# Experiment of the moment

16 February 2018

The BASE collaboration at CERN has measured the antiproton magnetic moment with extraordinary precision.

The enigma of why the universe contains more matter than antimatter has been with us for more than half a century. While charge–parity (CP) violation can, in principle, account for the existence of such an imbalance, the observed matter excess is about nine orders of magnitude larger than what is expected from known CP-violating sources within the Standard Model (SM). This striking discrepancy inspires searches for additional mechanisms for the universe’s baryon asymmetry, among which are experiments that test fundamental charge–parity–time (CPT) invariance by comparing matter and antimatter with great precision. Any measured difference between the two would constitute a dramatic sign of new physics. Moreover, experiments with antimatter systems provide unique tests of hypothetical processes beyond the SM that cannot be uncovered with ordinary matter systems.

The Baryon Antibaryon Symmetry Experiment (BASE) at CERN, in addition to several other collaborations at the Antiproton Decelerator (AD), probes the universe through exclusive antimatter “microscopes” with ever higher resolution. In 2017, following many years of effort at CERN and the University of Mainz in Germany, the BASE team measured the magnetic moment of the antiproton with a precision 350 times better than by any other experiment before, reaching a relative precision of 1.5 parts per billion (figure 1). The result followed the development of a multi-Penning-trap system and a novel two-particle measurement method and, for a short period, represented the first time that antimatter had been measured more precisely than matter.

### Non-destructive physics

The BASE result relies on a quantum measurement scheme to observe spin transitions of a single antiproton in a non-destructive manner. In experimental physics, non-destructive observations of quantum effects are usually accompanied by a tremendous increase in measurement precision. For example, the non-destructive observation of electronic transitions in atoms or ions led to the development of optical frequency standards that achieve fractional precisions on the 10–18 level. Another example, allowing one of the most precise tests of CPT invariance to date, is the comparison of the electron and positron g-factors. Based on quantum non-demolition detection of the spin state, such studies during the 1980s reached a fractional accuracy on the parts-per-trillion level.

The latest BASE measurement follows the same scheme but targets the magnetic moment of protons and antiprotons instead of electrons and positrons. This opens tests of CPT in a totally different particle system, which could behave entirely differently. In practice, however, the transfer of quantum measurement methods from the electron/positron to the proton/antiproton system constitutes a considerable challenge owing to the smaller magnetic moments and higher masses involved.

The idea is to store single particles in ultra-stable, high-precision Penning traps, where they oscillate at characteristic frequencies. By measuring those frequencies, we can access the cyclotron frequency, νc, which defines the particle’s revolutions per second in the trap’s magnetic field. Together with a measurement of the spin precession frequency νL, the g-factor can be extracted from the relation:

$\frac{{g}_{\overline{)p}}}{2}=\frac{{\nu }_{L}}{{\nu }_{c}}$

To determine νc we use a technique called image-current detection. The oscillation of the antiproton in the trap induces tiny image currents in the trap electrodes, which are picked up by highly sensitive superconducting tuned circuits.

The measurement of νL, on the other hand, relies on single-particle spin-transition spectroscopy – comparable to performing NMR with a single antiproton. The idea is to switch the spin of the individual antiproton from one state to the other and then detect the flip. To this end a smart trick is used: the continuous Stern–Gerlach effect, which imprints the collapsed spin state of the single antiproton on its axial oscillation frequency (a parameter that can be measured non-destructively). We use a special Penning trap configuration in which an inhomogeneous magnetic bottle is superimposed on the homogeneous magnetic field of the ideal Penning trap (figure 2, top). The inhomogeneous  field adds a spin-dependent quadratic magnetic potential to the axial electrostatic trapping potential and, consequently, the continuously measured axial oscillation frequency of the trapped antiproton becomes a function of the spin eigenstate.

In practice, to detect spin quantum-transitions we first measure the axial frequency, then inject a magnetic radio-frequency to drive spin transitions, and finally measure the axial frequency again. The observation of an axial frequency jump corresponds to the clear signature that a spin-transition was driven, and by repeating such measurements many times and for different drive frequencies, we obtain the spin-flip probability as a function of the drive frequency. The corresponding resonance curve gives νL (figure 2, bottom).

### Doubling up

This challenge has become the passion of the members of the BASE collaboration for the past decade. A trap was developed at Mainz with a superimposed magnetic inhomogeneity of 300,000 T/m2, which corresponds to a magnetic field change of about 1 T over a distance of about 1.5 mm! In this extreme magnetic environment, a proton/antiproton spin transition induces an axial frequency shift of only 170 mHz when driven at a frequency of around 650 kHz.

Using this unique device, in 2011 we reported the first observation of spin flips with a single trapped proton. This was followed by the unambiguous quantum-non-demolition detection of proton spin-transitions, which was later also demonstrated with antiprotons (figure 3). The high-fidelity detection of the spin state, however, requires the particle to be cooled to temperatures of the order of 100 mK. This was achieved by sub-thermal cooling of the particle’s cyclotron mode by means of cryogenic resistors, but is an inconceivably time-consuming procedure.

The high-fidelity resolution of single-spin quantum transitions is the key to measuring the antiproton magnetic moment at the parts-per-billion level. The elegant double-trap technique that makes this possible was invented at Mainz and applied with great success in tests of bound-state quantum electrodynamics, in collaboration with GSI Darmstadt and the Max Planck Institute for Nuclear Physics in Heidelberg, Germany, both institutes also being part of the BASE collaboration. This double Penning-trap technology separates the sensitive frequency measurements of νL and νc, and the spin analysis measurements into two traps: a homogeneous “precision trap” (PT) and the spin state “analysis trap” (AT) with the superimposed strong magnetic bottle. The magnetic field in the PT is about 100,000 times more homogeneous than that of the AT and allows sampling of the spin-flip resonance at much higher resolution, compared to measurements solely carried out in the inhomogeneous AT.

The single-particle “double-trap method”, however, comes with the drawback that each frequency measurement in the PT heats the particle’s radial mode to about room-temperature and requires repeated particle preparation to sub-thermal radial energy, a condition that is ultimately required for the high-fidelity detection of spin transitions. Each of these sub-thermal-energy preparation cycles takes several hours, while a well resolved g-factor resonance contains at least 400 individual data points. We applied this method at BASE to measure the proton magnetic moment with parts-per-billion precision in a measurement campaign that took, including systematic studies and maintenance of the instrument, about half a year.

To reduce the total measurement time, we invented the novel two-particle method in which the precision frequency measurements and the high-fidelity spin-state analysis are carried out using two particles: a hot “cyclotron particle” and a cold “Larmor particle”, in addition to adding a third trap called the “park trap” (figure 4). We first identify the spin state of the cold antiproton in the AT. Then we measure the cyclotron frequency with the hot particle in the PT, move this particle to the park trap and transport the cold antiproton to the PT, where spin-flip drives are irradiated. Afterwards, the cold particle is shuttled back to the AT and the hot particle to the PT. There, the cyclotron frequency is measured again, and in a last step the spin state of the cold particle in the AT is identified. By repeating this scheme many times and for different drive frequencies, the spin-flip probability as a function of the spin-flip drive frequency, normalized to the measured cyclotron frequency, is obtained – a g-factor resonance – with all the required frequency information sampled in the homogeneous PT. This novel two-particle scheme drastically reduces the measurement time, since it avoids the time-consuming preparation of sub-thermal radial energy-states.

Successfully implementing this new method, we were able to sample about 1000 data points over a period of just two months. From this campaign we extracted the antiproton magnetic moment as µ = –2.792 847 344 1 (42) μN, the value having a fractional precision of 1.5 parts per billion and thereby improving the previous best value by BASE by a factor of 350. The result is consistent with our most precise measurement of the proton magnetic moment, μp = 2.792 847 350 (9) µN, and thus supports CPT invariance.

### Trappings of success

Underpinning this rapid achievement of the initially defined major experimental goal of the BASE collaboration was another BASE invention called the reservoir trap (RT) method. This RT, being one of four traps in the BASE trap-stack, is loaded with a shot of antiprotons and provides single particles to the precision measurement traps on request. The method allows BASE to operate antiproton experiments even during the winter shut-down of CERN’s accelerators and practically doubles the available experiment time. Indeed, we have demonstrated antiproton trapping and experiment optimisation for a period of more than 400 days and operated the entire 2016 run with antiprotons captured in 2015. This long storage time also allows us to set limits on directly measured antiproton lifetime.

Together with the proton-to-antiproton charge-to-mass ratio comparison with a fractional precision of 69 parts in a trillion CERN Courier September 2015 p7), which was carried out during the 2014 antiproton run, BASE has set tighter constraints on all the fundamental antiproton parameters that are directly accessible by this type of experiment. So far, all the BASE results are consistent with CPT invariance.

The latest triple-trap measurement of the antiproton magnetic moment sets new constraints on CPT violating coefficients in the Standard Model extension (SME) – an effective theory that allows the sensitivities of different experiments at different locations to be compared with respect to CPT violation. The recent BASE magnetic-moment measurement addresses a total of six combinations of SME coefficients and improves the limits on all of them by more than two orders of magnitude. Finding a non-zero coefficient would, for example, indicate the discovery of a new type of exchange boson that couples exclusively to antimatter and immediately raise the question of its role in the universal baryon asymmetry.

Although up to now all results are CPT-consistent, this not-yet-understood asymmetry is one of the motivations to further improve the experimental resolution of the AD experiments. The recent successes reported by the ALPHA collaboration herald the first ultra-high-precision measurements on the optical spectrum of antihydrogen. Improved methods in measurements on antiprotonic helium by the ASACUSA collaboration will lead to even higher resolution results in comparisons of the antiproton-to-electron mass ratio, while the ATRAP collaboration continues to contribute independent measurements of antiprotons and antihydrogen.

### Gravitational sensitivity

A new branch of experiments at CERN’s AD, AEgIS, GBAR and ALPHA-g, will soon investigate the gravitational acceleration of antimatter in Earth’s gravitational field – which has never been directly observed before. Indirect measurements were carried out with antiprotons by the TRAP collaboration at the AD’s predecessor, LEAR, and by BASE, which set constrains on antigravity effects.

The AD community aims to verify the laws of physics with antimatter in various ways, thereby testing fundamental CPT invariance. The experiments are striving to access yet unmeasured quantities, or to improve their sensitivities to new physics. In this respect, the BASE–Mainz experiment succeeded recently in measuring the proton magnetic moment at an 11-fold improved precision, reaching a fractional uncertainty of 0.3 parts per billion. By applying these even further advanced methods to the antiproton, BASE will improve the sensitivity of the CPT invariance test by at least another factor of five.

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