g Factor of lithiumlike silicon 28Si11+

Stringent test of QED with hydrogen-like tin

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond 1015 V cm-1 for the innermost electrons1. Especially in few-electron, highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the past several decades2,3. Another approach is the measurement of gyromagnetic factors (g factors) in highly charged ions4-7. However, so far, either experimental accuracy or small field strength in low-Z ions5,6 limited the stringency of these QED tests. Here we report on our high-precision, high-field test of QED in hydrogen-like 118Sn49+. The highly charged ions were produced with the Heidelberg electron beam ion trap (EBIT)8 and injected into the ALPHATRAP Penning-trap setup9, in which the bound-electron g factor was measured with a precision of 0.5 parts per billion (ppb). For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about 0.012%, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests by means of the Lamb shift and, with anticipated advances in the g-factor theory, surpass them by more than an order of magnitude.

High frequency properties of a planar ion trap fabricated on a chip

We report on the measurement of the high frequency properties of a planar Penning ion trap fabricated on a chip. Two types of chips have been measured: the first manufactured by photolithographic metal deposition on a p-doped silicon substrate and the second made with printed circuit board technology on an alumina substrate. The input capacitances and the admittances between the different trap's electrodes play a critical role in the electronic detection of the trapped particles. The measured input capacitances of the photolithographic chip amount to 65-76 pF, while the values for the printed circuit board chips are in the range of 3-5 pF. The latter are small enough for detecting non-destructively a single trapped electron or ion with a specifically tuned LC resonator. We have also measured a mutual capacitance of ∼85 fF between two of the trap's electrodes in the printed circuit board chip. This enables the detection of single, or very few, trapped particles in a broader range of charge-to-mass ratios with a simple resistor on the chip. We provide analytic calculations of the capacitances and discuss their origin and possible further reduction.

g Factor of Lithiumlike Silicon and Calcium: Resolving the Disagreement between Theory and Experiment

The bound-electron g factor is a stringent tool for tests of the standard model and the search for new physics. The comparison between an experiment on the g factor of lithiumlike silicon and the two recent theoretical values revealed the discrepancies of 1.7σ [Glazov et al. Phys. Rev. Lett. 123, 173001 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.173001] and 5.2σ [Yerokhin et al. Phys. Rev. A 102, 022815 (2020)PLRAAN2469-992610.1103/PhysRevA.102.022815]. To identify the reason for this disagreement, we accomplish large-scale high-precision computation of the interelectronic-interaction and many-electron QED corrections. The calculations are performed within the extended Furry picture of QED, and the dependence of the final values on the choice of the binding potential is carefully analyzed. As a result, we significantly improve the agreement between the theory and experiment for the g factor of lithiumlike silicon. We also report the most accurate theoretical prediction to date for lithiumlike calcium, which perfectly agrees with the experimental value.

Ground-State g Factor of Highly Charged ^{229}Th Ions: An Access to the M1 Transition Probability between the Isomeric and Ground Nuclear States

A method is proposed to determine the M1 nuclear transition amplitude and hence the lifetime of the "nuclear clock transition" between the low-lying (∼8  eV) first isomeric state and the ground state of ^{229}Th from a measurement of the ground-state g factor of few-electron ^{229}Th ions. As a tool, the effect of nuclear hyperfine mixing in highly charged ^{229}Th ions such as ^{229}Th^{89+} or ^{229}Th^{87+} is used. The ground-state-only g-factor measurement would also provide first experimental evidence of nuclear hyperfine mixing in atomic ions. Combining the measurements for H-, Li-, and B-like ^{229}Th ions has a potential to improve the initial result for a single charge state and to determine the nuclear magnetic moment to a higher accuracy than that of the currently accepted value. The calculations include relativistic, interelectronic-interaction, QED, and nuclear effects.

g Factor of Lithiumlike Silicon: New Challenge to Bound-State QED

The recently established agreement between experiment and theory for the g factors of lithiumlike silicon and calcium ions manifests the most stringent test of the many-electron bound-state quantum electrodynamics (QED) effects in the presence of a magnetic field. In this Letter, we present a significant simultaneous improvement of both theoretical g_{th}=2.000 889 894 4 (34) and experimental g_{exp}=2.000 889 888 45 (14) values of the g factor of lithiumlike silicon ^{28}Si^{11+}. The theoretical precision now is limited by the many-electron two-loop contributions of the bound-state QED. The experimental value is accurate enough to test these contributions on a few percent level.

g Factor of Boronlike Argon ^{40}Ar^{13+}

We have measured the ground-state g factor of boronlike argon ^{40}Ar^{13+} with a fractional uncertainty of 1.4×10^{-9} with a single ion in the newly developed Alphatrap double Penning-trap setup. The value of g=0.663 648 455 32(93) obtained here is in agreement with our theoretical prediction of 0.663 648 12(58). The latter is obtained accounting for quantum electrodynamics, electron correlation, and nuclear effects within the state-of-the-art theoretical methods. Our experimental result distinguishes between existing predictions that are in disagreement, and lays the foundations for an independent determination of the fine-structure constant.

A quartz amplifier for high-sensitivity Fourier-transform ion-cyclotron-resonance measurements with trapped ions

Single-ion sensitivity is obtained in precision Penning-trap experiments devoted to light (anti)particles or ions with low mass-to-charge ratios, by adding an inductance coil to an amplifier connected to the trap, both operated at 4 K. However, single-ion sensitivity has not been reached on heavy singly or doubly charged ions. In this publication, we present a new system to reach this point, based on the use of a quartz crystal as an inductance, together with a newly developed broad-band (BB) amplifier. We detect the reduced-cyclotron frequency of ⁴⁰Ca⁺ ions stored in a 7-tesla open-ring Penning trap. By comparing the detected electric signal obtained with the BB amplifier and the fluorescence signal obtained by collecting the photons emitted by a trapped ion cloud, we show a detection limit below 110 ions. Adding the crystal, the electrical signal increases by a factor of about 30 at room temperature, which combined with the measured equivalent resistance and voltage noise, proves the feasibility of the system to reach single-ion sensitivity at 4 K.

Two-Loop Binding Corrections to the Electron Gyromagnetic Factor

We compute corrections to the gyromagnetic factor of an electron bound in a hydrogenlike ion at order α^{2}(Zα)^{5}. This result removes a major uncertainty in predictions for silicon and carbon ions, used to determine the atomic mass of the electron.

Recoil Effect on the g Factor of Li-Like Ions

The nuclear recoil effect on the g factor of Li-like ions is evaluated. The one-electron recoil contribution is treated within the framework of the rigorous QED approach to the first order in the electron-to-nucleus mass ratio m/M and to all orders in the parameter αZ. These calculations are performed in a range Z=3-92. The two-electron recoil term is calculated for low- and middle-Z ions within the Breit approximation using a four-component approach. The results for the two-electron recoil part obtained in the Letter strongly disagree with the previous calculations performed using an effective two-component Hamiltonian. The obtained value for the recoil effect is used to calculate the isotope shift of the g factor of Li-like ^{A}Ca^{17+} with A=40 and A=48 which was recently measured. It is found that the new theoretical value for the isotope shift is closer to the experimental one than the previously obtained value.

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.

Highly sensitive superconducting circuits at ∼700 kHz with tunable quality factors for image-current detection of single trapped antiprotons

We developed highly sensitive image-current detection systems based on superconducting toroidal coils and ultra-low noise amplifiers for non-destructive measurements of the axial frequencies (550-800 kHz) of single antiprotons stored in a cryogenic multi-Penning-trap system. The unloaded superconducting tuned circuits show quality factors of up to 500 000, which corresponds to a factor of 10 improvement compared to our previously used solenoidal designs. Connected to ultra-low noise amplifiers and the trap system, signal-to-noise-ratios of 30 dB at quality factors of >20 000 are achieved. In addition, we have developed a superconducting switch which allows continuous tuning of the detector's quality factor and to sensitively tune the particle-detector interaction. This allowed us to improve frequency resolution at constant averaging time, which is crucial for single antiproton spin-transition spectroscopy experiments, as well as improved measurements of the proton-to-antiproton charge-to-mass ratio.

g Factor of Light Ions for an Improved Determination of the Fine-Structure Constant

A weighted difference of the g factors of the H- and Li-like ions of the same element is theoretically studied and optimized in order to maximize the cancellation of nuclear effects between the two charge states. We show that this weighted difference and its combination for two different elements can be used to extract a value for the fine-structure constant from near-future bound-electron g factor experiments with an accuracy competitive with or better than the present literature value.

Isotope dependence of the Zeeman effect in lithium-like calcium

The magnetic moment μ of a bound electron, generally expressed by the g-factor μ=−g μ_Bs ħ⁻¹ with μ_B the Bohr magneton and s the electron's spin, can be calculated by bound-state quantum electrodynamics (BS-QED) to very high precision. The recent ultra-precise experiment on hydrogen-like silicon determined this value to eleven significant digits, and thus allowed to rigorously probe the validity of BS-QED. Yet, the investigation of one of the most interesting contribution to the g-factor, the relativistic interaction between electron and nucleus, is limited by our knowledge of BS-QED effects. By comparing the g-factors of two isotopes, it is possible to cancel most of these contributions and sensitively probe nuclear effects. Here, we present calculations and experiments on the isotope dependence of the Zeeman effect in lithium-like calcium ions. The good agreement between the theoretical predicted recoil contribution and the high-precision g-factor measurements paves the way for a new generation of BS-QED tests.

In addition to hyperfine splitting effects, isotope shifts of atomic electronic energy levels allow the investigation nuclear properties. Here, the authors study the isotope dependence of the Zeeman effect in litihium-like calcium isotopes in a Penning-trap setup and find good agreement with QED calculations.

Deceleration, precooling, and multi-pass stopping of highly charged ions in Be⁺ Coulomb crystals

Preparing highly charged ions (HCIs) in a cold and strongly localized state is of particular interest for frequency metrology and tests of possible spatial and temporal variations of the fine structure constant. Our versatile preparation technique is based on the generic modular combination of a pulsed ion source with a cryogenic linear Paul trap. Both instruments are connected by a compact beamline with deceleration and precooling properties. We present its design and commissioning experiments regarding these two functionalities. A pulsed buncher tube allows for the deceleration and longitudinal phase-space compression of the ion pulses. External injection of slow HCIs, specifically Ar(13+), into the linear Paul trap and their subsequent retrapping in the absence of sympathetic cooling is demonstrated. The latter proved to be a necessary prerequisite for the multi-pass stopping of HCIs in continuously laser-cooled Be(+) Coulomb crystals.

Precision Test of Many-Body QED in the Be+ 2p Fine Structure Doublet Using Short-Lived Isotopes

Absolute transition frequencies of the 2s 2S{1/2}→2p2P{1/2,3/2} transitions in Be^{+} were measured for the isotopes ^{7,9-12}Be. The fine structure splitting of the 2p state and its isotope dependence are extracted and compared to results of ab initio calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of mα(6) and mα(7) ⁢ln α. Accuracy has been improved in both the theory and experiment by 2 orders of magnitude, and good agreement is observed. This represents one of the most accurate tests of quantum electrodynamics for many-electron systems, being insensitive to nuclear uncertainties.

Many-electron QED corrections to the g factor of lithiumlike ions

A rigorous QED evaluation of the two-photon exchange corrections to the g factor of lithiumlike ions is presented. The screened self-energy corrections are calculated for the intermediate-Z region, and its accuracy for the high-Z region is essentially improved in comparison with that of previous calculations. As a result, the theoretical accuracy of the g factor of lithiumlike ions is significantly increased. The theoretical prediction obtained for the g factor of (28)Si(11+) g(th) = 2.000 889 892(8) is in an excellent agreement with the corresponding experimental value g(exp) = 2.000 889 889 9(21) [A. Wagner et al., Phys. Rev. Lett. 110, 033003 (2013).