Direct measurement of the 3He+ magnetic moments.

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics1-3, nuclear and atomic structure4,5, magnetometry and metrology6, as well as chemistry and medicine7,8. In particular, 3He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry6,9. This requires a high-accuracy value for the 3He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon10,11. Here we investigate the 3He+ ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of 3He+ [Formula: see text], the zero-field hyperfine splitting [Formula: see text] Hz and the bound electron g-factor [Formula: see text]. The latter is consistent with our theoretical value [Formula: see text] based on parameters and fundamental constants from ref. 12. Our measured value for the 3He+ nuclear g-factor enables determination of the g-factor of the bare nucleus [Formula: see text] via our accurate calculation of the diamagnetic shielding constant13 [Formula: see text]. This constitutes a direct calibration for 3He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value14 and enables us to determine the Zemach radius15 to [Formula: see text] fm.

A 16-parts-per-trillion measurement of the antiproton-to-proton charge-mass ratio.

The standard model of particle physics is both incredibly successful and glaringly incomplete. Among the questions left open is the striking imbalance of matter and antimatter in the observable universe1, which inspires experiments to compare the fundamental properties of matter/antimatter conjugates with high precision2-5. Our experiments deal with direct investigations of the fundamental properties of protons and antiprotons, performing spectroscopy in advanced cryogenic Penning trap systems6. For instance, we previously compared the proton/antiproton magnetic moments with 1.5 parts per billion fractional precision7,8, which improved upon previous best measurements9 by a factor of greater than 3,000. Here we report on a new comparison of the proton/antiproton charge-to-mass ratios with a fractional uncertainty of 16 parts per trillion. Our result is based on the combination of four independent long-term studies, recorded in a total time span of 1.5 years. We use different measurement methods and experimental set-ups incorporating different systematic effects. The final result, [Formula: see text], is consistent with the fundamental charge-parity-time reversal invariance, and improves the precision of our previous best measurement6 by a factor of 4.3. The measurement tests the standard model at an energy scale of 1.96 × 10-27 gigaelectronvolts (confidence level 0.68), and improves ten coefficients of the standard model extension10. Our cyclotron clock study also constrains hypothetical interactions mediating violations of the clock weak equivalence principle (WEPcc) for antimatter to less than 1.8 × 10-7, and enables the first differential test of the WEPcc using antiprotons11. From this interpretation we constrain the differential WEPcc-violating coefficient to less than 0.030.

Sympathetic cooling of a trapped proton mediated by an LC circuit.

Efficient cooling of trapped charged particles is essential to many fundamental physics experiments1,2, to high-precision metrology3,4 and to quantum technology5,6. Until now, sympathetic cooling has required close-range Coulomb interactions7,8, but there has been a sustained desire to bring laser-cooling techniques to particles in macroscopically separated traps5,9,10, extending quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions and antimatter. Here we demonstrate sympathetic cooling of a single proton using laser-cooled Be+ ions in spatially separated Penning traps. The traps are connected by a superconducting LC circuit that enables energy exchange over a distance of 9 cm. We also demonstrate the cooling of a resonant mode of a macroscopic LC circuit with laser-cooled ions and sympathetic cooling of an individually trapped proton, reaching temperatures far below the environmental temperature. Notably, as this technique uses only image-current interactions, it can be easily applied to an experiment with antiprotons1, facilitating improved precision in matter-antimatter comparisons11 and dark matter searches12,13.

Direct limits on the interaction of antiprotons with axion-like dark matter.

Astrophysical observations indicate that there is roughly five times more dark matter in the Universe than ordinary baryonic matter1, and an even larger amount of the Universe's energy content is attributed to dark energy2. However, the microscopic properties of these dark components remain unknown. Moreover, even ordinary matter-which accounts for five per cent of the energy density of the Universe-has yet to be understood, given that the standard model of particle physics lacks any consistent explanation for the predominance of matter over antimatter3. Here we present a direct search for interactions of antimatter with dark matter and place direct constraints on the interaction of ultralight axion-like particles (dark-matter candidates) with antiprotons. If antiprotons have a stronger coupling to these particles than protons do, such a matter-antimatter asymmetric coupling could provide a link between dark matter and the baryon asymmetry in the Universe. We analyse spin-flip resonance data in the frequency domain acquired with a single antiproton in a Penning trap4 to search for spin-precession effects from ultralight axions, which have a characteristic frequency governed by the mass of the underlying particle. Our analysis constrains the axion-antiproton interaction parameter to values greater than 0.1 to 0.6 gigaelectronvolts in the mass range from 2 × 10-23 to 4 × 10-17 electronvolts, improving the sensitivity by up to five orders of magnitude compared with astrophysical antiproton bounds. In addition, we derive limits on six combinations of previously unconstrained Lorentz- and CPT-violating terms of the non-minimal standard model extension5.

Orders of Magnitude Improved Cyclotron-Mode Cooling for Nondestructive Spin Quantum Transition Spectroscopy with Single Trapped Antiprotons.

We demonstrate efficient subthermal cooling of the modified cyclotron mode of a single trapped antiproton and reach particle temperatures T_{+}=E_{+}/k_{B} below 200 mK in preparation times shorter than 500 s. This corresponds to the fastest resistive single-particle cyclotron cooling to subthermal temperatures ever demonstrated. By cooling trapped particles to such low energies, we demonstrate the detection of antiproton spin transitions with an error rate <0.000 023, more than 3 orders of magnitude better than in previous best experiments. This method has enormous impact on multi-Penning-trap experiments that measure magnetic moments with single nuclear spins for tests of matter and antimatter symmetry, high-precision mass spectrometry, and measurements of electron g factors bound to highly charged ions that test quantum electrodynamics and establish standards for magnetometry.

Image-Current Mediated Sympathetic Laser Cooling of a Single Proton in a Penning Trap Down to 170 mK Axial Temperature.

We demonstrate a new temperature record for image-current mediated sympathetic cooling of a single proton in a cryogenic Penning trap by laser-cooled ^{9}Be^{+}. An axial mode temperature of 170 mK is reached, which is a 15-fold improvement compared to the previous best value. Our cooling technique is applicable to any charged particle, so that the measurements presented here constitute a milestone toward the next generation of high-precision Penning-trap measurements with exotic particles.

A parts-per-billion measurement of the antiproton magnetic moment.

Precise comparisons of the fundamental properties of matter-antimatter conjugates provide sensitive tests of charge-parity-time (CPT) invariance, which is an important symmetry that rests on basic assumptions of the standard model of particle physics. Experiments on mesons, leptons and baryons have compared different properties of matter-antimatter conjugates with fractional uncertainties at the parts-per-billion level or better. One specific quantity, however, has so far only been known to a fractional uncertainty at the parts-per-million level: the magnetic moment of the antiproton, . The extraordinary difficulty in measuring with high precision is caused by its intrinsic smallness; for example, it is 660 times smaller than the magnetic moment of the positron. Here we report a high-precision measurement of in units of the nuclear magneton µN with a fractional precision of 1.5 parts per billion (68% confidence level). We use a two-particle spectroscopy method in an advanced cryogenic multi-Penning trap system. Our result = -2.7928473441(42)µN (where the number in parentheses represents the 68% confidence interval on the last digits of the value) improves the precision of the previous best measurement by a factor of approximately 350. The measured value is consistent with the proton magnetic moment, µp = 2.792847350(9)µN, and is in agreement with CPT invariance. Consequently, this measurement constrains the magnitude of certain CPT-violating effects to below 1.8 × 10-24 gigaelectronvolts, and a possible splitting of the proton-antiproton magnetic moments by CPT-odd dimension-five interactions to below 6 × 10-12 Bohr magnetons.

High-precision comparison of the antiproton-to-proton charge-to-mass ratio.

Invariance under the charge, parity, time-reversal (CPT) transformation is one of the fundamental symmetries of the standard model of particle physics. This CPT invariance implies that the fundamental properties of antiparticles and their matter-conjugates are identical, apart from signs. There is a deep link between CPT invariance and Lorentz symmetry--that is, the laws of nature seem to be invariant under the symmetry transformation of spacetime--although it is model dependent. A number of high-precision CPT and Lorentz invariance tests--using a co-magnetometer, a torsion pendulum and a maser, among others--have been performed, but only a few direct high-precision CPT tests that compare the fundamental properties of matter and antimatter are available. Here we report high-precision cyclotron frequency comparisons of a single antiproton and a negatively charged hydrogen ion (H(-)) carried out in a Penning trap system. From 13,000 frequency measurements we compare the charge-to-mass ratio for the antiproton (q/m)p- to that for the proton (q/m)p and obtain (q/m)p-/(q/m)p − 1 =1(69) × 10(-12). The measurements were performed at cyclotron frequencies of 29.6 megahertz, so our result shows that the CPT theorem holds at the atto-electronvolt scale. Our precision of 69 parts per trillion exceeds the energy resolution of previous antiproton-to-proton mass comparisons as well as the respective figure of merit of the standard model extension by a factor of four. In addition, we give a limit on sidereal variations in the measured ratio of <720 parts per trillion. By following the arguments of ref. 11, our result can be interpreted as a stringent test of the weak equivalence principle of general relativity using baryonic antimatter, and it sets a new limit on the gravitational anomaly parameter of |α − 1| < 8.7 × 10(-7).

Direct high-precision measurement of the magnetic moment of the proton.

One of the fundamental properties of the proton is its magnetic moment, µp. So far µp has been measured only indirectly, by analysing the spectrum of an atomic hydrogen maser in a magnetic field. Here we report the direct high-precision measurement of the magnetic moment of a single proton using the double Penning-trap technique. We drive proton-spin quantum jumps by a magnetic radio-frequency field in a Penning trap with a homogeneous magnetic field. The induced spin transitions are detected in a second trap with a strong superimposed magnetic inhomogeneity. This enables the measurement of the spin-flip probability as a function of the drive frequency. In each measurement the proton's cyclotron frequency is used to determine the magnetic field of the trap. From the normalized resonance curve, we extract the particle's magnetic moment in terms of the nuclear magneton: µp = 2.792847350(9)µN. This measurement outperforms previous Penning-trap measurements in terms of precision by a factor of about 760. It improves the precision of the forty-year-old indirect measurement, in which significant theoretical bound state corrections were required to obtain µp, by a factor of 3. By application of this method to the antiproton magnetic moment, the fractional precision of the recently reported value can be improved by a factor of at least 1,000. Combined with the present result, this will provide a stringent test of matter/antimatter symmetry with baryons.

Measurement of Ultralow Heating Rates of a Single Antiproton in a Cryogenic Penning Trap.

We report on the first detailed study of motional heating in a cryogenic Penning trap using a single antiproton. Employing the continuous Stern-Gerlach effect we observe cyclotron quantum transition rates of 6(1) quanta/h and an electric-field noise spectral density below 7.5(3.4)×10^{-20} V^{2} m^{-2} Hz^{-1}, which corresponds to a scaled noise spectral density below 8.8(4.0)×10^{-12} V^{2} m^{-2}, results which are more than 2 orders of magnitude smaller than those reported by other ion-trap experiments.

Challenging the standard model by high-precision comparisons of the fundamental properties of protons and antiprotons.

The BASE collaboration investigates the fundamental properties of protons and antiprotons, such as charge-to-mass ratios and magnetic moments, using advanced cryogenic Penning trap systems. In recent years, we performed the most precise measurement of the magnetic moments of both the proton and the antiproton, and conducted the most precise comparison of the proton-to-antiproton charge-to-mass ratio. In addition, we have set the most stringent constraint on directly measured antiproton lifetime, based on a unique reservoir trap technique. Our matter/antimatter comparison experiments provide stringent tests of the fundamental charge-parity-time invariance, which is one of the fundamental symmetries of the standard model of particle physics. This article reviews the recent achievements of BASE and gives an outlook to our physics programme in the ELENA era.This article is part of the Theo Murphy meeting issue 'Antiproton physics in the ELENA era'.

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.

Resolution of single spin flips of a single proton.

The spin magnetic moment of a single proton in a cryogenic Penning trap was coupled to the particle's axial motion with a superimposed magnetic bottle. Jumps in the oscillation frequency indicate spin flips and were identified using a Bayesian analysis.

Ultra-thin polymer foil cryogenic window for antiproton deceleration and storage.

We present the design and characterization of a cryogenic window based on an ultra-thin aluminized biaxially oriented polyethylene terephthalate foil at T < 10 K, which can withstand a pressure difference larger than 1 bar at a leak rate <1×10-9 mbar l/s. Its thickness of ∼1.7 µm makes it transparent to various types of particles over a broad energy range. To optimize the transfer of 100 keV antiprotons through the window, we tested the degrading properties of different aluminum coated polymer foils of thicknesses between 900 and 2160 nm, concluding that 1760 nm foil decelerates antiprotons to an average energy of 5 keV. We have also explicitly studied the permeation as a function of coating thickness and temperature and have performed extensive thermal and mechanical endurance and stress tests. Our final design integrated into the experiment has an effective open surface consisting of seven holes with a diameter of 1 mm and will transmit up to 2.5% of the injected 100 keV antiproton beam delivered by the Antiproton Decelerator and Extra Low ENergy Antiproton ring facility of CERN.

BASE-STEP: A transportable antiproton reservoir for fundamental interaction studies.

Currently, the world's only source of low-energy antiprotons is the AD/ELENA facility located at CERN. To date, all precision measurements on single antiprotons have been conducted at this facility and provide stringent tests of fundamental interactions and their symmetries. However, magnetic field fluctuations from the facility operation limit the precision of upcoming measurements. To overcome this limitation, we have designed the transportable antiproton trap system BASE-STEP to relocate antiprotons to laboratories with a calm magnetic environment. We anticipate that the transportable antiproton trap will facilitate enhanced tests of charge, parity, and time-reversal invariance with antiprotons and provide new experimental possibilities of using transported antiprotons and other accelerator-produced exotic ions. We present here the technical design of the transportable trap system. This includes the transportable superconducting magnet, the cryogenic inlay consisting of the trap stack and detection systems, and the differential pumping section to suppress the residual gas flow into the cryogenic trap chamber.

BASE-high-precision comparisons of the fundamental properties of protons and antiprotons.

Abstract: The BASE collaboration at the antiproton decelerator/ELENA facility of CERN compares the fundamental properties of protons and antiprotons with ultra-high precision. Using advanced Penning trap systems, we have measured the proton and antiproton magnetic moments with fractional uncertainties of 300 parts in a trillion (p.p.t.) and 1.5 parts in a billion (p.p.b.), respectively. The combined measurements improve the resolution of the previous best test in that sector by more than a factor of 3000. Very recently, we have compared the antiproton/proton charge-to-mass ratios with a fractional precision of 16 p.p.t., which improved the previous best measurement by a factor of 4.3. These results allowed us also to perform a differential matter/antimatter clock comparison test to limits better than 3%. Our measurements enable us to set limits on 22 coefficients of CPT- and Lorentz-violating standard model extensions (SME) and to search for potentially asymmetric interactions between antimatter and dark matter. In this article, we review some of the recent achievements and outline recent progress towards a planned improved measurement of the antiproton magnetic moment with an at least tenfold improved fractional accuracy.

Trap-integrated fluorescence detection with silicon photomultipliers for sympathetic laser cooling in a cryogenic Penning trap.

We present a fluorescence-detection system for laser-cooled 9Be+ ions based on silicon photomultipliers (SiPMs) operated at 4 K and integrated into our cryogenic 1.9 T multi-Penning-trap system. Our approach enables fluorescence detection in a hermetically sealed cryogenic Penning-trap chamber with limited optical access, where state-of-the-art detection using a telescope and photomultipliers at room temperature would be extremely difficult. We characterize the properties of the SiPM in a cryocooler at 4 K, where we measure a dark count rate below 1 s-1 and a detection efficiency of 2.5(3)%. We further discuss the design of our cryogenic fluorescence-detection trap and analyze the performance of our detection system by fluorescence spectroscopy of 9Be+ ion clouds during several runs of our sympathetic laser-cooling experiment.

A high-Q superconducting toroidal medium frequency detection system with a capacitively adjustable frequency range >180 kHz.

We describe a newly developed polytetrafluoroethylene/copper capacitor driven by a cryogenic piezoelectric slip-stick stage and demonstrate with the chosen layout cryogenic capacitance tuning of ≈60 pF at ≈10 pF background capacitance. Connected to a highly sensitive superconducting toroidal LC circuit, we demonstrate tuning of the resonant frequency between 345 and 685 kHz, at quality factors Q > 100 000. Connected to a cryogenic ultra low noise amplifier, a frequency tuning range between 520 and 710 kHz is reached, while quality factors Q > 86 000 are achieved. This new device can be used as a versatile image current detector in high-precision Penning-trap experiments or as an LC-circuit-based haloscope detector to search for the conversion of axion-like dark matter to radio-frequency photons. This new development increases the sensitive detection bandwidth of our axion haloscope by a factor of ≈1000.

Direct measurement of the free cyclotron frequency of a single particle in a Penning trap.

A measurement scheme for the direct determination of the free cyclotron frequency ν(c) of a single particle stored in a Penning trap is described. The method is based on the dressed states of mode coupling. In this novel measurement scheme both radial modes of the single trapped particle are simultaneously coupled to the axial oscillation mode.

Observation of spin flips with a single trapped proton.

Radio-frequency induced spin transitions of one individual proton are observed. The spin quantum jumps are detected via the continuous Stern-Gerlach effect, which is used in an experiment with a single proton stored in a cryogenic Penning trap. This is an important milestone towards a direct high-precision measurement of the magnetic moment of the proton and a new test of the matter-antimatter symmetry in the baryon sector.