# News Archive 2022

*Precision measurements*

First direct

*g*-factor difference measurement of two co-trapped isotopes

Quantum electrodynamics (QED), the fundamental theory of light-matter interaction, has been shown to be in excellent agreement with
experimental results (see e.g. our news of 08.07.11 and
20.02.14). Modern advanced high precision Penning-trap measurements allow for
tests of state-of-the-art QED calculations. The magnetic moment (or *g* factor) of hydrogen-like ions, that provide a simple bound-state system,
can be accessed experimentally and is also predicted very precisely by theory. Thus, accurate measurements of the bound-electron *g* factor
of highly charged ions (HCI) in Penning traps provide stringent tests of the Standard Model in the strongest electromagnetic fields
(see e.g. our news of 25.02.19).

The *g* factor of the bound electron in hydrogen-like ions results from the *g* factor of a free electron modified mainly by the additional
electric field. Since many other contributing nuclear effects (e.g. nuclear mass, charge radius) are smaller than the QED contributions and
their uncertainties, it is difficult to study them. This theoretical limitation can be overcome by studying the *g*-factor difference of two
highly charged isotopes. In this case, the common identical QED contributions and their uncertainties do not have to be considered, emphasizing
the isotopic differences due to the nucleus. This e.g. enables to resolve and test the nuclear recoil contribution to the *g* factor, that
considers the nuclear recoil in elaborate QED calculations.

In order to perform high-precision tests of these accurate QED calculations, the experimental limitations due to the precision of the ion masses
and the achievable magnetic field stability (see our news of 18.01.16) have to be overcome.
By co-trapping two HCIs in a Penning trap and
measuring the difference of their *g* factors directly, the influence of the magnetic field fluctuations could be considerably reduced. The
drastically improved measurement accuracy would allow to test the corresponding QED calculations with very high precision.

In a recent article published in "*Nature*", our division members Dr. T. Sailer *et al.* report on the application of a newly developed technique
to measure the difference of *g* factors directly. The high-precision measurements were performed in the
ALPHATRAP Penning-trap experiment
at MPIK in Heidelberg, which can manipulate and spatially confine ions at low energies by a superposition of static electric and magnetic fields.
The setup consists of a cryogenic double-trap system in a superconducting 4-T magnet, with a precision trap (PT) and an analysis trap (AT).
The PT with a highly homogeneous magnetic field is used for high-precision spectroscopy, whereas in the AT with a strong magnetic bottle,
the Larmor frequency *ν*_{L} is determined by using the continuous Stern-Gerlach effect to detect millimetre-wave (MW) induced spin flips around
*ν*_{L}.

The determination of the *g*-factor of the stored ions is based on the measurement of the frequency ratio *ν*_{L}/*ν*_{c} of the
Larmor frequency (*ν*_{L}) and the cyclotron frequency (*ν*_{c}). *ν*_{c} can
be precisely determined with the PT from the three independent
harmonic oscillations of the ion motion *ν*_{z} (axial frequency), *ν*_{+} (modified cyclotron frequency)
and *ν*_{-} (magnetron frequency)
via the invariance theorem:
*ν*_{c}^{2}=*ν*_{+}^{2}+*ν*_{z}^{2}+*ν*_{-}^{2}.

In order to directly measure the *g*-factor difference of two HCI for stringent tests of accurate bound-state QED calculations, the
neon isotopes ^{20}Ne^{9+} and ^{22}Ne^{9+} were stored simultaneously in the Penning trap system.
For this purpose, the scientists developed
a novel measurement technique based on the principle of the "*Two-Ion-Balance*", developed at MIT
(see Phys. Rev. A 45, 3049 (1992) and
Science 303, 334–338 (2004) ).

Here, the ^{20}Ne^{9+} and ^{22}Ne^{9+} ions were coupled on a common magnetron orbit separated by only about 400 μm in the PT. This allowed
for a coherent measurement of their Larmor frequency difference by performing a Ramsey-type measurement (i.e. irradiation of two
short MW π/2-pulses, with a variable time between them). From the extracted difference of the Larmor frequencies Δ*ν*_{L},
the *g*-factor difference Δ*g* of ^{20}Ne^{9+} and ^{22}Ne^{9+} was derived.
The achieved precision of 5.6 × 10^{−13} (0.56 p.p.t.)
relative to the absolute *g* factors is more than two orders of magnitude better than all previous such comparisons.

This improved accuracy allows resolving and testing the QED contribution to the nuclear recoil for the very first time.
A. V. Volotka and members of the theory division of Prof. C. H. Keitel performed accurate QED calculations for the comparison
of the experimental result with theoretical prediction.
The experimental value is in perfect agreement with the calculated value of Δ*g* and 10 times more accurate.
Alternatively, the theory can therefore be taken as input and to improve the uncertainty of the charge radius difference of the two isotopes
by about one order of magnitude.

Furthermore, the excellent agreement between theory and experiment allows setting constraints on the search for new physics beyond the
Standard Model of particle physics.

Please read more in the "*Nature*" article
and the associated article in *News & Views*

Further information also in the press release of the MPIK (idw ).

Further press releases:

*Precision measurements*

First direct measurement of the helium-3 nuclear magnetic moment

The Helium isotope ^{3}He plays an important role for modern physics, particularly fundamental physics (see e.g. our
news of 03.09.20), e.g.
sensitive tests of the bound state QED theory and muon *g*-2 experiments as well as for chemistry, medicine and other scientific fields.

In magnetometry, ^{3}He nuclear magnetic resonance (NMR) probes allow for measurements of the absolute magnetic field with higher accuracy and serve
as a new standard for ultra-sensitive absolute magnetometry.

However, this requires a high-accuracy and independent determination of the ^{3}He nuclear magnetic moment. Even so, up to now, the
^{3}He nuclear magnetic moment has been measured only indirectly by comparison to water based NMR probes with a relative precision of
12 parts per billion (p.p.b.), only.

The so-called *g*-factor is a proportionality constant relating the magnetic moment of a charged particle to its spin. Thus, a direct
high-precision determination of the nuclear *g*-factor of ^{3}He will provide an independent calibration for ^{3}He NMR
probes for accurate magnetometry.

In a recent article published in "*Nature*", researchers of our "Stored and Cooled Ions" division, University Mainz and RIKEN report the first
direct measurements of the bound electron *g*-factor and nuclear *g*-factor of ^{3}He^{+} with a relative precision
of 10^{–10}. The accuracy of the ^{3}He^{+} zero-field ground-state hyperfine splitting value (magnetic interaction of electron and
nucleus) could be improved by two orders of magnitude.

The precision measurements were performed in a novel Penning-trap system. The system is placed in the homogeneous field of a 5.7 T superconducting
magnet and consists of a precision trap (PT) and an analysis trap (AT) with a spatially separated strong magnetic inhomogeneity.

In a Penning trap, the motion of a single stored charged particle - in this case the ^{3}He^{+} ion - consists of three independent harmonic
oscillations: the axial frequency *ν*_{z}, the modified cyclotron frequency *ν*_{+} and the magnetron frequency
*ν*_{-}. These
eigenfrequencies can be detected with high precision in the PT. The free cyclotron frequency *ν*_{c} can be determined from the three
eigenfrequencies using the so-called invariance theorem
*ν*_{c}^{2}=*ν*_{+}^{2}+*ν*_{z}^{2}+*ν*_{-}^{2}.

The electron spin and the nuclear spin of ^{3}He^{+} are aligned parallel or antiparallel to an external magnetic field. This leads to a
hyperfine splitting in ^{3}He^{+} with four different hyperfine states. In the PT, two electronic and two nuclear spin transition frequencies
between these hyperfine states were determined by measuring the cyclotron frequency while a microwave excitation was driving one of the four
hyperfine transitions.

The electronic transitions and the nuclear transitions correspond to an electronic or nuclear spin-flip. The AT with the strong magnetic
inhomogeneity is used for spin-state detection by applying the continuous Stern-Gerlach effect. A spin-flip changes the magnetic moment of the
stored ^{3}He^{+}. Due to the coupling of the magnetic moment to the axial frequency of ^{3}He^{+} this change results in a shift of the
axial frequency. Thus, a spin-flip can be detected by measuring the axial frequency in the AT before and after resonantly driving the hyperfine
transition.

From the resonance curves for each of the four hyperfine transitions, the nuclear *g*-factor of ^{3}He^{+}, the bound electron *g*-factor
and the zero-field hyperfine splitting were extracted. The reached relative precision of 10^{–10} improved previous results
by a factor of 10.

In order to compare the experimental results with modern theoretical predictions, members of the MPIK theory group around Zoltán Harman in the
division of Christoph H. Keitel performed highly accurate QED calcuations. The theoretical value of the ^{3}He^{+} bound electron
*g*-factor is consistent with the experimental result. The difference between the experimental ^{3}He^{+} zero-field ground-state hyperfine splitting
value and the calculated value is 6 parts per million (p.p.m.).

Further, from the measured shielded nuclear *g*-factor of ^{3}He^{+} and an accurate QED calculation of the diamagnetic shielding constant, the
*g*-factor of the "bare" (i.e. unshielded) ^{3}He nucleus was derived.

This first direct calibration for ^{3}He NMR probes improves previous indirect results by one order of magnitude (1 p.p.b. instead of
12 p.p.b.). It is planned to further improve the Penning trap measurements by reducing the magnetic inhomogeneity of the PT. Additionally,
applying fast phase-sensitive detection methods - e.g. the "Pulse and Amplify" method - will allow for more precise magnetic field measurements.
The new measurement method used for helium-3 can also be applied to determine the nuclear magnetic moment of heavier hydrogen-like ions.
A direct Penning trap measurement of the magnetic moment of the bare ^{3}He nucleus is the next step. By implementing sympathetic laser
cooling, a relative precision on the order of 1 p.p.b. or better will be achieved.

Please read more in the "*Nature*" article ... >

Further information also in the press releases of the MPIK (idw ) and the MPG .

Further press releases:

*Precision measurements*

Precision laser spectroscopy tests modern nuclear theories in the nickel region

Modern nuclear theories beyond the simple shell-model aim to consistently describe atomic nuclei across the entire nuclear chart.
In recent years, there has been significant theoretical progress in nuclear many-body methods as well as in the development of
*ab initio* methods based on chiral effective field theory (EFT) interactions. Today, nuclear charge radii can be measured with
high accuracy and thus serve as robust benchmarks for *ab initio* calculations and well-calibrated energy density functionals,
such as the Fayans functional (see e.g. our
news of 08.02.16,
04.09.18 and
16.05.19). For the development of a coherent
theoretical nuclear framework, *ab initio* models have to be connected to nuclear density functional theory (DFT).

In a recent article published in "*Physical Review Letters*", S. Malbrunot-Ettenauer *et al.* report the determined nuclear
charge radii of short-lived nickel isotopes ^{58-68,70}Ni (*Z*=28). In terms of nuclear charge radii, these nickel isotopes
constitute the last unexplored "magic" isotopic chain in this mass region. The precision experiments were conducted with the
collinear laser spectroscopy apparatus COLLAPS
at the radioactive ion beam facility ISOLDE /CERN ,
Geneva. Details on the COLLAPS setup can be found in
R. Neugart *et al.* (2017)
(see our news of 24.04.17).

In the presented laser spectroscopy experiment the charge radii of ^{59,63,65-67,70}Ni have been determined. The charge radius
of ^{68}Ni has already been reported in the article of
S. Kaufmann *et al.* (2020)
which also gives a detailed description of the experiment at ISOLDE/CERN.

After neutralization of the Ni ions in a charge exchange cell, collinear laser spectroscopy on the neutral Ni atoms was performed.
The 3*d*^{9} 4*s* ^{3}*D*_{3} -> 3*d*^{9} 4*p* ^{3}*P*_{2}
transition at 352.45 nm was excited by a frequency-doubled single-mode cw titanium-sapphire
laser. All nickel isotopes were measured alternating with the reference isotope ^{60}Ni to compensate for remaining long-term
drifts in ion velocity or laser frequency. The frequency-time spectrum of the Ni resonances was recorded with the new data
acquisition system "TILDA".

The isotope shifts δ*ν*^{60,A} = *ν*^{A} - *ν*^{60} were calculated
from the center frequency *ν*^{A} of a Ni isotope with respect to the center frequency *ν*^{60}
of the reference isotope ^{60}Ni.

From the isotope shifts, the changes in mean-square nuclear charge radii δ<*r*_{c}^{2}>^{60,A}
of the measured nickel isotopes with respect to the reference isotope ^{60}Ni were extracted. The absolute charge radii
*R*_{c} were determined from δ<*r*_{c}^{2}>^{60,A} utilising
*R*_{c} (^{60}Ni).

The experimental results for *R*_{c} and δ<*r*_{c}^{2}> were compared with two
DFT approaches (the Skyrme functional SV-min and the
Fayans functional Fy(Δ*r*, HFB)) as well as three independent *ab initio* methods based on chiral EFT interactions.

Charge radii *R*_{c} allow a comparison between theory and experiment on the absolute scale. Since various theoretical uncertainties
cancel in the differential charge radii δ<*r*_{c}^{2}>,
δ<*r*_{c}^{2}> probe local variations in the nuclear charge distribution more closely.

When the same chiral EFT based nuclear potential NNLO_{sat} was utilized in all *ab initio* calculations, their results for
*R*_{c} and δ<*r*_{c}^{2}> showed excellent consistency and they agreed well with the
experiment. *Ab initio* calculations exploiting
other nuclear interactions deviated notably from experiment in the absolute charge radii *R*_{c} and only performed well
for δ<*r*_{c}^{2}>.

Unusually-large odd-even staggering or kinks in *R*_{c} at shell closures have been successfully described by Fayans-based
functionals (see e.g. our
news of 08.02.16,
04.09.18 and
16.05.19). However, in the absence of such features,
as is the case with the investigated "magic" nickel isotopic chain, interestingly, Skyrme-based DFT yields results closer to
experiment than the Fayans functional.

The reported comparative work combining experiment, density functional theory and *ab initio* calculations established a theoretical
accuracy of about 1% for the description of nuclear charge radii in the Ni region.

Please read more in the article ... >

*Precision measurements*

BASE improves the experimental constraints on the violation of CPT invariance and the Weak Equivalence Principle

The Standard Model (SM) is the most successful theory of particle physics. It describes three of the four known fundamental forces
(the electromagnetic, weak, and strong interaction) and classifies all known elementary particles. A great success of the SM was
e.g. the prediction of the Higgs Boson in 1964, which was finally discovered in 2012 at CERN, Geneva.

However, there is also strong observational evidence that the Standard Model of particle physics is incomplete. As a local, unitary
and Lorentz-invariant quantum field theory, the SM is Charge, Parity, and Time Reversal (CPT) invariant. Thus, according to the SM
the fundamental properties (e.g. mass, magnetic moment, lifetime) of a particle and its antiparticle are exactly equal. Therefore,
particles and antiparticles should have been created in equal amounts in the early universe. This means that the SM is unable to
explain the striking imbalance of matter and antimatter in the observable universe. This problem inspires tests of the CPT symmetry
by comparing the fundamental properties of matter/antimatter conjugates with high precision. Together with new theoretical models
that induce CPT-violation, experiments with further improved measurement precision might lead to Physics Beyond the SM.

Another hot topic in physics is whether antimatter obeys the weak equivalence principle (WEP), which is a cornerstone of General
Relativity and other gravity theories. The WEP states that the gravitational mass and inertial mass are equivalent. It has been
tested for matter to high accuracy by various experiments. An experimental test of the WEP with antimatter has not been available
up to now. In particular, cyclotron-clock-studies with matter/antimatter conjugates allow to test the "cyclotron clock weak
equivalence principle" (WEP_{cc}).

In a recent article published in "*Nature*", the
BASE collaboration
addresses both mentioned fundamental questions. The researchers performed high-precision tests of the CPT symmetry and the
WEPcc. For this purpose, they used the cryogenic BASE multi-Penning trap system consisting of a measurement trap and a reservoir trap
at the Antiproton Decelerator
(AD) facility of CERN, Geneva.

To test the CPT invariance with baryons, the BASE-team compared the proton/antiproton charge-to-mass ratios by measuring the free cyclotron
frequencies *ν*_{c}=(*q*·*B*)/(2π·*m*) of single trapped antiprotons and negatively
charged hydrogen ions H^{-} in their advanced Penning-trap system. H^{-} was used as an excellent negatively charged proxy
for the proton, since comparing particles of the same charge sign avoids inversion of the trapping voltages, and greatly reduces systematic
frequency-ratio shifts.

The Brown-Gabrielse invariance theorem *ν*_{c}^{2}=*ν*_{+}^{2}+*ν*_{z}^{2}+*ν*_{-}^{2}
relates the modified cyclotron frequency *ν*_{+}, the axial frequency *ν*_{z}, and
the magnetron frequency *ν*_{-} to *ν*_{c}. The comparison of
*ν*_{c} of antiprotons and H^{-} ions in the same magnetic field *B*_{0} gives access to the
ratio of their charge-to-mass ratios.

To improve the accuracy of the previous best proton/antiproton charge-to-mass ratio comparison of BASE (see our
news of 12.08.15,
[Nature 524, 196-199 (2015) ]),
numerous experimental upgrades have been implemented: a rigorous re-design of the cryogenic experiment
stage (CERN Document 2702758 ),
the development of an advanced multi-layer magnetic shielding system
(Phys. Rev. Applied 12, 044012 (2019) )
and of a frequency adjustable image-current detector (see our
news of 18.07.17,
[Phys. Rev. Lett. 119, 033001 (2017) ]).

The axial frequency *ν*_{z} was determined from a dip spectrum. The modified cyclotron frequency *ν*_{+}
(and similarly the magnetron frequency *ν*_{-})
was measured with the well-established sideband-technique observing a "double-dip" spectrum. Additionally, a "peak-technique" with
enhanced accuracy was used.

The new value 1.000000000003(16) of the ratio of the proton/antiproton charge-to-mass ratios with a fractional uncertainty of 16
parts-per-trillion (ppt, 10^{-12}) is consistent with CPT invariance. The final result is based on the combination of four independent
long term studies, recorded in a total time span of 1.5 years (December 2017 - May 2019). It improves the precision of the previous
best measurement of the BASE collaboration by a factor of 4.3 (see our
news of 12.08.15) and constrains the CPT violating effects to an energy scale
of about 2·10^{−27} GeV.

WEP_{cc} violating gravitational anomalies for antimatter would result in a frequency difference between a proton cyclotron-clock at
*ν*_{c,p} and its CPT conjugate antiproton clock at *ν*_{c,anti-p}. The four measurement
campaigns between December 2017 and May 2019 allowed to study the cyclotron frequencies
*ν*_{c} of the proton and the antiproton at
different gravitational potentials in the BASE laboratory due to the elliptical orbit of the earth around the sun. This enabled the
first differential test of the WEP_{cc} using antiprotons, which allowed to circumvent the problem of a potential modification
of the absolute value of the gravitational potential by a WEP-violating force. The researchers derived a differential
constraint |α_{g,D}−1|<0.030 of the WEP_{cc} violation.

The BASE collaboration plans to reach even higher sensitivity in future experiments by improving magnetic field stability and homogeneity, and by the development of transportable antiproton traps, named BASE-STEP (STEP: Symmetry Tests in Experiments with Portable Antiprotons) to move the antiprotons from noisy accelerator environments to calm precision laboratory space.

Please read more in the "*Nature*" article ... >

Further information also in the press releases of the MPIK (idw ), the Physikalisch-Technische Bundesanstalt (PTB) , the Leibniz University Hannover , the Johannes Gutenberg University Mainz (STEP) , and CERN .

Further press releases (selection):