Laser cooling of the alkaline-earth-metal monohydrides: Insights from an<i>ab initio</i>theory study

Abstract

The feasibility of laser cooling $M\mathrm{H}$ ($M=\mathrm{Be},\phantom{\rule{0.16em}{0ex}}\mathrm{Mg},\phantom{\rule{0.16em}{0ex}}\mathrm{Ca},\phantom{\rule{0.16em}{0ex}}\mathrm{Sr},\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.16em}{0ex}}\mathrm{Ba}$) 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 $M\mathrm{H}$ species are calculated using the multireference configuration interaction (MRCI) level of theory. For $\mathrm{CaH}$, $\mathrm{SrH}$, and $\mathrm{BaH}$, the spin-orbit coupling effects are also taken into account in electronic structure calculations at the MRCI level. Calculated spectroscopic constants for $^{9}\mathrm{BeH}$, $^{24}\mathrm{MgH}$, $^{40}\mathrm{CaH}$, $^{86}\mathrm{SrH}$, and $^{138}\mathrm{BaH}$ 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 $M\mathrm{H}$ 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 ${f}_{00}\left({}^{9}\mathrm{BeH}:0.998{,}^{24}\mathrm{MgH}:0.954{,}^{40}\mathrm{CaH}:0.961{,}^{86}\mathrm{SrH}:0.978,\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{138}\mathrm{BaH}:0.971\right)$ 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 (${}^{9}\mathrm{BeH}:82.0\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$, ${}^{24}\mathrm{MgH}:48.6\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$, ${}^{40}\mathrm{CaH}:33.3\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$, ${}^{86}\mathrm{SrH}:33.2\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$, and $^{138}\mathrm{BaH}$: 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 $M\mathrm{H}$ species, and provide a promising theoretical reference for further theoretical and experimental research on alkaline-earth-metal monohydrides.