Imagine a soundproof room where you tune a tuning fork: the faintest rustle throws off the tuning. In the world of ultra-precise atomic measurements, that rustle is the magnetic field. It imperceptibly shifts transition frequencies, and to get a reliable standard, physicists had to carefully calibrate the field. For potassium-40, this was especially painful: out of a million potassium atoms, only 117 are the desired isotope, making it nearly impossible to produce a dense beam for traditional methods.
In the new work, they took a different approach: instead of measuring the field and subtracting its effect, they chose a pair of transitions that barely respond to the field. It's like tuning a tuning fork not in silence, but so that it doesn't hear the noise itself. Two transitions between hyperfine sublevels, α and β, are insensitive to the magnetic field to first order. Their frequencies depend weakly on field fluctuations, and the frequency difference allows the field to be completely eliminated from the calculations.
The experiment was conducted in a trap made of crossed beams at 1064 nm, where a degenerate Fermi gas of 40K was cooled to 0.3 TF. 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 shift from the AC Stark effect created by the trap, frequencies were measured at several intensities and extrapolated to zero intensity.
Ramsey coherence reached 378 ms at a field of 0.76 G and dropped to 108 ms at 2.35 G. After extrapolation to zero trap intensity and averaging with inverse-variance weights, they obtained A = −h × 285.730536(2) MHz. The total uncertainty of 2 Hz comes from contributions of magnetic noise, extrapolation of the Stark shift, and uncertainties in g-factors. Density shifts were not observed: when the density was varied by a factor of 8, the value of A changed by only fractions of a hertz.
Now potassium-40 stands alongside 6Li, 87Rb, and 133Cs in terms of hyperfine constant precision. The method requires no magnetic shielding or field calibration, which simplifies experiments and reduces systematic errors. The tuning fork is tuned: it no longer hears the magnetic field noise, and its tone can be used as a standard for calibrating fields, tuning Feshbach resonances, and determining spin interactions.
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.