Modeling of theX1Σ+,a3Σ+→E(4)1Σ+→X1Σ+(v=0,J=0)optical cycle for ultracold KCs molecule production

Abstract

We present experimental relative intensity distribution and theoretical radiative probabilities for the spin-allowed $E(4){\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+}\ensuremath{-}X{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+}$ and spin-forbidden $E(4){\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+}\ensuremath{-}a{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+}$ rovibronic transitions studied in the KCs molecule. The absorbtion and emission Einstein coefficients were predicted in a wide range of vibrational $v$ and rotational $J$ quantum numbers for both singlet-singlet $E\ensuremath{-}X$ and singlet-triplet $E\ensuremath{-}a$ rovibronic transitions along with radiative lifetimes of the upper $E$ state and branching ratios of spontaneous emission into the lower-lying electronic states, including both bound-bound and bound-continuum parts of the spectra. The required spin-allowed $E(4){\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+}\ensuremath{-}X;A;C{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+};B{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Pi}$ transition dipole moments were obtained in the framework of quasirelativistic electronic structure calculations. The regular spin-orbit coupling with the nearest ${}^{3}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Pi}$ states is found to be sufficient to induce the spin-forbidden $E(4){\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+}\ensuremath{-}a;c{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+};b{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Pi}$ transitions by borrowing probabilities from the relevant $(1\ensuremath{-}5){\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Pi}\ensuremath{-}(a;c){\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+};b{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Pi}$ transitions. Relative intensity distributions in rotationally resolved $E\ensuremath{\rightarrow}X$ and $E\ensuremath{\rightarrow}a$ laser-induced fluorescence (LIF) progressions were determined from Fourier transform spectra. Experimental LIF intensity distributions demonstrated good agreement with their predicted counterparts. The simulations demonstrate that the translationally ultracold KCs molecules could be efficiently produced in their absolute ground state in one stimulated Raman step $X{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+};a{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}\ensuremath{'}})\ensuremath{\rightarrow}E(4){\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+}({v}_{E}^{\ensuremath{'}}=44,{J}_{E}^{\ensuremath{'}}=1)\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}^{+}({v}_{X}^{\ensuremath{'}\ensuremath{'}}=0,{J}_{X}^{\ensuremath{'}\ensuremath{'}}=0)$ from the weakly bound rovibronic levels ${v}^{\ensuremath{'}\ensuremath{'}}$ of both singlet $X$ and triplet $a$ states.