Numerical simulations of hyperfine transitions of antihydrogen
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Numerical simulations of hyperfine transitions of antihydrogen B. Kolbinger · A. Capon · M. Diermaier · S. Lehner · C. Malbrunot · O. Massiczek · C. Sauerzopf · M. C. Simon · E. Widmann
© Springer International Publishing Switzerland 2015
Abstract One of the ASACUSA (Atomic Spectroscopy And Collisions Using Slow Antiprotons) collaboration’s goals is the measurement of the ground state hyperfine transition frequency in antihydrogen, the antimatter counterpart of one of the best known systems in physics. This high precision experiment yields a sensitive test of the fundamental symmetry of CPT. Numerical simulations of hyperfine transitions of antihydrogen atoms have been performed providing information on the required antihydrogen events and the achievable precision. Keywords Antihydrogen · Hyperfine transitions · Precision measurement
1 Introduction Through a precise measurement of the hyperfine splitting of antihydrogen and a comparison with hydrogen, the ASACUSA collaboration aims at testing the CPT symmetry [1]. In ground state hydrogen the interaction between proton and electron spin leads to a singlet state with quantum number F = 0 and a triplet state with F = 1 (see Fig. 1). The transition frequency between these two levels is one of the most accurately measured quantities and is therefore well suited to test CPT with very high precision [2, 3]. In the presence of a
Proceedings of the International Conference on Exotic Atoms and Related Topics (EXA 2014), Vienna, Austria, 15-19 September 2014 B. Kolbinger () · A. Capon · M. Diermaier · S. Lehner · O. Massiczek · C. Sauerzopf · M. C. Simon · E. Widmann Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria e-mail: [email protected] C. Malbrunot CERN, 1211 Geneva 23, Switzerland
B. Kolbinger et al.
Fig. 1 1s groundstate levels of antihydrogen and level splitting in a magnetic field, as well as the two transitions π1 (F = 1, MF = −1) → (F = 0, MF = 0) and σ1 (F = 1, MF = 0) → (F = 0, MF = 0)
magnetic field the degenerated F = 1 level splits up (see Fig. 1) and the energies of all four states shift. This is described by the Breit-Rabi formulae [4]: E(1,1) = 14 E0 − 12 (gJ + gI )μB B √ E(1,0) = − 14 E0 + 12 E0 1 + x 2 E(1,−1) = 14 E0 − 12 (gJ + gI )μB B √ E(0,0) = − 14 E0 − 12 E0 1 + x 2
(1) (2) (3) (4)
where E0 = hν0 with the zero magnetic field transition frequency ν0 and the shifted energies E(1,1) etc. of the four hyperfine levels. B denotes the external magnetic field, x = B/B0 and B0 = 2π ν0 /((gJ − gI )μB ) with the electron g-factor gJ = −2.0023193043718 [5] and gI = gp me /mp = 0.003042064412 [5] with the proton g-factor gp (both in units of the Bohr magneton μB ). Consequently not only one but several transitions can be observed. These states can be classified into low- and high-field seekers (LFS and HFS) depending on their behaviour in an inhomogeneous magnetic field. Depending on the alignment of their mangetic moment in a field, atoms with parallel magnentic moment w
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