Magic radio-frequency dressing of nuclear spins in high-accuracy optical clocks

TL;DR

This paper introduces a method to engineer Zeeman-insensitive optical clock transitions by dressing nuclear spins with a non-resonant radio-frequency field, significantly reducing magnetic field sensitivities.

Contribution

It demonstrates the creation of 'magic' magnetic values for nuclear spins in optical clocks, enabling ultra-precise timekeeping with minimized magnetic perturbations.

Findings

Achieved Zeeman shift cancellation below 10^-18 uncertainty.

Derived analytical and numerical models for RF-dressed nuclear spins.

Identified specific RF parameters for optimal clock stability.

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 $^{87}$Sr, $^{171}$Yb, and $^{199}$Hg, 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.