Electronic bridge mechanisms driving the ${}^{229}\mathrm{Th}$ nuclear clock transition in the vacuum-ultraviolet-transparent crystals ${}^{229}\text{Th:LiCAF}$ (${\mathrm{LiCaAlF}}_6$) and ${}^{229}\text{Th:LiSAF}$ (${\mathrm{LiSrAlF}}_6$) are investigated theoretically. Due to doping-induced symmetry breaking within the host crystal, electronic defect states emerge around the thorium nucleus and can facilitate nuclear (de)excitation via laser-assisted electronic bridge mechanisms. We investigate spontaneous and laser-assisted electronic bridge schemes for different charge compensation mechanisms. While the calculated spontaneous electronic bridge rates are very low, laser-assisted electronic bridge schemes for nuclear (de)excitation turn out to be significantly more efficient than both spontaneous nuclear decay and direct laser excitation, offering promising prospects for future clock operation.

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• Electromagnetic transitions
• Electronic structure of atoms & molecules
• Isomer decays
• Metrology