A comprehensive theoretical study of direct laser excitation of a nuclear state based on the density matrix formalism is presented. The nuclear clock isomer \(^{229\text {m}}\)Th is discussed in detail, as it could allow for direct laser excitation using existing technology and provides the motivation for this work. The optical Bloch equations are derived for the simplest case of a pure nuclear two-level system and for the more complex cases taking into account the presence of magnetic sub-states, hyperfine-structure and Zeeman splitting in external fields. Nuclear level splitting for free atoms and ions as well as for nuclei in a solid-state environment is discussed individually. Based on the obtained equations, nuclear population transfer in the low-saturation limit is reviewed. Further, nuclear Rabi oscillations, power broadening and nuclear two-photon excitation are considered. Finally, the theory is applied to the special cases of \(^{229\text {m}}\)Th and \(^{235\text {m}}\)U, being the nuclear excited states of lowest known excitation energies. The paper aims to be a didactic review with many calculations given explicitly.

中文翻译：

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核跃迁的直接激光激发理论

提出了基于密度矩阵形式主义的直接激光激发核态的综合理论研究。核钟异构体\（^ {229 \ text {m}} \）对此进行了详细讨论，因为它可以允许使用现有技术进行直接激光激发，并为这项工作提供了动力。光学Bloch方程是针对纯核两能级系统的最简单情况而得出的，对于更复杂的情况，则要考虑到存在外部磁场中的磁性子状态，超精细结构和塞曼分裂，从而得出光学Bloch方程。分别讨论了固态环境中自由原子和离子以及原子核的能级分裂。基于所获得的方程，对低饱和度极限内的核种群迁移进行了回顾。此外，考虑了核拉比振荡，功率展宽和核双光子激发。最后，该理论适用于\（^ {229 \ text {m}} \） Th和\（^ {235 \ text {m}} \） U，是已知最低激发能的核激发态。本文旨在成为一个教学评论，其中明确给出了许多计算方法。