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 ${}^{87}$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.

arXiv commentaccepted for publication in Phys. Rev. Lett

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• Restoring Narrow Linewidth to a Gradient-Broadened Magnetic Resonance by Inhomogeneous Dressing
• A theoretical study of the g-factor of the 6s6p 3P0 state of mercury
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• Quadrupole transitions and quantum gates protected by continuous dynamic decoupling
• Harmonic dual dressing of spin one-half systems
• Dual atomic interferometer with a tunable point of minimum magnetic sensitivity
• Quantum Control of Two Critically Dressed Spin 1/2 Species in Magnetic Fluctuations
• Continued fraction analysis of dressed systems: application to periodically driven optical lattices
• Theory of composite Ramsey sequences of radiofrequency pulses beyond the rotating wave approximation