关键词: ²²⁹Th nuclear clock, electronic bridge, external field effects

Abstract: Recent advances in atomic optical clocks based on electronic transitions have achieved frequency uncertainties at the $10^{-19}$ level, enabling wide applications in testing variations of physical constants, exploring dark matter signatures, and enhancing precision metrology for position, navigation, and timing systems. To pursue higher-precision optical clocks, the development of nuclear optical clocks has emerged, with the ²²⁹Th system distinguished by its unique low-lying isomeric state at $\sim8.4$ eV and a natural linewidth of approximately 100 μHz, promising uncertainties below $10^{-19}$. The intrinsic insensitivity of nuclear transitions to external perturbations and their subatomic-scale spatial confinement provide significant advantages over electronic transitions in mitigating environmental shifts. Recent experimental breakthroughs include the excitation of the nuclear clock transition in solid-state ²²⁹Th-doped crystals with spectral resolution at the kHz level. However, critical challenges persist, particularly in implementing effective laser excitation schemes (e.g., via the electronic bridge mechanism) and closed-loop quantum control in trapped ion systems. Addressing these requires comprehensive understanding of complex many-body interactions in ²²⁹Th, encompassing electronic structure, nuclear deformation, hyperfine and field shift, and solid-state environmental coupling. This review synthesizes recent advancements in (i) the characterization of nuclear and atomic structures of the ²²⁹Th nuclear clock, and (ii) precise evaluation and mitigation of external perturbations affecting the clock transitions. The analysis provides a solid theoretical and experimental foundation for optimizing ²²⁹Th-based nuclear clock performance.

Key words: ²²⁹Th nuclear clock, electronic bridge, external field effects