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1. Investigation of the fine structure of antihydrogen

   https://doi.org/10.1038/s41586-020-2006-5  

   Ahmadi, M.; Alves, B. X.; Baker, C. J.; Bertsche, W.; Capra, A.; Carruth, C.; Cesar, C. L.; Charlton, M.; Cohen, S.; Collister, R.; et al (February 2020, Nature)

   At the historic Shelter Island Conference on the Foundations of Quantum Mechanics in 1947, Willis Lamb reported an unexpected feature in the fine structure of atomic hydrogen: a separation of the 2S1/2 and 2P1/2 states1. The observation of this separation, now known as the Lamb shift, marked an important event in the evolution of modern physics, inspiring others to develop the theory of quantum electrodynamics2–5. Quantum electrodynamics also describes antimatter, but it has only recently become possible to synthesize and trap atomic antimatter to probe its structure. Mirroring the historical development of quantum atomic physics in the twentieth century, modern measurements on anti-atoms represent a unique approach for testing quantum electrodynamics and the foundational symmetries of the standard model. Here we report measurements of the fine structure in the n = 2 states of antihydrogen, the antimatter counterpart of the hydrogen atom. Using optical excitation of the 1S–2P Lyman-α transitions in antihydrogen6, we determine their frequencies in a magnetic field of 1 tesla to a precision of 16 parts per billion. Assuming the standard Zeeman and hyperfine interactions, we infer the zero-field fine-structure splitting (2P1/2–2P3/2) in antihydrogen. The resulting value is consistent with the predictions of quantum electrodynamics to a precision of 2 per cent. Using our previously measured value of the 1S–2S transition frequency6,7, we find that the classic Lamb shift in antihydrogen (2S1/2–2P1/2 splitting at zero field) is consistent with theory at a level of 11 per cent. Our observations represent an important step towards precision measurements of the fine structure and the Lamb shift in the antihydrogen spectrum as tests of the charge– parity–time symmetry8 and towards the determination of other fundamental quantities, such as the antiproton charge radius9,10, in this antimatter system. 

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2. Be+ assisted, simultaneous confinement of more than 15000 antihydrogen atoms

   https://doi.org/10.1038/s41467-025-65085-4  

   Akbari, R; de_Araujo_Azevedo, L O; Baker, C J; Bertsche, W; Bhatt, N M; Bonomi, G; Capra, A; Carli, I; Cesar, C L; Charlton, M; et al (December 2025, Nature Communications)

   Abstract Antihydrogen, the bound state of a positron and an antiproton, is the only pure anti-atomic system ever studied. It is produced exclusively in the laboratory, as it has never been observed in nature. This unique system is of great interest for searching for tentative differences between matter and antimatter. Antihydrogen has been routinely trapped since 2010 and accumulated since 2017, enabling, for example, the first precision spectroscopic study of the anti-atom in 2018 and the first observation of the influence of gravity in 2023. Here we report an eight-fold increase in the trapping rate of antihydrogen, enabled by sympathetic cooling of positrons with laser-cooled beryllium ions. With beryllium sympathetic cooling, we now accumulate over 15000 antihydrogen atoms in under seven hours. This technique transforms our ability to study systematic and sidereal effects in existing experiments while paving the way for studies that would otherwise remain out of reach. 

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3. Four ppm measurement of the antihydrogen ground-state hyperfine splitting

   https://doi.org/10.1038/s41586-026-10556-x  

   Akbari, R; de_Araujo_Azevedo, L O; Baker, C J; Bertsche, W; Bhatt, N M; Bonomi, G; Capra, A; Carli, I; L_Cesar, C; Charlton, M; et al (May 2026, Nature)

   Abstract The hydrogen atom is a touchstone for the foundations, evolution and frontiers of quantum theory^1–9. Key spectral lines of this atom have been determined to remarkable precision^10,11. Our research focuses on the study of antihydrogen, the antimatter counterpart of hydrogen. We test fundamental symmetries of nature (such as simultaneous charge conjugation, parity inversion, and time reversal or CPT symmetry) through precision comparisons of these atomic systems¹². Recent 1S–2S spectroscopic measurements on trapped antihydrogen have achieved relative precisions of parts per trillion (refs. ^13,14). However, the ground-state hyperfine splitting, which is sensitive to the internal structure of the antiproton, has only been measured to 400 parts per million (ppm). Here we report a 4 ppm measurement of the antihydrogen ground-state hyperfine splitting energya_1S, advancing the state-of-the-art precision¹⁵by two orders of magnitude. From microwave spectroscopy experiments with roughly 24,000 anti-atoms, we determine$${a}_{1{\rm{S}}}/h=\mathrm{1,420,404.8}\pm 1.1(\mathrm{stat.})\pm 5.6\,(\mathrm{sys.})\,\text{kHz}$$ $a_{1S}/h=\mathrm{1,420,404.8}\pm 1.1\left(\mathrm{stat.}\right)\pm 5.6\left(\mathrm{sys.}\right)\text{kHz}$ in a 1-T magnetic field, consistent with expectations for hydrogen¹¹. At this level, our measurement is sensitive to the internal structure of the antiproton, which contributes at about 40 ppm and is approaching the limit of existing theoretical analyses¹⁶. The gains we report are the product of marked advances in magnetic trap field control, stabilization and characterization; anti-atom spin-state manipulation; and improved antihydrogen accumulation rate¹⁷. 

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4. Magic Wavelengths for 1S–nS and 2S–nS Transitions in Hydrogenlike Systems

   https://doi.org/10.3390/atoms10010001  

   Adhikari, Chandra M.; Canales, Jonathan C.; Arthanayaka, Thusitha P.; Jentschura, Ulrich D. (March 2022, Atoms)

   We study the magic wavelength for two-photon 1S–nS transitions in a hydrogen and deuterium atom, as well as 2S–nS transitions, where the lower level is the metastable 2S state. At the magic wavelength, the dynamic Stark shifts of the ground and the excited state of the transition coincide, so that the transition frequency is independent of the intensity of the trapping laser field. Experimentally feasible magic wavelengths of transitions with small slopes in the atomic polarizabilities are determined; these are the most stable magic wavelengths against variations of the laser frequency. We provide data for the magic wavelengths for the 1S–nS and 2S–nS transitions in hydrogen and deuterium, with n=2,⋯,8. We also analyze the stability of the elimination of the ac Stark shift at the magic wavelength against tiny variations of the trapping laser frequency from the magic value. 

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5. Observation of the effect of gravity on the motion of antimatter

   https://doi.org/10.1038/s41586-023-06527-1  

   Anderson, E. K.; Baker, C. J.; Bertsche, W.; Bhatt, N. M.; Bonomi, G.; Capra, A.; Carli, I.; Cesar, C. L.; Charlton, M.; Christensen, A.; et al (September 2023, Nature)

   Abstract Einstein’s general theory of relativity from 1915¹remains the most successful description of gravitation. From the 1919 solar eclipse²to the observation of gravitational waves³, the theory has passed many crucial experimental tests. However, the evolving concepts of dark matter and dark energy illustrate that there is much to be learned about the gravitating content of the universe. Singularities in the general theory of relativity and the lack of a quantum theory of gravity suggest that our picture is incomplete. It is thus prudent to explore gravity in exotic physical systems. Antimatter was unknown to Einstein in 1915. Dirac’s theory⁴appeared in 1928; the positron was observed⁵in 1932. There has since been much speculation about gravity and antimatter. The theoretical consensus is that any laboratory mass must be attracted⁶by the Earth, although some authors have considered the cosmological consequences if antimatter should be repelled by matter^7–10. In the general theory of relativity, the weak equivalence principle (WEP) requires that all masses react identically to gravity, independent of their internal structure. Here we show that antihydrogen atoms, released from magnetic confinement in the ALPHA-g apparatus, behave in a way consistent with gravitational attraction to the Earth. Repulsive ‘antigravity’ is ruled out in this case. This experiment paves the way for precision studies of the magnitude of the gravitational acceleration between anti-atoms and the Earth to test the WEP. 

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