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 spacetimealthough 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 2 ) carried out in a Penning trap system. From 13,000 frequency measurements we compare the charge-to-mass ratio for the antiproton (q=m) p to that for the proton q=m ð Þ p and obtain q=m ð{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-toproton 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 a g {1 , 8.7 3 10 27 . 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 searches for physics beyond the standard model, such as tests of CPT invariance that compare the fundamental properties of matterto-antimatter equivalents at the lowest energies and with the greatest precision [12][13][14][15] . For leptons, for example, the magnetic anomalies of electron and positron were compared with a fractional uncertainty of about 2 parts per billion 4 , and by applying similar techniques to protons and antiprotons, the resulting g-factor (a proportionality constant which links the spin of a particle to its magnetic moment) comparison reached a precision of 4.4 parts per million 8 . We are planning to improve this measurement by at least a factor of a thousand 16,17 . In this context, we recently reported the most precise and first direct high-precision measurement of the proton magnetic moment, with a fractional precision of 3.3 parts per billion 18 . Complementary to these efforts, spectroscopic comparisons of hydrogen and antihydrogen are underway; recent progress has been...

Precise comparisons of the fundamental properties of matterantimatter 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, μ p . The extraordinary difficulty in measuring μ p 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 μ p 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 μ p = −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 μ p 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 protonantiproton magnetic moments by CPT-odd dimension-five interactions to below 6 × 10 −12 Bohr magnetons 11 .Within the physics programme at the Antiproton Decelerator of CERN, the properties of protons and antiprotons 5,6 , antiprotons and electrons 12 , and hydrogen 13 and antihydrogen 14,15 are compared with high precision. Such experiments, including those described here, provide stringent tests of CPT invariance. Our presented antiproton magnetic moment measurement reaches a fractional precision of 1.5 parts per billion (p.p.b.) at 68% confidence level, enabled by our new measurement scheme. Compared to the double-Penning trap technique 16 used in the measurement of the proton magnetic moment 9 , this new method eliminates the need for cyclotron cooling in each measurement cycle and increases the sampling rate.Our technique uses a hot cyclotron antiproton for measurements of the cyclotron frequency ν c , and a cold Larmor antiproton to determine the Larmor frequency ν L . By evaluating the ratio of the frequencies measured in the same magnetic field, the magnetic moment of the antiproton (in units of the nuclear magneton, the g-factor) ν ν μ μN is obtained. With this new technique we have improved the precision of the previous best antiproton magnetic moment measurement 8 by a factor of approximately 350 (Fig. 1a).Our experiment 17 is located in the Antiproton Decelerator facility, which provides bunches of 30 million antiprotons at a...

Precise knowledge of the fundamental properties of the proton is essential for our understanding of atomic structure as well as for precise tests of fundamental symmetries. We report on a direct high-precision measurement of the magnetic moment μ of the proton in units of the nuclear magneton μ The result, μ = 2.79284734462 (±0.00000000082) μ, has a fractional precision of 0.3 parts per billion, improves the previous best measurement by a factor of 11, and is consistent with the currently accepted value. This was achieved with the use of an optimized double-Penning trap technique. Provided a similar measurement of the antiproton magnetic moment can be performed, this result will enable a test of the fundamental symmetry between matter and antimatter in the baryonic sector at the 10 level.

One of the fundamental properties of the proton is its magnetic moment, mu(p). So far mu(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: mu(p) = 2.792847350(9)mu(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 mu(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)

Radio-frequency induced spin transitions of one individual proton are observed for the first time. The spin quantum jumps are detected via the continuous Stern-Gerlach effect, which is used in an experiment with a single proton stored in a cryogenic Penning trap. This is an important milestone towards a direct high-precision measurement of the magnetic moment of the proton and a new test of the matter-antimatter symmetry in the baryon sector.

Abstract. The Baryon Antibaryon Symmetry Experiment (BASE) aims at performing a stringent test of the combined charge parity and time reversal (CPT) symmetry by comparing the magnetic moments of the proton and the antiproton with high precision. Using single particles in a Penning trap, the proton/antiproton g-factors, i.e. the magnetic moment in units of the nuclear magneton, are determined by measuring the respective ratio of the spin-precession frequency to the cyclotron frequency. The spin precession frequency is measured by non-destructive detection of spin quantum transitions using the continuous Stern-Gerlach effect, and the cyclotron frequency is determined from the particle's motional eigenfrequencies in the Penning trap using the invariance theorem. By application of the double Penningtrap method we expect that in our measurements a fractional precision of δg/g 10

We report on the precise measurement of the atomic mass of a single proton with a purpose-built Penning-trap system. With a precision of 32 parts-per-trillion our result not only improves on the current CODATA literature value by a factor of three, but also disagrees with it at a level of about 3 standard deviations.The properties of the basic building blocks of matter shape a network of fundamental parameters, which are crucial to develop precise quantitative understanding of nature and its symmetries. One of these fundamental constants is the mass of the proton m p , which has always been a target and yardstick of precision experiments [1][2][3][4][5]. It is thus correlated with most other parameters of atomic physics. For example, its value influences the Rydberg constant [6], and it is also required for the precise comparison of the masses of the proton and antiproton, in order to perform a stringent test of CPT invariance via a hydrogen anion [7].All recent proton mass values are based on Penningtrap measurements, where the cyclotron frequencies ν c = 1 2π q m B of the proton (or H + 2 ) and a reference ion with respective charge-to-mass ratios q /m are compared in the same magnetic field B. In this letter we report on a high-precision measurement of m p in atomic mass units, which is based on cyclotron frequency comparisons of protons and highly charged carbon ( 12 C 6+ ) ions. While the largely different charge-to-mass ratio between the proton and the 12 C 6+ ion imposes technical challenges to be discussed later, the comparison with the atomic mass standard allows us to determine the mass of the proton directly in atomic mass units. In order to do so, we have to relate the mass of the 12 C 6+ ion to that of a 12 C atom:Here, E b,i denotes the binding energies of the six removed electrons, c the speed of light in vacuum and m e the electron mass [8]. Since m( 12 C) is 12 u by definition and the atomic mass of the electron has been previously determined by our group with 2.9 × 10 −11 relative uncertainty, this relation is limited only by the knowledge of electronic binding energies. The currently tabulated values in the NIST table of ionization energies [9] allow to derive m( 12 C 6+ ) = 11.996 709 626 413 9(10) u with a relative precision of 0.08 parts-per-trillion (ppt), which does not pose any limitation on the precision of the proton's atomic mass reported here.

The spin magnetic moment of a single proton in a cryogenic Penning trap was coupled to the particle's axial motion with a superimposed magnetic bottle. Jumps in the oscillation frequency indicate spin flips and were identified using a Bayesian analysis.