Metrology in a two-electron atom: The ionization energy of metastable triplet helium ($\mathbf{2\,^3S}_\mathbf{1}$)

Abstract: Helium (He) is the ideal atom to perform tests of ab-initio calculations in two-electron systems that consider all known effects, including quantum-electrodynamics and nuclear-size contributions. Recent state-of-the-art calculations and measurements of energy intervals involving the He $2\;^3S_1$ metastable state reveal discrepancies at the level of $7\,σ$ that require clarification both from the experimental and theoretical sides. We report on a new determination, with unprecedented accuracy, of the ionization energy $E_\mathrm{I}\,(2\;^3S_1)$ of the $(1s)(2s)\;^3S_1$ metastable state of He. The measurements rely on a new approach combining interferometric laser-alignment control, SI-traceable frequency calibration and imaging-assisted Doppler-free spectroscopy. With this approach we record spectra of the $np$ Rydberg series in a highly-collimated cold supersonic beam of metastable He generated by a cryogenic valve and an electric discharge. Extrapolation of the Rydberg series yields a new value of the ionization energy ($E_\mathrm{I}\,(2\;^3S_1)/h= 1\,152\,842\,742.7082(55)\mathrm{stat}(25)\mathrm{sys}\,\mathrm{MHz}$) that deviates by $9\,σ$ from the most precise theoretical result ($1\,152\,842\,742.231(52)\;\mathrm{MHz}$), reported by Patkóš, Yerokhin and Pachucki [Phys. Rev. A. 103, 042809 (2021)], confirming earlier discrepancies between experiment and theory in this fundamental system.

• The paper introduces an innovative experimental method combining cold supersonic helium beams, interferometric laser alignment, and SI-traceable calibration to achieve unprecedented precision in measuring ionization energy.
• It finds that the measured ionization energy of metastable helium deviates by 9σ from theoretical predictions, highlighting crucial discrepancies in QED calculations.
• The study's methods mitigate Doppler shifts using a retroreflection setup and imaging-assisted spectroscopy, setting new benchmarks for precision metrology in atomic physics.

Metrology in a Two-Electron Atom: The Ionization Energy of Metastable Triplet Helium ($2\,^3S_1$)

Introduction

Helium ($^4$He), particularly in its metastable $(1s)(2s)\;^3S_1$ state, offers an ideal platform for precision tests of quantum electrodynamics (QED) and nuclear effects in few-electron systems. The paper "Metrology in a two-electron atom: The ionization energy of metastable triplet helium ($2\,^3S_1$)" (2501.02983) introduces an innovative approach to determine the ionization energy of $^4$He with unprecedented accuracy, addressing discrepancies between experimental measurements and theoretical predictions, which previously stood at $7\sigma$ and now extend to $9\sigma$.

Experimental Approach

The authors developed a new experimental setup that improves the precision of helium spectroscopy. This setup utilizes a cold, supersonic beam of metastable helium, produced by a cryogenic valve and electric discharge. Key to the setup is an interferometric laser-alignment control combined with SI-traceable frequency calibration and imaging-assisted Doppler-free spectroscopy. This allows for the recording of spectra of the $np$ Rydberg series in $^4$He and the extrapolation of these series to determine the ionization energy.

Figure 1: The experimental setup for measuring ionization energy, featuring high-vacuum conditions, a cryogenically cooled pulsed valve, and interferometric alignment.

By employing this approach, the ionization energy $E_\mathrm{I}\,(2\;^3S_1)$ was determined to be $$1\,152\,842\,742.7082(55)_\mathrm{stat}(25)_\mathrm{sys}\,\mathrm{MHz}$$, deviating significantly from the theoretical value of $1\,152\,842\,742.231(52)\;\mathrm{MHz}$ and thus confirming the aforementioned $9\sigma$ discrepancy.

Laser System and Calibration

The UV laser system, integral to the precision achieved, was finely tuned to the transitions under observation. The paper details the laser's frequency stabilization and calibration, involving a frequency-doubled optical frequency comb with a stabilized reference laser. This establishment of SI-traceable measurements ensures accuracy in frequency determination, critical for high-resolution spectroscopy.

Figure 2: Schematic of the frequency-calibration procedure for the UV laser system using frequency combs.

Suppression of Doppler Shifts

To mitigate Doppler shifts, a retroreflection setup was utilized. The laser beam was intersected at near-perfect orthogonal angles to the atomic beam, allowing for correction of first-order Doppler shifts via geometric alignment, improving spectral readings' precision. Further, Imaging-Assisted Single-photon Spectroscopy (IASS) permitted the collection of reduced Doppler-width spectra, enhancing the clarity and accuracy of the readings.

Figure 3: Geometry of the IASS setup minimizing Doppler shifts through careful beam alignment.

Results and Implications

The refined measurement of the ionization energy resulted in a robust confirmation of a significant deviation from theoretical predictions. This has profound implications for QED calculations in light atomic systems, suggesting limitations or necessary revisions in current theoretical frameworks. The advancements in precision metrology proposed in this study set new benchmarks in atomic physics, offering potential for improved isotopic shift measurements. Such measurements could facilitate determining $^3$He and $^4$He nuclear charge radii differences, addressing long-standing discrepancies in muonic helium ions' spectroscopic measurements.

Figure 4: The post-selection Doppler shift arrangement and its mitigation in the experimental sequence.

Conclusion

The innovative methodology and its application to determine $^4$He ionization energy with enhanced precision represent a significant step in quantum metrology. The persisting $9\sigma$ discrepancy between precise experimental data and theoretical values emphasizes the need for continued theoretical verification and potentially new physics insights in atomic interactions. Future work aims to extend these precision measurements to $^3$He, which may resolve inconsistencies in nuclear charge radius determinations and further test the prevailing quantum mechanical models.