Cyclotron frequency shifts arising from polarization forces

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.

Effects of an Oscillating Electric Field on and Dipole Moment Measurement of a Single Molecular Ion

We characterize and model the Stark effect due to the radio-frequency (rf) electric field experienced by a molecular ion in an rf Paul trap, a leading systematic in the uncertainty of the field-free rotational transition. The ion is deliberately displaced to sample different known rf electric fields and measure the resultant shifts in transition frequencies. With this method, we determine the permanent electric dipole moment of CaH^{+}, and find close agreement with theory. The characterization is performed by using a frequency comb which probes rotational transitions in the molecular ion. With improved coherence of the comb laser, a fractional statistical uncertainty for a transition line center of as low as 4.6×10^{-13} was achieved.

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 precision^2-5. 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 precision^7,8, 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 (WEP_cc) for antimatter to less than 1.8 × 10^-7, and enables the first differential test of the WEP_cc using antiprotons¹¹. From this interpretation we constrain the differential WEP_cc-violating coefficient to less than 0.030.

Penning trap mass measurements of the deuteron and the HD+ molecular ion

The masses of the lightest atomic nuclei and the electron mass¹ are interlinked, and their values affect observables in atomic², molecular^3-5 and neutrino physics⁶, as well as metrology. The most precise values for these fundamental parameters come from Penning trap mass spectrometry, which achieves relative mass uncertainties of the order of 10^-11. However, redundancy checks using data from different experiments reveal considerable inconsistencies in the masses of the proton, the deuteron and the helion (the nucleus of helium-3), suggesting that the uncertainty of these values may have been underestimated. Here we present results from absolute mass measurements of the deuteron and the HD⁺ molecular ion using ¹²C as a mass reference. Our value for the deuteron mass, 2.013553212535(17) atomic mass units, has better precision than the CODATA value⁷ by a factor of 2.4 and differs from it by 4.8 standard deviations. With a relative uncertainty of eight parts per trillion, this is the most precise mass value measured directly in atomic mass units. Furthermore, our measurement of the mass of the HD⁺ molecular ion, 3.021378241561(61) atomic mass units, not only allows a rigorous consistency check of our results for the masses of the deuteron (this work) and the proton⁸, but also establishes an additional link for the masses of tritium⁹ and helium-3 (ref. ¹⁰) to the atomic mass unit. Combined with a recent measurement of the deuteron-to-proton mass ratio¹¹, the uncertainty of the reference value of the proton mass⁷ can be reduced by a factor of three.

High-Precision Atomic Mass Measurements for Fundamental Constants

Atomic mass measurements are essential for obtaining several of the fundamental constants. The most precise atomic mass measurements, at the 10−10 level of precision or better, employ measurements of cyclotron frequencies of single ions in Penning traps. We discuss the relation of atomic masses to fundamental constants in the context of the revised SI. We then review experimental methods, and the current status of measurements of the masses of the electron, proton, neutron, deuteron, tritium, helium-3, helium-4, oxygen-16, silicon-28, rubidium-87, and cesium-133. We conclude with directions for future work.

Rotational Energy as Mass in H_{3}^{+} and Lower Limits on the Atomic Masses of D and ^{3}He

We have made precise measurements of the cyclotron frequency ratios H_{3}^{+}/HD^{+} and H_{3}^{+}/^{3}He^{+} and observe that different H_{3}^{+} ions result in different cyclotron frequency ratios. We interpret these differences as due to the molecular rotational energy of H_{3}^{+} changing its inertial mass. We also confirm that certain high J, K rotational levels of H_{3}^{+} have mean lifetimes exceeding several weeks. From measurements with the lightest H_{3}^{+} ion we obtain lower limits on the atomic masses of deuterium and helium-3 with respect to the proton.

Recent progress of laser spectroscopy experiments on antiprotonic helium

The Atomic Spectroscopy and Collisions Using Slow Antiprotons (ASACUSA) collaboration is currently carrying out laser spectroscopy experiments on antiprotonic helium [Formula: see text] atoms at CERN's Antiproton Decelerator facility. Two-photon spectroscopic techniques have been employed to reduce the Doppler width of the measured [Formula: see text] resonance lines, and determine the atomic transition frequencies to a fractional precision of 2.3-5 parts in 109 More recently, single-photon spectroscopy of buffer-gas cooled [Formula: see text] has reached a similar precision. By comparing the results with three-body quantum electrodynamics calculations, the antiproton-to-electron mass ratio was determined as [Formula: see text], which agrees with the known proton-to-electron mass ratio with a precision of 8×10-10 The high-quality antiproton beam provided by the future Extra Low Energy Antiproton Ring (ELENA) facility should enable further improvements in the experimental precision.This article is part of the Theo Murphy meeting issue 'Antiproton physics in the ELENA era'.

Precision laser spectroscopy experiments on antiprotonic helium

At CERN‘s Antiproton Decelerator (AD) facility, the Atomic Spectroscopyand Collisions Using Slow Antiprotons (ASACUSA) collaboration is carrying out precise laser spectroscopy experiments on antiprotonic helium (p̅He+ ≡ p̅+He2++e−) atoms. By employing buffer-gas cooling techniquesin a cryogenic gas target, samples of atoms were cooled to temperatureT = 1.5–1.7 K, thereby reducing the Doppler width in the single-photon resonance lines. By comparing the results with three-body quantum electrodynamics calculations, the antiproton-to-electron mass ratio was determined as Mp̅/me = 1836.1526734(15). This agreed with the known proton-to-electron mass ratio with a precision of 8 . 1010. Further improvements in the experimental precision are currently being attempted. The high-quality antiproton beam provided by the future Extra Low Energy Antiproton Ring (ELENA) facility should further increase the experimental precision.

Buffer-gas cooling of antiprotonic helium to 1.5 to 1.7 K, and antiproton-to-electron mass ratio

Charge, parity, and time reversal (CPT) symmetry implies that a particle and its antiparticle have the same mass. The antiproton-to-electron mass ratio [Formula: see text] can be precisely determined from the single-photon transition frequencies of antiprotonic helium. We measured 13 such frequencies with laser spectroscopy to a fractional precision of 2.5 × 10^-9 to 16 × 10^-9 About 2 × 10⁹ antiprotonic helium atoms were cooled to temperatures between 1.5 and 1.7 kelvin by using buffer-gas cooling in cryogenic low-pressure helium gas; the narrow thermal distribution led to the observation of sharp spectral lines of small thermal Doppler width. The deviation between the experimental frequencies and the results of three-body quantum electrodynamics calculations was reduced by a factor of 1.4 to 10 compared with previous single-photon experiments. From this, [Formula: see text] was determined as 1836.1526734(15), which agrees with a recent proton-to-electron experimental value within 8 × 10^-10.

Photodissociation of an Internally Cold Beam of CH^{+} Ions in a Cryogenic Storage Ring

We have studied the photodissociation of CH^{+} in the Cryogenic Storage Ring at ambient temperatures below 10 K. Owing to the extremely high vacuum of the cryogenic environment, we were able to store CH^{+} beams with a kinetic energy of ∼60  keV for several minutes. Using a pulsed laser, we observed Feshbach-type near-threshold photodissociation resonances for the rotational levels J=0-2 of CH^{+}, exclusively. In comparison to updated, state-of-the-art calculations, we find excellent agreement in the relative intensities of the resonances for a given J, and we can extract time-dependent level populations. Thus, we can monitor the spontaneous relaxation of CH^{+} to its lowest rotational states and demonstrate the preparation of an internally cold beam of molecular ions.

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).

Precision spectroscopy of polarized molecules in an ion trap

Polar molecules are desirable systems for quantum simulations and cold chemistry. Molecular ions are easily trapped, but a bias electric field applied to polarize them tends to accelerate them out of the trap. We present a general solution to this issue by rotating the bias field slowly enough for the molecular polarization axis to follow but rapidly enough for the ions to stay trapped. We demonstrate Ramsey spectroscopy between Stark-Zeeman sublevels in (180)Hf(19)F(+) with a coherence time of 100 milliseconds. Frequency shifts arising from well-controlled topological (Berry) phases are used to determine magnetic g factors. The rotating-bias-field technique may enable using trapped polar molecules for precision measurement and quantum information science, including the search for an electron electric dipole moment.

Accurate high-N rest frequencies for CO+, an ideal tracer of photon-dominated regions

The submillimeter-wave rotational spectra of CO(+), (13)CO(+) and C(18)O(+) in the v = 0 and 1 vibrational states were measured through a hollow cathode dc discharge in a cryogenic cell cooled to liquid nitrogen temperature. In addition, a few transitions of the main isotopic species have been measured between 1.1 and 1.3 THz. An updated isotopically invariant fit, including Born-Oppenheimer breakdown corrections, is presented: the derived set of independent molecular parameters, valid for all the isotopologues of the molecule included in the fit, allows to predict the rotational spectrum with calculated 1σ uncertainty of 280 kHz at 2 THz.

Two-photon laser spectroscopy of antiprotonic helium and the antiproton-to-electron mass ratio

Physical laws are believed to be invariant under the combined transformations of charge, parity and time reversal (CPT symmetry). This implies that an antimatter particle has exactly the same mass and absolute value of charge as its particle counterpart. Metastable antiprotonic helium (pHe(+)) is a three-body atom consisting of a normal helium nucleus, an electron in its ground state and an antiproton (p) occupying a Rydberg state with high principal and angular momentum quantum numbers, respectively n and l, such that n ≈ l + 1 ≈ 38. These atoms are amenable to precision laser spectroscopy, the results of which can in principle be used to determine the antiproton-to-electron mass ratio and to constrain the equality between the antiproton and proton charges and masses. Here we report two-photon spectroscopy of antiprotonic helium, in which p(3)He(+) and p(4)He(+) isotopes are irradiated by two counter-propagating laser beams. This excites nonlinear, two-photon transitions of the antiproton of the type (n, l) → (n - 2, l - 2) at deep-ultraviolet wavelengths (λ = 139.8, 193.0 and 197.0 nm), which partly cancel the Doppler broadening of the laser resonance caused by the thermal motion of the atoms. The resulting narrow spectral lines allowed us to measure three transition frequencies with fractional precisions of 2.3-5 parts in 10(9). By comparing the results with three-body quantum electrodynamics calculations, we derived an antiproton-to-electron mass ratio of 1,836.1526736(23), where the parenthetical error represents one standard deviation. This agrees with the proton-to-electron value known to a similar precision.

Why is sideband mass spectrometry possible with ions in a Penning trap?

Many masses, particularly the masses of unstable nuclei, are measured with ions in Penning traps by determining the frequency of a driving force that most efficiently couples two of the three motions of trapped ions. A missing explanation of why such sideband mass spectroscopy works, contrary to simple estimates, begins with the established Brown-Gabrielse invariance theorem.

Dipole moment of PH+ and the atomic masses of 28Si, 31P by comparing cyclotron frequencies of two ions simultaneously trapped in a penning trap

By trapping pairs of ions in a Penning trap, alternating each ion between large and small cyclotron orbits, we have measured the cyclotron frequency ratios 12C2H4+/28Si+, 13C2H2+/28Si+, 28SiH3+/31P+, and 16O2+/31PH+, all to <30 ppt precision. The 16O2+/31PH+ data exhibit a bimodal distribution due to the polarizability of the Lambda-doubling components of the PH+ ground state, from which we obtain the electric dipole moment of 31PH+, 0.331(8) ea0. Combined with other atomic mass measurements we also obtain improved values for m(28Si), 27.976 926 535 0(6) u, and m(31P), 30.973 761 998 9(9) u.

A direct test of E=mc2

One of the most striking predictions of Einstein's special theory of relativity is also perhaps the best known formula in all of science: E=mc(2). If this equation were found to be even slightly incorrect, the impact would be enormous--given the degree to which special relativity is woven into the theoretical fabric of modern physics and into everyday applications such as global positioning systems. Here we test this mass-energy relationship directly by combining very accurate measurements of atomic-mass difference, Delta(m), and of gamma-ray wavelengths to determine E, the nuclear binding energy, for isotopes of silicon and sulphur. Einstein's relationship is separately confirmed in two tests, which yield a combined result of 1-Delta(mc2)/E=(-1.4+/-4.4)x10(-7), indicating that it holds to a level of at least 0.00004%. To our knowledge, this is the most precise direct test of the famous equation yet described.