Synthesis of a high intensity, superthermal muonium beam for gravity and laser spectroscopy experiments

Abstract

The universality of free fall, a cornerstone of Einstein's theory of gravity, has so far only been tested with neutral composite states of first-generation Standard Model (SM) particles, such as atoms or neutrons, and, most recently, antihydrogen. Extending these gravitational measurements to other sectors of the SM requires the formation of neutral bound states using higher-generation, unstable particles. Muonium, the bound state of an antimuon ($μ^+$) and an electron ($e^-$), offers the possibility to probe gravity with second-generation (anti)leptons, in the absence of the strong interaction. However, the short $μ^+$ lifetime ($τ_μ\approx 2.2~μ$s) and the existing diffuse thermal muonium sources rendered such measurements unfeasible. Here, we report the synthesis of a high-brightness muonium beam, extracted from a thin layer of superfluid helium by exploiting its chemical potential and unique transport properties. The mean longitudinal velocity (${v}\approx 2180~\rm{m/s}$) and narrow distribution (${Δv}< 150 ~\rm{m/s}$) of the atoms characterise a superthermal beam, while yields are similar to the highest intensity diffuse sources. This new beam is expected to enable muonium interferometry and a percent-level measurement of its gravitational acceleration, providing the first direct test of the Weak Equivalence Principle with second-generation (anti)matter. Its unprecedented brightness also opens the way to sub-kHz 1S-2S spectroscopy, enabling precise determination of the muon mass and stringent tests of bound-state quantum electrodynamics.

Figures (9)

• Figure 1: Experimental principle and layout. (a) The superfluid helium (He II) chamber and dilution refrigerator. After traversing the entrance detector and several thin foils, the $\mu^+$ comes to rest in a thin horizontal He II layer. (b) Principle of Mu stopping and formation in He II, with the simulated $\mu^+$ stopping distribution (coloured gradient in background). The incoming $\mu^+$ comes to rest in an average $\approx 35~\mu$m depth, and captures an electron from the ionization trail. The formed Mu diffuses ballistically to the surface and is emitted perpendicularly with a velocity defined by the chemical potential. (c) Schematic of the positron tracking system to localize $\mu^+$ decays. The acceptance areas of selected detector coincidences are sketched, with red shaded areas outlying Layer 1 and Layer 4 coincidences on the left side (LC1$\land$LF1, LC4$\land$LF4), and blue denoting one of the coincidence conditions (RC1$\land$RF4) monitoring the target liquid.
• Figure 2: Time spectra in the four horizontal detector layers Lifetime compensated spectra with background subtraction, when (a) He II is filled, and (b) in an empty target. In (a), a forward shifting peak is observed in the consecutive detector layers, implying Mu propagation. A Gumbel test function was fit to obtain the center of each peak, used to determine the mean propagation velocity of the Mu atoms. The error bars are statistical uncertainties of the measured counts prior to lifetime correction, scaled by $e^{t/\tau_\mu}$.
• Figure 3: Comparison of measured and simulated time spectra. Examples of three measured time spectra (solid histograms) superimposed with simulated ones (coloured bands) with $\pm 1 \sigma$ statistical deviations. Lifetime- and background compensated histograms show the Mu decays sampled with (a) C1$\land$F1 (Layer 1) coincidences close to the surface, and (b) far from it, with C4$\land$F4 (Layer 4) coincidence conditions. The simulated superthermal beam (blue) fits both spectra well, while even the best-fitting thermal beam (yellow) visibly deviates. (c) Lifetime compensated decays originating from the target bottom (C1$\land$F4 coincidence conditions) when filled with He II (black) and empty (red), superimposed with the corresponding simulations showing the escape of Mu from He II.
• Figure 4: Beam characteristics of the superthermal beam and possible applications. (a) Velocity distribution of the Mu in vacuum, using the most pessimistic estimate ($\Delta v=150~$m/s) for the new superthermal source (red), thermal sources at room temperature (dark blue), and the coldest demonstrated (low intensity) source at 100 K (light blue). (b) Simulated intensity profile of the superthermal beam traversing the interferometer (grayscale gradient), with the schematic of the optimised grating positions. A zoom into G3 (right) shows the interference pattern. (c) Sensitivity to gravitational acceleration in 1 day at the $\pi$E5 beamline of PSI, assuming $d=100$ nm grating pitch, as a function of interaction time $t_i$. (d) Simulated Mu distributions, 3.5 after the Mu formation, overlapping with a laser beam. The superthermal beam and a thermal source at 100 K are compared assuming the same diffusion time.
• Figure 5: Simulation of the new beamline segment and the measured beam profile (a) Monte-Carlo simulations of the muon beamline, using magnetic field maps from finite element simulations. (b) Measured beam profile at the position of the entrance counter, using a retractable beam scanner with scintillator tiles and silicon photomultipliers.