Magic radio-frequency dressing of nuclear spins in high-accuracy optical clocks
Abstract
A Zeeman-insensitive optical clock atomic transition is engineered when nuclear spins are dressed by a non resonant radio-frequency field. For fermionic species as 87Sr, 171Yb, and 199Hg, particular ratios between the radiofrequency driving amplitude and frequency lead to "magic" magnetic values where a net cancelation of the Zeeman clock shift and a complete reduction of first order magnetic variations are produced within a relative uncertainty below the 10-18 level. An Autler-Townes continued fraction describing a semi-classical radio-frequency dressed spin is numerically computed and compared to an analytical quantum description including higher order magnetic field corrections to the dressed energies.
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