A. Mooser

Observation of Spin Flips with a Single Trapped Proton

Radio-frequency induced spin transitions of one individual proton are observed. 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.

High-precision comparison of the antiproton-to-proton charge-to-mass ratio

Invariance under the charge, parity, time-reversal (CPT) transformation 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. 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, but only a few direct high-precision CPT tests that compare the fundamental properties of matter and antimatter are available. 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 as well as the respective figure of merit of the standard model extension 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.

Resolution of single spin flips of a single proton.

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

Direct high-precision measurement of the magnetic moment of the proton

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

The quality factor of a superconducting rf resonator in a magnetic field

The quality factor of a superconducting NbTi resonator at 1.6 MHz in a magnetic field up to 1.2 T as well as its temperature dependence is investigated. A hysteresis effect in the superconducting surface resistance as a function of the magnetic field is observed. An unloaded Q-value of the resonator of 40,500 is achieved at 3.9 K. It is shown that this Q-value is limited by dielectric losses in the FORMVAR insulation of the coils wire. The details of the Q-value optimization are discussed. In the temperature dependence of the Q-value a steep decrease is observed above T approximately = 7.5 K. Finally, the implications of these measurements for real trap experiments are discussed in detail.

An experiment for the direct determination of the g-factor of a single proton in a Penning trap

A new apparatus has been designed that aims at a direct precision measurement of the g-factor of a single isolated proton or antiproton in a Penning trap. We present a thorough discussion on the trap design and a method for the experimental trap optimization using a single stored proton. A first attempt at the g-factor determination has been made in a section of the trap with a magnetic bottle. The Larmor frequency of the proton has been measured with a relative uncertainty of 1.8◊10 6 and the magnetic moment has been determined with a relative uncertainty of 8.9◊10 6 . Ag-factor of 5.585696(50) has been obtained, which is in excellent agreement with previous measurements and predictions. Future experiments shall drive the spin-flip transition in a section of the trap with a homogeneous magnetic field. This has the potential to improve the precision of the measured g-factor of the proton and the antiproton by several orders of magnitude.

High-Precision Measurement of the Proton’s Atomic Mass

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 3, but also disagrees with it at a level of about 3 standard deviations.

A parts-per-billion measurement of the antiproton magnetic moment

Precise comparisons of the fundamental properties of matter–antimatter conjugates provide sensitive tests of charge–parity–time (CPT) invariance, which is an important symmetry that rests on basic assumptions of the standard model of particle physics. Experiments on mesons, leptons and baryons 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: 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. Here we report a high-precision measurement of in units of the nuclear magneton μN 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)μN (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 by a factor of approximately 350. The measured value is consistent with the proton magnetic moment, μp = 2.792847350(9)μN, and is in agreement with CPT invariance. Consequently, this measurement constrains the magnitude of certain CPT-violating effects 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.

Sixfold improved single particle measurement of the magnetic moment of the antiproton

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 gp/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.

g-factor experiments on simple systems in Penning traps

Penning traps serve for the precise measurement of magnetic moments of simple atomic systems and fundamental particles. Here we present attempts to measure the magnetic moment of the electron bound in hydrogen-like or lithium-like heavy ions as well as of the proton and antiproton. While the first experiment aims for a more stringent test of bound-state quantum-electrodynamic calculations the second experiment provides a new high-precision test of the CPT theorem in the baryonic sector.