## Laser excitation of the 1s-hyperfine transition in muonic hydrogen

P. Amaro, A. Adamczak, M. Abdou Ahmed, L. Affolter, F. D. Amaro, P. Carvalho, T. -L. Chen, L. M. P. Fernandes, M. Ferro, D. Goeldi, T. Graf, M. Guerra, T. W. Hänsch, C. A. O. Henriques, Y. -C. Huang, P. Indelicato, O. Kara, K. Kirch, A. Knecht, F. Kottmann, Y. -W. Liu, J. Machado, M. Marszalek, R. D. P. Mano, C. M. B. Monteiro, F. Nez, J. Nuber, A. Ouf, N. Paul, R. Pohl, E. Rapisarda, J. M. F. dos Santos, J. P. Santos, P. A. O. C. Silva, L. Sinkunaite, J. -T. Shy, K. Schuhmann, S. Rajamohanan, A. Soter, L. Sustelo, D. Taqqu, L. -B. Wang, F. Wauters, P. Yzombard, M. Zeyen, A. Antognini

SciPost Phys. 13, 020 (2022) · published 15 August 2022

- doi: 10.21468/SciPostPhys.13.2.020
- Submissions/Reports

### Abstract

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with $2\times10^{-4}$ relative accuracy. In the proposed experiment, the $\mu$p atom undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, then is quenched back to the singlet state by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after the collisional deexcitation is used as a signature of a successful laser transition between hyperfine states. In this paper, we calculate the combined probability that a $\mu$p atom initially in the singlet hyperfine state undergoes a laser excitation to the triplet state followed by a collisional-induced deexcitation back to the singlet state. This combined probability has been computed using the optical Bloch equations including the inelastic and elastic collisions. Omitting the decoherence effects caused by the laser bandwidth and collisions would overestimate the transition probability by more than a factor of two in the experimental conditions. Moreover, we also account for Doppler effects and provide the matrix element, the saturation fluence, the elastic and inelastic collision rates for the singlet and triplet states, and the resonance linewidth. This calculation thus quantifies one of the key unknowns of the HFS experiment, leading to a precise definition of the requirements for the laser system and to an optimization of the hydrogen gas target where $\mu$p is formed and the laser spectroscopy will occur.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Pedro Amaro, -
^{2}A. Adamczak, -
^{3}M. Abdou Ahmed, -
^{4}L. Affolter, -
^{5}F. D. Amaro, -
^{1}Patricia Carvalho, -
^{6}T. -L. Chen, -
^{5}L. M. P. Fernandes, -
^{1}M. Ferro, -
^{4}D. Goeldi, -
^{3}T. Graf, -
^{1}M. Guerra, -
^{7}^{8}Theodor Hänsch, -
^{5}C. A. O. Henriques, -
^{6}Y. -C. Huang, -
^{9}P. Indelicato, -
^{4}O. Kara, -
^{4}^{10}Klaus Kirch, -
^{10}Andreas Knecht, -
^{4}^{10}Franz Kottmann, -
^{6}Y. -W. Liu, -
^{1}Jorge Machado, -
^{10}M. Marszalek, -
^{5}R. D. P. Mano, -
^{5}C. M. B. Monteiro, -
^{9}F. Nez, -
^{4}^{10}J. Nuber, -
^{11}A. Ouf, -
^{9}N. Paul, -
^{11}Randolf Pohl, -
^{10}E. Rapisarda, -
^{5}J. M. F. dos Santos, -
^{1}J. P. Santos, -
^{5}P. A. O. C. Silva, -
^{10}L. Sinkunaite, -
^{6}J. -T. Shy, -
^{4}K. Schuhmann, -
^{11}S. Rajamohanan, -
^{4}Anna Soter, -
^{1}L. Sustelo, -
^{4}^{10}David Taqqu, -
^{6}L. -B. Wang, -
^{11}Frederik Wauters, -
^{9}P. Yzombard, -
^{4}M. Zeyen, -
^{4}^{10}Aldo Antognini

^{1}Universidade NOVA de Lisboa / NOVA University Lisbon [NOVA]^{2}Institute of Nuclear Physics Polish Academy of Sciences [IFJ PAN]^{3}Universität Stuttgart / University of Stuttgart^{4}Eidgenössische Technische Hochschule Zürich / Swiss Federal Institute of Technology in Zurich (ETH) [ETH Zurich]^{5}Universidade de Coimbra / University of Coimbra^{6}National Tsing Hua University [NTHU]^{7}Max-Planck-Institut für Quantenoptik / Max Planck Institute of Quantum Optics [MPQ]^{8}Ludwig-Maximilians-Universität München / Ludwig Maximilian University of Munich [LMU]^{9}Laboratoire Kastler Brossel / Kastler-Brossel Laboratory [LKB]^{10}Paul Scherrer Institute [PSI]^{11}Johannes Gutenberg-Universität Mainz / Johannes Gutenberg University of Mainz

- Agence Nationale de la Recherche [ANR]
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- European Research Council [ERC]
- Fundação para a Ciência e a Tecnologia (through Organization: Fundação para a Ciência e Tecnologia [FCT])
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung / Swiss National Science Foundation [SNF]