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Author(s): C. Smorra (corresponding author) [1, 2]; S. Sellner [1]; M. J. Borchert [1, 3]; J. A. Harrington [4]; T. Higuchi [1, 5]; H. Nagahama [1]; T. Tanaka [1, 5]; [...]

Invariance under the charge, parity, time-reversal (CPT) transformation (1) is one of the fundamental symmetries of the standard model of particle physics. This CPT invariance implies that the fundamental properties of antiparticles and their matter-conjugates are identical, apart from signs. There is a deep link between CPT invariance and Lorentz symmetry--that is, the laws of nature seem to be invariant under the symmetry transformation of spacetime--although it is model dependent (2). A number of high-precision CPT and Lorentz invariance tests--using a co-magnetometer, a torsion pendulum and a maser, among others--have been performed (3), but only a few direct high-precision CPT tests that compare the fundamental properties of matter and antimatter are available (4-8). Here we report high-precision cyclotron frequency comparisons of a single antiproton and a negatively charged hydrogen ion ([H.sup.-]) carried out in a Penning trap system. From 13,000 frequency measurements we compare the charge-to-mass ratio for the antiproton [(q/m).sub.[bar.p]] to that for the proton [(q/m).sub.p] and obtain [(q/m).sub.[bar.p]]/[(q/m).sub.p] - 1 = 1(69) x [10.sup.-12]. The measurements were performed at cyclotron frequencies of 29.6 megahertz, so our result shows that the CPT theorem holds at the atto-electronvolt scale. Our precision of 69 parts per trillion exceeds the energy resolution of previous antiproton-to-proton mass comparisons (7,9) as well as the respective figure of merit of the standard model extension (10) by a factor of four. In addition, we give a limit on sidereal variations in the measured ratio of < 720 parts per trillion. By following the arguments of ref. 11, our result can be interpreted as a stringent test of the weak equivalence principle of general relativity using baryonic antimatter, anti it sets a new limit on the gravitational anomaly parameter of [absolute value of ([α.sub.g] - 1)] < 8.7 x [10.sup.-7]., The standard model is the theory that describes particles and their fundamental interactions, although without taking into account gravitation. However, this model is known to be incomplete, which has inspired [...]

The magnetic moment of the proton is directly measured with unprecedented precision using a double Penning trap. An important moment for matter-antimatter symmetry Although less prominent than large synchrotron experiments, measurements of fundamental constants or atomic properties can still make valuable contributions to the search of physical laws beyond the Standard Model -- if the measurement precision is high enough. In a direct measurement, Andreas Mooser et al. determine the magnetic moment of the proton with unprecedented precision. The measurement is performed using a double Penning trap, a system in which a single ion is confined and manipulated in a powerful homogeneous magnetic field. In combination with a direct measurement of the antiproton magnetic moment, this work will pave the way for a rigorous test of matter-antimatter symmetry. One of the fundamental properties of the proton is its magnetic moment, [micro].sub.p. So far [micro].sub.p has been measured only indirectly, by analysing the spectrum of an atomic hydrogen maser in a magnetic field.sup.1. Here we report the direct high-precision measurement of the magnetic moment of a single proton using the double Penning-trap technique.sup.2. We drive proton-spin quantum jumps by a magnetic radio-frequency field in a Penning trap with a homogeneous magnetic field. The induced spin transitions are detected in a second trap with a strong superimposed magnetic inhomogeneity.sup.3. This enables the measurement of the spin-flip probability as a function of the drive frequency. In each measurement the proton's cyclotron frequency is used to determine the magnetic field of the trap. From the normalized resonance curve, we extract the particle's magnetic moment in terms of the nuclear magneton: [mu].sub.p = 2.792847350(9)[mu].sub.N. This measurement outperforms previous Penning-trap measurements.sup.4,5 in terms of precision by a factor of about 760. It improves the precision of the forty-year-old indirect measurement, in which significant theoretical bound state corrections.sup.6 were required to obtain [micro].sub.p, by a factor of 3. By application of this method to the antiproton magnetic moment, the fractional precision of the recently reported value.sup.7 can be improved by a factor of at least 1,000. Combined with the present result, this will provide a stringent test of matter/antimatter symmetry with baryons.sup.8., Author(s): A. Mooser [sup.1] [sup.2] [sup.7] , S. Ulmer [sup.3] , K. Blaum [sup.4] , K. Franke [sup.3] [sup.4] , H. Kracke [sup.1] [sup.2] , C. Leiteritz [sup.1] , W. [...]

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics1–3, nuclear and atomic structure4,5, magnetometry and metrology6, as well as chemistry and medicine7,8. In particular, 3He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry6,9. This requires a high-accuracy value for the 3He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon10,11. Here we investigate the 3He+ ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of 3He+ g I ′ = − 4.2550996069 (30) stat (17) sys , the zero-field hyperfine splitting E HFS exp = − 8 , 665 , 649 , 865.77 (26) stat (1) sys Hz and the bound electron g-factor g e exp = − 2.00217741579 (34) stat (30) sys . The latter is consistent with our theoretical value g e theo = − 2.00217741625223 (39) based on parameters and fundamental constants from ref. 12. Our measured value for the 3He+ nuclear g-factor enables determination of the g-factor of the bare nucleus g I = − 4.2552506997 (30) stat (17) sys (1) theo via our accurate calculation of the diamagnetic shielding constant13 σ 3 He + = 0.00003550738 (3) . This constitutes a direct calibration for 3He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value14 and enables us to determine the Zemach radius15 to r Z = 2.608 (24) fm.Measuring the hyperfine structure of a single helium-3 ion in a Penning trap enables direct measurement of the nuclear magnetic moment of helium-3 and provides the high accuracy needed for NMR-based magnetometry. [ABSTRACT FROM AUTHOR]

Many powerful tests of the standard model of particle physics and searches for new physics with precision atomic spectroscopy are hindered by our lack of knowledge of nuclear properties. Ideally, these properties may be derived from precise measurements of the most sensitive and theoretically best-understood observables, often found in hydrogen-like systems. Although these measurements are abundant for the electric properties of nuclei, they are scarce for the magnetic properties, and precise experimental results are limited to the lightest of nuclei 1-4 . Here we focus on 9 Be, which offers the unique possibility to use comparisons between different charge states available for high-precision spectroscopy in Penning traps to test theoretical calculations typically obscured by nuclear structure. In particular, we perform high-precision spectroscopy of the 1s hyperfine and Zeeman structure in hydrogen-like 9 Be 3+ . We determine the effective Zemach radius with an uncertainty of 500 ppm, and the bare nuclear magnetic moment with an uncertainty of 0.6 parts per billion- uncertainties unmatched beyond hydrogen. Moreover, we compare our measurements with the measurements conducted on the three-electron charge state 9 Be + (ref.  5 ), which enables testing the calculation of multi-electron diamagnetic shielding effects of the nuclear magnetic moment at the parts per billion level. Furthermore, we test the quantum electrodynamics methods used for the calculation of the hyperfine splitting. Our results serve as a crucial benchmark for transferring high-precision results of nuclear magnetic properties across different electronic configurations., (© 2024. The Author(s).)

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics 1-3 , nuclear and atomic structure 4,5 , magnetometry and metrology 6 , as well as chemistry and medicine 7,8 . In particular, 3 He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry 6,9 . This requires a high-accuracy value for the 3 He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon 10,11 . Here we investigate the 3 He + ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of 3 He + [Formula: see text], the zero-field hyperfine splitting [Formula: see text] Hz and the bound electron g-factor [Formula: see text]. The latter is consistent with our theoretical value [Formula: see text] based on parameters and fundamental constants from ref. 12 . Our measured value for the 3 He + nuclear g-factor enables determination of the g-factor of the bare nucleus [Formula: see text] via our accurate calculation of the diamagnetic shielding constant 13 [Formula: see text]. This constitutes a direct calibration for 3 He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value 14 and enables us to determine the Zemach radius 15 to [Formula: see text] fm., (© 2022. The Author(s).)