In a recent publication in the Nature magazine, the BASE collaboration reports on the first high-precision measurement of the antiproton magnetic moment with parts per billion uncertainty (see https://www.nature.com/articles/nature24048). The antiproton magnetic moment is now determined with 350-fold improved precision to be -2.792 847 344 1(42) times the nuclear magneton. Two single antiprotons confined separately in a multi Penning trap system with extremely high vacuum have been probed in a novel measurement scheme to unveil this number with nine significant digits.

The BASE collaboration set their sails in 2013 in the Antiproton Decelerator (AD) to compare the fundamental properties of protons and antiprotons with highest precision. The team around Stefan Ulmer, spokesperson of the BASE collaboration, has made comparisons of the proton and antiproton charge-to-mass ratios, set lower limits on the antiproton lifetime, and reported including the recent study two record values for the antiproton magnetic moment. Such measurements challenge an important symmetry in the Standard Model of particle physics: The combined charge, parity and time-reversal (CPT) invariance. This symmetry is imbedded into the quantum field theories of the Standard Model and requires protons and antiprotons to have the same fundamental properties. Masses, lifetimes, charges and magnetic moments must be identical, but the latter two have opposite signs. Any observed deviation in their fundamental properties would hint to yet unknown interactions that would act differently on protons and antiprotons, such as those described by the Standard Model Extension or CPT-odd dimension-five operators.

g-factor resonance: spin-flip probability as a function of the irradiated frequency ratio. The red line is the result of a direct likelihood estimation of g_p and Ω_R.The grey area indicates the 68% error band.The black data points are binned averages of the measured P_SF(l')  displayed with error bars corresponding to 1 standard deviation. 
 

To make these high-precision studies, the BASE team operates a multi Penning trap system placed in a cryogenic vacuum chamber inside the bore of a superconducting magnet with 1.9 T field strength. The electrode system provides four harmonic Penning trap configurations and is shown in Fig 1. One of them is the reservoir trap, which serves as interface between the AD and the single-particle precision Penning traps. Antiprotons injected from the AD, and in the future from ELENA, are confined and cooled in this trap to temperatures of a few Kelvin. A potential tweezer method allows pulling out single antiprotons from the reservoir, and using them for precision experiments. In this way, the BASE team operated their experiment for 405 days from a single shot of antiprotons.

Fig. 1: The assembly of the BASE Penning trap system. The trap stack consists of gold-plated electrodes made from oxygen-free copper, which are spaced by sapphire rings. The electrodes form four harmonic field configurations. One of them, the analysis trap, has a ferromagnetic ring electrode to provide the strong magnetic bottle (B₂ = 30T/m²) for the spin state identification (Photo: Stefan Sellner, RIKEN).

The magnetic moment measurement requires to measure two frequencies of the trapped antiprotons, the Larmor frequency, which is the precession frequency of the antiproton’s spin around the magnetic field lines and the cyclotron frequency, the revolution frequency in the magnetic field. The cyclotron frequency is non-destructively measured by detecting tiny image currents of a few fA induced by the antiproton’s motion in the trap electrodes. This is an established technique, which has also been used for the determination of atomic masses in high-precision mass spectrometers, such as the antiproton q/m spectrometer operated by the TRAP collaboration at LEAR, or MPIK’s PENTATRAP mass spectrometer.

The major challenge is the measurement of the Larmor frequency, which is not directly accessible by image currents. One possibility is to induce spin transitions between the two Zeeman levels of the antiproton’s spin in the magnetic field and observing that the spin orientation changes. But how can you observe the orientation of a single nuclear spin?

Nobel laureate H. G. Dehmelt invented a technique, which he called the continuous Stern-Gerlach effect. It allows making quantum non-demolition measurements of the spin state of a trapped charged particle. This technique has been successfully applied to make the most precise measurements of the electron and positron magnetic moments; the most precise values for these quantities have been obtained at Harvard University and the University of Washington, respectively. To this end, an inhomogeneous magnetic field is superimposed to the Penning trap, and the curvature term B₂ of the magnetic field in units T/m² couples the magnetic moment of the particle to its axial oscillation. In a homogeneous magnetic field, the axial motion is a harmonic oscillation generated by electric field preventing the particle from moving along the magnetic field lines. The result from adding the magnetic bottle B₂, is that the particle changes its axial frequency when a spin transition occurs.

The application of this technique to the antiproton comes with a major challenge. The frequency shift caused by a spin transition is proportional to the factor magnetic moment over mass mu/m, which is more than one million times smaller for the antiproton compared to the electron. To compensate this, the BASE team uses a magnetic bottle at the technical limit B₂=300 000 T/m² to couple the antiproton’s spin magnetic moment to its axial oscillation. Even in this strong inhomogeneous magnetic field, a spin flip changes the axial frequency of about 700 kHz only by 180 mHz. The strong magnetic bottle complicates the experiment since frequency measurements exhibit also line broadening due to the dependence of the magnetic field on the antiproton’s motional amplitudes. This has been the major limitation in the measurements reported by the ATRAP collaboration in 2013 and also in the BASE measurement reported earlier this year.

The so-called double Penning trap technique for magnetic moments overcomes these limitations. In this scheme, the two frequencies are measured in a homogeneous trap, the precision trap, and the trap with the magnetic bottle, the analysis trap, is only used to identify the spin state before and after spin transitions are driven in the precision trap. This measurement scheme has been conventionally applied with one particle used for the measurement of both frequencies.

The BASE team developed in their newest measurement a scheme, which separates the two frequency measurements onto two particles: a cyclotron antiproton to calibrate the magnetic field, and a Larmor antiproton for the spin transition spectroscopy. The two antiprotons are placed alternatingly in the precision trap, and the magnetic field is interrogated by the cyclotron antiproton before and after driving a spin transition of the Larmor antiproton in the same magnetic field. This novel scheme allows to keep the Larmor antiproton at a radial temperature below 0.2 K during the whole measurement procedure, whereas the cyclotron antiproton is heated by each magnetic field measurement to a temperature of about 350 K.

Spin transitions in the analysis trap can only be observed at temperatures below 0.2 K, because spurious voltage noise of about 10 pV/Hz^1/2 destabilizes the axial frequency due to mode coupling in the magnetic bottle. The transition rate in the radial modes becomes only small enough to identify individual spin transitions for ultra-cold particles below the 0.2 K threshold. The re-cooling of the radial modes after the cyclotron frequency measurement has been limiting the statistical uncertainty in past measurement. The new accelerated two-particle measurement scheme allowed to accumulate more statistics and is therefore about a factor of 2 more precise than the double trap measurement of the proton magnetic moment in 2014, which was carried out in the BASE-Mainz experiment.

The reported measurement reveals that protons and antiprotons have the same magnetic moments up to nine digits of precision. CPT-odd interactions in the baryon sector, which would manifest in a measured difference in the magnetic moments, have been excluded with an energy resolution of
10^-24 GeV. The BASE collaboration continues to improve their methods to make even more precise tests of CPT invariance in the future and probe for effects of beyond Standard Model physics with an even higher energy resolution.