Quantum electrodynamics (QED) is part of the "Standard Model" of particle physics, which has the ambitious goal of describing all physical effects with the exception of gravity. Tests of the Standard Model are of interest to find clues as to why some predictions do not match experimental observations. With respect to QED, some theoretical predictions, for example in muonic systems, do not agree with experimental observations. Thanks to the precise measurements of the researchers at the MPIK, the current models of QED could be tested with unprecedented accuracy.
The measurements at the ALPHATRAP and PENTATRAP experiments are aimed at determining the g-factor of a single electron bound to a neon nucleus. The electron as an elementary particle is, alongside the protons and neutrons in the nucleus, a main component of neutral atoms and thus of all matter with which we are in everyday contact. Electrons have a negative charge, the elementary charge, and a spin, a kind of internal angular momentum. It follows from these two properties that the electron also has a magnetic moment: an electron generates a magnetic field through its charge and spin, analogous to the current in the coil of an electromagnet.
The strength of this magnetic moment is determined by the g-factor and in relativistic quantum mechanics this should have exactly the value 2 for the free electron. On closer inspection, however, the electron constantly interacts with the photons of the electromagnetic field. Even in an apparently empty vacuum, the electron constantly absorbs and emits so-called virtual photons, which in turn can interact with other virtual particles. In the case of an electron bound to an atomic nucleus, there is also the influence of the attraction between the charged particles. Depending on the mass of the nucleus and the charge contained in it by the protons, the contributions of the respective corrections also vary in size. Therefore, certain corrections can be tested more precisely with selected systems.
The MPIK researchers now measured the g-factor of a single electron bound to a neon nucleus (an atomic nucleus with 10 protons) and can thus test how well the theoretical predictions of all these corrections are correct. In this one-electron neon nucleus system, the corrections due to the electron's self-interaction are tested in sensitively.
In order to measure the g-factor, the behaviour of the spin in strong magnetic fields was used in this experiment: There, the spin aligns itself vertically like a gyroscope in the Earth's gravitational field. If this alignment is disturbed and the gyroscope is nudged at the top, it begins to precess: The now tilted axis rotates around the vertical at a frequency that depends on the g-factor. This behaviour of magnetic moments is called Larmor precession and is the same physical effect that MRIs use for medical imaging. In addition to the Larmor frequency, the mass of the nucleus is also required to determine the g-factor.
The Larmor frequency was determined in the ALPHATRAP experiment. In this Penning trap experiment, the Larmor frequency is determined indirectly via the orientation of the magnetic moment in the magnetic field of the ion trap: It can be aligned parallel or anti-parallel (upside down). In the ALPHATRAP trap, a magnetic bottle, i.e. a magnetic field that increases quadratically along the axis, causes an ion with a spin aligned parallel to the magnetic field to be bound somewhat more strongly in the trap than with a reversed spin alignment. As the ion is electrically charged, it constantly induces so-called mirror charges in the metallic electrodes. When the ion oscillates in the trap, these mirror charges also oscillate, which can be measured with very sensitive amplifiers. When the spin of the ion is flipped, the frequency of the ion movement changes slightly, but easily measurable.
An attempt is now made to inverse the magnetic moment, to cause a "spin flip": If the previously mentioned Larmor frequency is roughly known (e.g. from theory), it can be sent into the trap as a microwave signal. The irradiated frequency is changed slightly for each measurement attempt, i.e. tuned over the investigated range. If the exact Larmor frequency is hit, the microwave field drives the precession so strongly that the gyroscope not only tilts, but can also change its orientation in the magnetic field, so that after microwave irradiation the orientation is randomly parallel or anti-parallel. The data is analyzed like a coin toss, each change in spin orientation to the previous orientation is evaluated as 1 and no change is evaluated as 0. This procedure is now repeated several times in order to collect sufficient statistics. The ratio of change to no change at a tested frequency indicates the probability of a spin flip caused by the irradiated microwave frequency. The highest spin flip probability will occur at the resonant microwave frequency, i.e. the one that matches the Larmor frequency, and thus determines the Larmor frequency.
The required nuclear mass was determined with the highest accuracy by the PENTATRAP experiment. Here, highly charged ions are also stored in Penning traps, but the magnetic field is kept as homogeneous and stable as possible in order to measure the natural frequencies of the stored ion with the highest precision. From this, the free cyclotron frequency of the ions can be determined and compared with that of a reference ion. When measuring the neon 20 isotope, carbon ions were used as a mass reference, as the atomic mass unit is defined via this atom. Both the neon ion and the carbon ion were used in the highest charge states (10+ and 6+), without any electrons. The alternating determination of the cyclotron frequencies of the two ions allows the determination of the ratio of the cyclotron frequencies and thus directly the determination of the mass ratio of the ions. Thanks to the particularly stable storage fields in the PENTATRAP experiment and careful investigation of systematic measurement shifts, PENTATRAP succeeded in measuring the mass of neon 20 with an accuracy of 5 parts-per-trillion (5 · 10–12), a world record for mass measurements in atomic mass units.
With the help of these two measured values, the nuclear mass and the Larmor frequency, the g-factor of the bound electron can be calculated. The comparison of the experimental g-factor and the g-factor calculated from QED models shows an agreement to ten decimal places and provides the most precise test of the theory of self-interaction of the bound electron.
In future, the measurements at ALPHATRAP and PENTATRAP are to be further improved in order to test QED models even more precisely and to significantly increase the accuracy of the electron mass through similar measurements with helium or carbon nuclei.
Original publication:
High-Precision Determination of g Factors and Masses of 20Ne9+ and 22Ne9+
F. Heiße, M. Door, T. Sailer, P. Filianin, J. Herkenhoff, C. M. König, K. Kromer, D. Lange, J. Morgner, A. Rischka, Ch. Schweiger, B. Tu, Y. N. Novikov, S. Eliseev, S. Sturm and K. Blaum
Physical Review Letters 131, 253002 (2023). DOI: 10.1103/PhysRevLett.131.253002
Weblinks:
ALPHATRAP experiment (Division Blaum) at MPIK
PENTATRAP-experiment (Division Blaum) at MPIK
