229Thorium-doped calcium fluoride for nuclear laser spectroscopy.

The (229)thorium isotope presents an extremely low-energy isomer state of the nucleus which is expected around 7.8 eV, in the vacuum ultraviolet (VUV) regime. This unique system may bridge between atomic and nuclear physics, enabling coherent manipulation and precision spectroscopy of nuclear quantum states using laser light. It has been proposed to implant (229)thorium into VUV transparent crystal matrices to facilitate laser spectroscopy and possibly realize a solid-state nuclear clock. In this work, we validate the feasibility of this approach by computer modelling of thorium doping into calcium fluoride single crystals. Using atomistic modelling and full electronic structure calculations, we find a persistent large band gap and no additional electronic levels emerging in the middle of the gap due to the presence of the dopant, which should allow direct optical interrogation of the nuclear transition.Based on the electronic structure, we estimate the thorium nuclear quantum levels within the solid-state environment. Precision laser spectroscopy of these levels will allow the study of a broad range of crystal field effects, transferring Mössbauer spectroscopy into the optical regime.