em}{0ex}}({v}^{\ensuremath{'}}=0)$ transition are highly diagonally distributed, and the calculated radiative lifetime (74.87 ns) of the $2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}$ state is found to be short enough for rapid laser cooling. The results demonstrate that LiBe could be a very promising candidate for laser cooling and a three-cycle laser cooling scheme for the molecule has been proposed.

DOI
10.1103/physreva.92.032502

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We propose to utilize the $^{1}\mathrm{\ensuremath{\Sigma}}{\ensuremath{-}}^{1}\mathrm{\ensuremath{\Sigma}}$ electronic transition system for direct laser cooling of heteronuclear diatomic molecules. AgH, as well as its deuterium isotopolog AgD, is used as an example to illustrate the cooling schemes. Potential-energy curves and relevant molecular parameters of both AgH and AgD, including the spin-orbit constants and the electronic transition dipole moments, are determined in internally contracted multiconfiguration-reference configuration interaction calculations. The highly diagonal Franck-Condon matrices of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{-}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ transitions predicted by the calculations suggest the existence of quasi-closed-cycle transitions, which renders these molecules suitable for direct laser cooling. By solving rate equations numerically, we demonstrated that both AgH and AgD molecules can be cooled from 25 K to 2 mK temperature in approximately 20 ms. Our investigation elucidates and supports the hypothesis that molecules in the simplest $^{1}\mathrm{\ensuremath{\Sigma}}{\ensuremath{-}}^{1}\mathrm{\ensuremath{\Sigma}}$ system can serve as favorable candidates for direct laser cooling.

Physical Review A•Jun 5, 2018•28 citations
An optical scheme to create the simplest heteronuclear metal ultracold LiBe molecule is proposed based on ab initio quantum chemistry calculations. The potential energy curves, dipole moments, and transition dipole moments of 12\ensuremathΣ+,22\ensuremathΣ+,12\ensuremathΠ1\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}, 2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}, 1\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Pi}}12\ensuremathΣ+,22\ensuremathΣ+,12\ensuremathΠ, and 22\ensuremathΠ2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Pi}}22\ensuremathΠ states are calculated using the multireference configuration interaction and large basis sets. The analytical functions deduced from the obtained curves are used to determine the rovibrational energy levels, the Franck-Condon factors, and the Einstein coefficients of the states through solving the Schr"odinger equation of nuclear movement. The spectroscopic parameters are deduced with the obtained rovibrational energy levels. The Franck-Condon factors (f00:0.998,f11:0.986,f22:0.920)({f}_{00}:0.998, {f}_{11}:0.986, {f}_{22}:0.920)(f00​:0.998,f11​:0.986,f22​:0.920) for the 22\ensuremathΣ+(v=0)\ensuremath↔12\ensuremathΣ+(v\ensuremath′=0)2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}\phantom{\rule{0.28em}{0ex}}(v=0)\ensuremath{\leftrightarrow}1\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}\phantom{\rule{0.28em}{0ex}}({v}^{\ensuremath{'}}=0)22\ensuremathΣ+(v=0)\ensuremath↔12\ensuremathΣ+(v\ensuremath′=0) transition are highly diagonally distributed, and the calculated radiative lifetime (74.87 ns) of the 22\ensuremathΣ+2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}22\ensuremathΣ+ state is found to be short enough for rapid laser cooling. The results demonstrate that LiBe could be a very promising candidate for laser cooling and a three-cycle laser cooling scheme for the molecule has been proposed.
The feasibility of laser cooling MHM\mathrm{H}MH (M=Be,Mg,Ca,Sr,andBaM=\mathrm{Be},\phantom{\rule{0.16em}{0ex}}\mathrm{Mg},\phantom{\rule{0.16em}{0ex}}\mathrm{Ca},\phantom{\rule{0.16em}{0ex}}\mathrm{Sr},\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.16em}{0ex}}\mathrm{Ba}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 MHM\mathrm{H}MH species are calculated using the multireference configuration interaction (MRCI) level of theory. For CaH\mathrm{CaH}CaH, SrH\mathrm{SrH}SrH, and BaH\mathrm{BaH}BaH, the spin-orbit coupling effects are also taken into account in electronic structure calculations at the MRCI level. Calculated spectroscopic constants for 9BeH^{9}\mathrm{BeH}9BeH, 24MgH^{24}\mathrm{MgH}24MgH, 40CaH^{40}\mathrm{CaH}40CaH, 86SrH^{86}\mathrm{SrH}86SrH, and 138BaH^{138}\mathrm{BaH}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 MHM\mathrm{H}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){f}_{00}\left({}^{9}\mathrm{BeH}:0.998{,}^{24}\mathrm{MgH}:0.954{,}^{40}\mathrm{CaH}:0.961{,}^{86}\mathrm{SrH}:0.978,\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{138}\mathrm{BaH}:0.971\right)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{}^{9}\mathrm{BeH}:82.0\phantom{\rule{0.16em}{0ex}}\mathrm{ns}9BeH:82.0ns, 24MgH:48.6ns{}^{24}\mathrm{MgH}:48.6\phantom{\rule{0.16em}{0ex}}\mathrm{ns}24MgH:48.6ns, 40CaH:33.3ns{}^{40}\mathrm{CaH}:33.3\phantom{\rule{0.16em}{0ex}}\mathrm{ns}40CaH:33.3ns, 86SrH:33.2ns{}^{86}\mathrm{SrH}:33.2\phantom{\rule{0.16em}{0ex}}\mathrm{ns}86SrH:33.2ns, and 138BaH^{138}\mathrm{BaH}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 MHM\mathrm{H}MH species, and provide a promising theoretical reference for further theoretical and experimental research on alkaline-earth-metal monohydrides.
The spin-forbidden cooling of the LiRb molecule is investigated based on ab initio quantum chemistry calculations. The multireference configuration interaction method is used to generate the potential energy curves (PECs) of the ground state X(1)Σ(+) and the low-lying excited states a(3)Σ(+), B(1)Π, and b(3)Π. The spin-orbit coupling effects for the PECs and the transition dipole moments (TDMs) between the X(1)Σ(+), b(3)Π and a(3)Σ(+) states are also calculated. The analytical functions for the PECs are deduced. The rovibrational energy levels, the spectroscopic parameters and the Franck-Condon factors (FCF) are determined by solving the Schrödinger equation of nuclear movement with the obtained analytical functions. The b(3)Π0 ↔ X(1)Σ(+) and b(3)Π1 ↔ X(1)Σ(+) transitions have highly diagonal distributed FCFs and non-zero TDMs, demonstrating that the LiRb molecule could be a very promising candidate for laser cooling. Therefore, a three-cycle laser cooling scheme for the molecule has been proposed based on these two spin-forbidden transitions. Using the radiative lifetime and linewidth calculated from the obtained TDM functions, we present further analysis of the cooling of LiRb and the corresponding KRb molecule. The transition b(3)Π0 ↔ X(1)Σ(+) is found to be a practical transition to cool the LiRb molecule, and a sub-microkelvin cool temperature could be reached for the KRb molecule using a similar laser cooling scheme.
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.
Ab initio calculations for three low-lying electronic states (X(2)Σ(+), A(2)Π, and 2(2)Π) of MgCl and MgBr molecules, including spin-orbit coupling, are performed using multi-reference configuration interaction plus Davidson correction method. The calculations involve all-electronic basis sets and Douglas-Kroll scalar relativistic correction. Spectroscopic parameters well agree with available theoretical and experimental data. Highly diagonally distributed Franck-Condon factors f00 for A(2)Π3/2,1/2 (υ' = 0) → X(2)Σ(+) 1/2 (υ″ = 0) are determined for both MgCl and MgBr molecules. Suitable radiative lifetimes τ of A(2)Π3/2,1/2 (υ' = 0) states for rapid laser cooling are also obtained. The proposed laser drives A(2)Π3/2 (υ' = 0) → X(2)Σ(+) 1/2 (υ″ = 0) transition by using three wavelengths (main pump laser λ00; two repumping lasers λ10 and λ21). These results indicate the probability of laser cooling MgCl and MgBr molecules.
The potential energy curves and transition dipole moments of seven Λ-S states and six Ω states of LuH+ cation are calculated by using the multireference configuration interaction method plus Davidson correction with the pseudopotential electron basis set, and the spectroscopic parameters of the bound states are obtained. The spin–orbit coupling effect is considered in the calculations. The Franck–Condon factors (FCFs) and the Einstein spontaneous emission coefficients are obtained. The results indicate that the A2Δ3/2(ν′ = 0) ↔ X2Σ+1/2(ν″ = 0) and B2Π1/2(ν′ = 0) ↔ X2Σ+1/2 (ν″ = 0) transitions provide highly diagonally distributed FCFs. Spontaneous radiative lifetimes of A2Δ3/2 (ν′ = 0) and B2Π1/2 (ν′ = 0) excited states are both obtained. The cooling schemes of LuH+ cation are obtained using the ab initio method. For the B2Π1/2 ↔ X2Σ+1/2 transition, the influence of the intermediate state on the construction of quasi-closed cyclic transitions can be neglected. A main pump laser and two repumping lasers are required to construct the A2Δ3/2 ↔ X2Σ+1/2 and B2Π1/2 ↔ X2Σ+1/2 quasi-cycling transitions for laser cooling of LuH+ molecular cation. The results in this work provide reliable theoretical guidance for further experiments of laser cooling of LuH+ cation.
We propose to utilize the $^{1}\mathrm{\ensuremath{\Sigma}}{\ensuremath{-}}^{1}\mathrm{\ensuremath{\Sigma}}$ electronic transition system for direct laser cooling of heteronuclear diatomic molecules. AgH, as well as its deuterium isotopolog AgD, is used as an example to illustrate the cooling schemes. Potential-energy curves and relevant molecular parameters of both AgH and AgD, including the spin-orbit constants and the electronic transition dipole moments, are determined in internally contracted multiconfiguration-reference configuration interaction calculations. The highly diagonal Franck-Condon matrices of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{-}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ transitions predicted by the calculations suggest the existence of quasi-closed-cycle transitions, which renders these molecules suitable for direct laser cooling. By solving rate equations numerically, we demonstrated that both AgH and AgD molecules can be cooled from 25 K to 2 mK temperature in approximately 20 ms. Our investigation elucidates and supports the hypothesis that molecules in the simplest $^{1}\mathrm{\ensuremath{\Sigma}}{\ensuremath{-}}^{1}\mathrm{\ensuremath{\Sigma}}$ system can serve as favorable candidates for direct laser cooling.