The theory of direct laser excitation of nuclear transitions
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Regular Article - Theoretical Physics
The theory of direct laser excitation of nuclear transitions Lars von der Wense1,a , Pavlo V. Bilous2 , Benedict Seiferle1, Simon Stellmer3 , Johannes Weitenberg4 , Peter G. Thirolf1, Adriana Pálffy2 , Georgy Kazakov5,6 1
LMU Munich, 85748 Garching, Germany Max Planck Institute for Nuclear Physics, 69117 Heidelberg, Germany 3 University of Bonn, 53105 Bonn, Germany 4 Max Planck Institute of Quantum Optics, 85748 Garching, Germany 5 WPI c/o Fak. Mathematik Univ. Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria 6 Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
2
Received: 22 January 2020 / Accepted: 5 June 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Communicated by Vittorio Somà
Abstract A comprehensive theoretical study of direct laser excitation of a nuclear state based on the density matrix formalism is presented. The nuclear clock isomer 229m 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 229m Th and 235m U, being the nuclear excited states of lowest known excitation energies. The paper aims to be a didactic review with many calculations given explicitly.
1 Introduction Direct excitation of a nuclear state using narrow-bandwidth laser radiation remains an outstanding experimental challenge. When achieved, potential applications in various physical fields open up. These include the development of a highly stable source of light for metrology [1], the development of a nuclear optical clock [2,3], a nuclear γ -ray laser [4,5] and a nuclear qubit for quantum computing [6]. Further, it will advance the field of experimental nuclear quantum optics [7– a e-mail:
[email protected] (corresponding author)
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9]. With an expected accuracy of 1.5 · 10−19 [3] a nuclear optical clock may even surpass the best optical atomic clocks operational today [10,11], having the potential for utilization in, e.g., satellite-based navigation [12], relativistic geodesy [13], probing for time-variations of fundamental constants [14] and the search for topological dark matter [15]. Two different concepts of nuclear laser excitation have to be distinguished: direct excitation and excitation via the inverse electronic bridge (IEB) mechanism. In the IEB process, a virtual level of the
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