Measurement of the 1s-2s energy interval in muonium

Searching for Ultralight Scalar Dark Matter with Muonium and Muonic Atoms

Ultralight scalar dark matter may induce apparent oscillations of the muon mass, which may be directly probed via temporal shifts in the spectra of muonium and muonic atoms. Existing datasets and ongoing spectroscopy measurements with muonium are capable of probing scalar-muon interactions that are up to 12 orders of magnitude more stringent than astrophysical bounds. Ongoing free-fall experiments with muonium can probe forces associated with the exchange of virtual ultralight scalar bosons between muons and standard-model particles, offering up to 5 orders of magnitude improvement in sensitivity over complementary laboratory and astrophysical bounds.

Update of Muonium 1S-2S transition frequency

Abstract

We present an updated value of the Muonium 1S-2S transition frequency, highlighting contributions from different QED corrections as well as the large uncertainty in the Dirac contribution, stemming from the uncertainty of the electron to muon mass ratio. Improving the measurement of this spectral line would allow to extract a more accurate determination of fundamental constants, such as the electron to muon mass ratio or, combined with the Muonium hyperfine splitting, an independent value of the Rydberg constant. Furthermore, we report on the current status of the Mu-MASS experiment, which aims at measuring the Muonium 1S-2S transition frequency at a 10 kHz uncertainty level.

Graphic abstract

Measurement of the transition frequency from 2S1/2, F = 0 to 2P1/2, F = 1 states in Muonium

Muons are puzzling physicists since their discovery when they were first thought to be the meson predicted by Yukawa to mediate the strong force. The recent result at Fermilab on the muon g-2 anomaly puts the muonic sector once more under the spotlight and calls for further measurements with this particle. Here, we present the results of the measurement of the 2S_1/2, F = 0 → 2P_1/2, F = 1 transition in Muonium. The measured value of 580.6(6.8) MHz is in agreement with the theoretical calculations. A value of the Lamb shift of 1045.5(6.8) MHz is extracted, compatible with previous experiments. We also determine the 2S hyperfine splitting in Muonium to be 559.6(7.2) MHz. The measured transition being isolated from the other hyperfine levels holds the promise to provide an improved determination of the Muonium Lamb shift at a level where bound state QED recoil corrections not accessible in hydrogen could be tested. This result would be sensitive to new physics in the muonic sector, e.g., to new bosons which might provide an explanation of the g-2 muon anomaly and allow to test Lorentz and CPT violation. We also present the observation of Muonium in the n = 3 excited state opening up the possibility of additional precise microwave measurements.

Precision Measurement of the Lamb Shift in Muonium

We report a new measurement of the n=2 Lamb shift in Muonium. Our result of 1047.2(2.3)_{stat}(1.1)_{syst}  MHz comprises an order of magnitude improvement upon the previous best measurement. This value matches the theoretical calculation within 1 standard deviation allowing us to set limits on Lorentz and CPT violation in the muonic sector, as well as on new physics coupled to muons and electrons which could provide an explanation of the muon g-2 anomaly.

Towards an Independent Determination of Muon g-2 from Muonium Spectroscopy

We show that muonium spectroscopy in the coming years can reach a precision high enough to determine the anomalous magnetic moment of the muon below one part per million (ppm). Such an independent determination of muon g-2 would certainly shed light on the ∼2  ppm difference currently observed between spin-precession measurements and (R-ratio based) standard model predictions. The magnetic dipole interaction between electrons and (anti)muons bound in muonium gives rise to a hyperfine splitting (HFS) of the ground state which is sensitive to the muon anomalous magnetic moment. A direct comparison of the muonium frequency measurements of the HFS at J-PARC and the 1S-2S transition at PSI with theory predictions will allow us to extract muon g-2 with high precision. Improving the accuracy of QED calculations of these transitions by about 1 order of magnitude is also required. Moreover, the good agreement between theory and experiment for the electron g-2 indicates that new physics interactions are unlikely to affect muonium spectroscopy down to the envisaged precision.

Intense beam of metastable Muonium

Precision spectroscopy of the Muonium Lamb shift and fine structure requires a robust source of 2S Muonium. To date, the beam-foil technique is the only demonstrated method for creating such a beam in vacuum. Previous experiments using this technique were statistics limited, and new measurements would benefit tremendously from the efficient 2S production at a low energy muon ( < 20  keV) facility. Such a source of abundant low energyμ + has only become available in recent years, e.g. at the Low-Energy Muon beamline at the Paul Scherrer Institute. Using this source, we report on the successful creation of an intense, directed beam of metastable Muonium. We find that even though the theoretical Muonium fraction is maximal in the low energy range of 2-5 keV, scattering by the foil and transport characteristics of the beamline favor slightly higherμ + energies of 7-10 keV. We estimate that an event detection rate of a few events per second for a future Lamb shift measurement is feasible, enabling an increase in precision by two orders of magnitude over previous determinations.

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.

Use of a Continuous Wave Laser and Pockels Cell for Sensitive High-Resolution Collinear Resonance Ionization Spectroscopy

New technical developments have led to a 2 orders of magnitude improvement of the resolution of the collinear resonance ionization spectroscopy (CRIS) experiment at ISOLDE, CERN, without sacrificing the high efficiency of the CRIS technique. Experimental linewidths of 20(1) MHz were obtained on radioactive beams of francium, allowing us for the first time to determine the electric quadrupole moment of the short lived [t_{1/2}=22.0(5) ms] ^{219}Fr Q_{s}=-1.21(2) eb, which would not have been possible without the advantages offered by the new method. This method relies on a continuous-wave laser and an external Pockels cell to produce narrow-band light pulses, required to reach the high resolution in two-step resonance ionization. Exotic nuclei produced at rates of a few hundred ions/s can now be studied with high resolution, allowing detailed studies of the anchor points for nuclear theories.

An experimental limit on the charge of antihydrogen

The properties of antihydrogen are expected to be identical to those of hydrogen, and any differences would constitute a profound challenge to the fundamental theories of physics. The most commonly discussed antiatom-based tests of these theories are searches for antihydrogen-hydrogen spectral differences (tests of CPT (charge-parity-time) invariance) or gravitational differences (tests of the weak equivalence principle). Here we, the ALPHA Collaboration, report a different and somewhat unusual test of CPT and of quantum anomaly cancellation. A retrospective analysis of the influence of electric fields on antihydrogen atoms released from the ALPHA trap finds a mean axial deflection of 4.1 ± 3.4 mm for an average axial electric field of 0.51 V mm(-1). Combined with extensive numerical modelling, this measurement leads to a bound on the charge Qe of antihydrogen of Q=(-1.3 ± 1.1 ± 0.4) × 10(-8). Here, e is the unit charge, and the errors are from statistics and systematic effects.

High-precision spectroscopy with counterpropagating femtosecond pulses

An experimental realization of high-precision direct frequency comb spectroscopy using counterpropagating femtosecond pulses on two-photon atomic transitions is presented. The Doppler broadened background signal, hampering precision spectroscopy with ultrashort pulses, is effectively eliminated with a simple pulse shaping method. As a result, all four 5S-7S two-photon transitions in a rubidium vapor are determined with both statistical and systematic uncertainties below 10(-11), which is an order of magnitude better than previous experiments on these transitions.

Muonium emission into vacuum from mesoporous thin films at cryogenic temperatures

We report on muonium (Mu) emission into vacuum following μ(+) implantation in mesoporous thin SiO(2) films. We obtain a yield of Mu into vacuum of (38±4)% at 250 K and (20±4)% at 100 K for 5 keV μ(+) implantation energy. From the implantation energy dependence of the Mu vacuum yield we determine the Mu diffusion constants in these films: D(Mu)(250 K)=(1.6±0.1)×10(-4)  cm(2)/s and D(Mu)(100 K)=(4.2±0.5)×10(-5) cm(2)/s. Describing the diffusion process as quantum mechanical tunneling from pore to pore, we reproduce the measured temperature dependence ∼T(3/2) of the diffusion constant. We extract a potential barrier of (-0.3±0.1) eV which is consistent with our computed Mu work function in SiO(2) of [-0.3,-0.9] eV. The high Mu vacuum yield, even at low temperatures, represents an important step toward next generation Mu spectroscopy experiments.

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.

Chirp-corrected, nanosecond Ti:sapphire laser with 6 MHz linewidth for spectroscopy of antiprotonic helium

A nanosecond titanium sapphire laser with spectral linewidth Gamma(pl)~6 MHz and pulse energy of 50-100 mJ was demonstrated by using an intracavity electro-optic modulator to correct the frequency chirp in the output beam. The laser was referenced against a femtosecond frequency comb and used to measure the 6s-8s (F=4) two-photon transition frequency of Cs with a precision of 1.4 parts in 10(9).

Determination of the antiproton-to-electron mass ratio by precision laser spectroscopy of pHe+

A femtosecond optical frequency comb and continuous-wave pulse-amplified laser were used to measure 12 transition frequencies of antiprotonic helium to fractional precisions of (9-16)x10(-9). One of these is between two states having microsecond-scale lifetimes hitherto unaccessible to our precision laser spectroscopy method. Comparisons with three-body QED calculations yielded an antiproton-to-electron mass ratio of Mp/me=1836.152674(5).

Relativistic linear response wave functions and dynamic scattering tensor for the ns1/2 states in hydrogenlike atoms

We report a novel closed-form analytic representation for the linear response relativistic wave function of the hydrogenic ns(1/2) level that is exposed to dipole radiation of frequency omega. This result is derived by means of a direct analytical solution of the inhomogeneous omega-dependent Dirac equation. The utility of the formulas obtained is demonstrated by new analytic and numerical calculations of the static and dynamic relativistic dynamic polarizabilities of the lowest hydrogenic ns(1/2) states.