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Precision measurements comparing the fundamental properties of conjugate particles and antiparticles constitute stringent tests of CPT invariance. We review recent precision measurements of the BASE collaboration, which improved the uncertainty of the proton and antiproton magnetic moments and the comparison of the proton-to-antiproton charge-to-mass ratio. These measurements constitute the most stringent tests of CPT invariance with antiprotons. Further, we discuss the improved limit on the antiproton lifetime based on the storage of a cloud of antiprotons in the unique BASE reservoir trap. Based on these recent advances, we discuss ongoing technical developments which comprise a coupling trap for the sympathetic cooling of single (anti-)protons with laser-cooled beryllium ions, a transportable trap to relocate antiproton measurements into a high-precision laboratory, and a new experiment to measure the magnetic moment of helium-3 ions, which will improve absolute precision magnetometry.

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 + 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 3 He + 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 constant 13 σ 3 He + = 0.00003550738 ( 3 ) . 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 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.

The magnetic moment of the antiproton is measured at the parts-per-billion level, improving on previous measurements by a factor of about 350. Magnetic moment of the antiproton Comparing the fundamental properties of normal-matter particles with their antimatter counterparts tests charge–parity–time (CPT) invariance, which is an important part of the standard model of particle physics. Many properties have been measured to the parts-per-billion level of uncertainty, but the magnetic moment of the antiproton has not. Christian Smorra and colleagues have now done so, and report that it is −2.7928473441 ± 0.0000000042 in units of the nuclear magneton. This is consistent with the magnetic moment of the proton, 2.792847350 ± 0.000000009 in the same units. Assuming CPT invariance, these two values should be the same, except for the difference in sign, so this result provides a more stringent constraint on certain CPT-violating effects. Precise comparisons of the fundamental properties of matter–antimatter conjugates provide sensitive tests of charge–parity–time (CPT) invariance 1 , which is an important symmetry that rests on basic assumptions of the standard model of particle physics. Experiments on mesons 2 , leptons 3 , 4 and baryons 5 , 6 have compared different properties of matter–antimatter conjugates with fractional uncertainties at the parts-per-billion level or better. One specific quantity, however, has so far only been known to a fractional uncertainty at the parts-per-million level 7 , 8 : the magnetic moment of the antiproton, . The extraordinary difficulty in measuring with high precision is caused by its intrinsic smallness; for example, it is 660 times smaller than the magnetic moment of the positron 3 . Here we report a high-precision measurement of in units of the nuclear magneton μ N with a fractional precision of 1.5 parts per billion (68% confidence level). We use a two-particle spectroscopy method in an advanced cryogenic multi-Penning trap system. Our result  = −2.7928473441(42) μ N (where the number in parentheses represents the 68% confidence interval on the last digits of the value) improves the precision of the previous best measurement 8 by a factor of approximately 350. The measured value is consistent with the proton magnetic moment 9 , μ p  = 2.792847350(9) μ N , and is in agreement with CPT invariance. Consequently, this measurement constrains the magnitude of certain CPT-violating effects 10 to below 1.8 × 10 −24 gigaelectronvolts, and a possible splitting of the proton–antiproton magnetic moments by CPT-odd dimension-five interactions to below 6 × 10 −12 Bohr magnetons 11 .

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, µ p . So far µ p has been measured only indirectly, by analysing the spectrum of an atomic hydrogen maser in a magnetic field 1 . Here we report the direct high-precision measurement of the magnetic moment of a single proton using the double Penning-trap technique 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 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: μ p = 2.792847350(9) μ N . This measurement outperforms previous Penning-trap measurements 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 6 were required to obtain µ p , by a factor of 3. By application of this method to the antiproton magnetic moment, the fractional precision of the recently reported value 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 8 .

The CPT theorem (the assumption that physical laws are invariant under simultaneous charge conjugation, parity transformation and time reversal) is central to the standard model of particle physics; here the charge-to-mass ratio of the antiproton is compared to that of the proton, with a precision of 69 parts per trillion, and the result supports the CPT theorem at the atto-electronvolt scale. CPT theorem put to the test The CPT theorem, the assumption that physical laws are invariant under simultaneous charge conjugation, parity transformation and time reversal, is central to the standard model of particle physics. Consequently, precision tests of the CPT theorem are a window onto the physics beyond the standard model. Here, Stefan Ulmer et al . test the CPT theorem by measuring whether particles and antiparticles, apart from a sign change, are identical. In a Penning-trap measurement, they compare the antiproton charge-to-mass ratio to its proton counterpart, showing that the CPT theorem holds at the atto-electronvolt scale. Their experiment improves the precision of previous proton–antiproton mass comparisons by a factor of four. 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 , 5 , 6 , 7 , 8 . Here we report high-precision cyclotron frequency comparisons of a single antiproton and a negatively charged hydrogen ion (H − ) carried out in a Penning trap system. From 13,000 frequency measurements we compare the charge-to-mass ratio for the antiproton to that for the proton and obtain . 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, and it sets a new limit on the gravitational anomaly parameter of < 8.7 × 10 −7 .

Astrophysical observations indicate that there is roughly five times more dark matter in the Universe than ordinary baryonic matter 1 , and an even larger amount of the Universe’s energy content is attributed to dark energy 2 . However, the microscopic properties of these dark components remain unknown. Moreover, even ordinary matter—which accounts for five per cent of the energy density of the Universe—has yet to be understood, given that the standard model of particle physics lacks any consistent explanation for the predominance of matter over antimatter 3 . Here we present a direct search for interactions of antimatter with dark matter and place direct constraints on the interaction of ultralight axion-like particles (dark-matter candidates) with antiprotons. If antiprotons have a stronger coupling to these particles than protons do, such a matter–antimatter asymmetric coupling could provide a link between dark matter and the baryon asymmetry in the Universe. We analyse spin-flip resonance data in the frequency domain acquired with a single antiproton in a Penning trap 4 to search for spin-precession effects from ultralight axions, which have a characteristic frequency governed by the mass of the underlying particle. Our analysis constrains the axion–antiproton interaction parameter to values greater than 0.1 to 0.6 gigaelectronvolts in the mass range from 2 × 10 −23 to 4 × 10 −17 electronvolts, improving the sensitivity by up to five orders of magnitude compared with astrophysical antiproton bounds. In addition, we derive limits on six combinations of previously unconstrained Lorentz- and CPT-violating terms of the non-minimal standard model extension 5 . Spin-flip resonance data are used to place direct constraints on the interaction of ultralight axion-like particles with antiprotons, improving the sensitivity to the corresponding coupling coefficient by five orders of magnitude.

Continuous monitoring of a cloud of antiprotons stored in a Penning trap for 405 days enables us to set an improved limit on the directly measured antiproton lifetime. From our measurements we extract a storage time of 3.15 × 10 8 equivalent antiproton-seconds, resulting in a lower lifetime limit of τ p ¯ > 10.2 a with a confidence level of 68 % . This result improves the limit on charge-parity-time violation in antiproton decays based on direct observation by a factor of 7.

Our current understanding of the Universe comes, among others, from particle physics and cosmology. In particle physics an almost perfect symmetry between matter and antimatter exists. On cosmological scales, however, a striking matter/antimatter imbalance is observed. This contradiction inspires comparisons of the fundamental properties of particles and antiparticles with high precision. Here we report on a measurement of the g -factor of the antiproton with a fractional precision of 0.8 parts per million at 95% confidence level. Our value /2=2.7928465(23) outperforms the previous best measurement by a factor of 6. The result is consistent with our proton g -factor measurement g p /2=2.792847350(9), and therefore agrees with the fundamental charge, parity, time (CPT) invariance of the Standard Model of particle physics. Additionally, our result improves coefficients of the standard model extension which discusses the sensitivity of experiments with respect to CPT violation by up to a factor of 20. High-precision measurements could disclose fundamental dissimilarities between matter and antimatter, which are found imbalanced in the Universe. Here, the authors measure the magnetic moment of the antiproton with six-fold higher accuracy than before, finding it consistent with that of the proton.

Cooling of particles to mK-temperatures is essential for a variety of experiments with trapped charged particles. However, many species of interest lack suitable electronic transitions for direct laser cooling. We study theoretically the remote sympathetic cooling of a single proton with laser-cooled 9 Be + in a double-Penning-trap system. We investigate three different cooling schemes and find, based on analytical calculations and numerical simulations, that two of them are capable of achieving proton temperatures of about 10 mK with cooling times on the order of 10 s. In contrast, established methods such as feedback-enhanced resistive cooling with image-current detectors are limited to about 1 K in 100 s. Since the studied techniques are applicable to any trapped charged particle and allow spatial separation between the target ion and the cooling species, they enable a variety of precision measurements based on trapped charged particles to be performed at improved sampling rates and with reduced systematic uncertainties.

Efficient cooling of trapped charged particles is essential to many fundamental physics experiments 1 , 2 , to high-precision metrology 3 , 4 and to quantum technology 5 , 6 . Until now, sympathetic cooling has required close-range Coulomb interactions 7 , 8 , but there has been a sustained desire to bring laser-cooling techniques to particles in macroscopically separated traps 5 , 9 , 10 , extending quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions and antimatter. Here we demonstrate sympathetic cooling of a single proton using laser-cooled Be + ions in spatially separated Penning traps. The traps are connected by a superconducting LC circuit that enables energy exchange over a distance of 9 cm. We also demonstrate the cooling of a resonant mode of a macroscopic LC circuit with laser-cooled ions and sympathetic cooling of an individually trapped proton, reaching temperatures far below the environmental temperature. Notably, as this technique uses only image–current interactions, it can be easily applied to an experiment with antiprotons 1 , facilitating improved precision in matter–antimatter comparisons 11 and dark matter searches 12 , 13 . A single electromagnetically trapped proton is sympathetically cooled to below ambient temperature by coupling it through a superconducting LC circuit to a laser-cooled cloud of Be + ions stored in a spatially separated trap.