The hyperfine structure of an atom is a fine 'score' of energy levels arising from the interaction between the electron and the nucleus. For alkali isotopes such as 6Li, 87Rb, or 133Cs, the constants A have been measured to hertz-level precision or better. But 40K remained a blank spot: its natural abundance is only 0.0117%, making it difficult to produce a dense atomic beam or fountain. The previous value A = −h × 285.7308(24) MHz, adopted back in 1977, became a bottleneck for calibrating magnetic fields, describing Feshbach resonances, and extracting spin interactions in ultracold gas experiments. This work joins a line of research where precision spectroscopy on ultracold atoms replaces traditional beam and fountain methods, but it stands out by using a degenerate Fermi gas in an optical trap and requiring no magnetic shielding.
In a trap made of crossed 1064 nm beams, a degenerate Fermi gas of 40K was prepared at a temperature of 0.3 TF. Two transitions between hyperfine sublevels were chosen: α (|9/2, −1/2⟩ ↔ |7/2, 1/2⟩) and β (|9/2, 1/2⟩ ↔ |7/2, −1/2⟩). Both transitions are first-order insensitive to the magnetic field, so their frequencies depend weakly on field fluctuations. First, resonances were roughly located with Gaussian π pulses, then Ramsey spectroscopy was performed with two square π/2 pulses of 0.15 ms duration. Transition frequencies were extracted from population oscillations as the free evolution time was varied. To remove the AC Stark shift from the trap, frequencies were measured at several intensities and extrapolated to zero intensity. The magnetic field was not calibrated: its value was replaced by the frequency difference of the two transitions, and the constant A was computed using a formula where the field is analytically eliminated.
Measurements were taken at six magnetic field values from 0.76 to 2.35 G. Ramsey coherence reached 378 ms at 0.76 G and dropped to 108 ms at 2.35 G. After extrapolating to zero trap intensity and averaging with inverse-variance weights, they obtained A = −h × 285.730536(2) MHz. The total uncertainty of 2 Hz comprises contributions from magnetic noise (from 1.29 to 13.45 Hz depending on the field), Stark shift extrapolation (from 1.11 to 26.70 Hz), and g-factor uncertainties (0.15 Hz from gI and negligible from gJ). No density shifts were detected: varying the density by a factor of 8 changed A by only fractions of a hertz, consistent with suppression of s-wave collisions in the Fermi gas. Compared to the previous recommended value, the precision is improved by nearly 1200 times.
This work closes a long-standing gap in alkali atom metrology: 40K now stands alongside 6Li, 87Rb, and 133Cs in terms of hyperfine constant precision. The method requires no magnetic shielding or field calibration, simplifying experiments and reducing systematic errors. Unlike neighboring studies where hyperfine constants were measured in beams or fountains, here a degenerate Fermi gas in an optical trap was used. This allowed high density and long coherence times without complex magnetic infrastructure. Such an approach could become standard for other rare isotopes.
Further precision gains are possible by suppressing magnetic noise: more stable current sources or magnetic shielding would extend Ramsey coherence. The trap's Stark shift could be entirely eliminated by choosing a 'magic' wavelength or polarization where the differential shift vanishes. The method transfers to other atoms and transitions where precision spectroscopy without field calibration is needed.
The refined constant A will improve magnetic field calibration in ultracold gas experiments, fitting of Feshbach resonances, and determination of spin interactions. This directly impacts the accuracy of quantum simulators and atomic clocks based on 40K.
Test the method's reproducibility on other potassium isotopes or on 6Li. Investigate the use of 'magic' trap conditions to completely eliminate the Stark shift.
In ultracold atom physics, precise magnetic field calibration remains a bottleneck: it limits the reproducibility of Feshbach resonances and comparison of results across laboratories. This work removes that problem for 40K by providing a field-independent frequency reference. This enables more precise measurements of spin interactions and possibly new tests of fundamental symmetries.
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What the work does
This work measures the hyperfine constant A for 40K with an accuracy of 2 Hz using a pair of magnetically insensitive transitions in a degenerate Fermi gas in an optical trap. The magnetic field dependence is eliminated analytically through the frequency difference of the transitions, and the Stark shift is removed by extrapolating to zero intensity.
Where its strength is
The method requires no magnetic field calibration or magnetic shielding, making it transferable to other isotopes and conditions. The high Ramsey coherence (up to 378 ms) in the Fermi gas paves the way for further improvements in precision.
Where it could go next
Worth trying
Why this may matter
The precise value of A for 40K improves magnetic field calibration in ultracold gas experiments, enhances the reliability of Feshbach resonance calculations, and refines spin interactions, which is important for quantum simulations and metrology.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.50, against a usual 0.64. It looks like few have drilled nearby.
The natural abundance of 40K is only 0.0117%: out of a million potassium atoms, just 117 are this isotope. To obtain millions of atoms for experiments, costly enrichment is required.