Figure 2

Ground-state hyperfine level scheme and coarse tuning of the quantisation field. (a) Relevant Zeeman sub levels of the S_1/2 hyperfine ground state of ²⁵Mg⁺ with a nuclear spin of 5/2 near \(|{{\bf{B}}}_{0}|\,\simeq \,10.9\) mT. In our experiments, we use the marked transitions for internal state manipulation via pulsed microwave or radio-frequency radiation, cf. Table 1. (b) Measured () and calculated variation Δω_{MW, 2} of the \(|\mathrm{3,1}\rangle \leftrightarrow |\mathrm{2,0}\rangle \) transition frequency \({\omega }_{\text{MW},2}\mathrm{/(2}\pi )\simeq 1762.974\,\) MHz as a function of ΔB₀, and residual (measured - calculated Δω_{MW, 2}) plot. Tuning of the magnetic field strength (on site of a single trapped atom) via variation of the distance between the solid-state magnets within a full span of \({\rm{\Delta }}d\simeq 16\,\) mm. The local magnetic field strength is probed with a relative precision of better than \(\simeq \,0.2\times {10}^{-4}\) via the \(|\mathrm{3,3}\rangle \) to \(|\mathrm{2,2}\rangle \) transition frequency, ω_{MW, 0}.