This paper is an extension of a part of the talk delivered under the more general title Narrow spectral lines in fundamental metrology: state of the art, prospects, and problems' at the session of the 90th anniversary of Physics–Uspekhi. The talk reviewed past developments and the current status of the metrology of length, frequency/time, and magnetic fields. The measurement of these quantities currently relies on the high stability of energies of standard transitions between metastable atomic states. Because of space restrictions in the journal, all metrology topics other than the title one were omitted in the present review.
Quantum magnetometry represents a fundamental component of quantum metrology, where trapped-ion systems have achieved pT/Hz sensitivity in single-ion radio-frequency magnetic field measurements via dressed states based dynamical decoupling. Here we propose a scalable trapped-ion magnetometer utilizing the mixed dynamical decoupling method, combining dressed states with periodic sequences to suppress decoherence and spatial magnetic field inhomogeneity. With numerical simulations for a 104 ion system with realistic experimental parameters, we demonstrate that a sensitivity of 13 fT/Hz for the radio-frequency field could be reached. Such a sensitivity could be obtained via robust resilience to magnetic field drift noise and inhomogeneity, where coherence time could be extended to the order of several minutes on average. This method enables scalable trapped-ion magnetometry, demonstrating its potential as a robust and practical solution for advancing quantum sensing applications.