Experimental access to higher-order Zeeman effects by precision spectroscopy of highly charged ions in a Penning trap

We present an experimental concept and setup for laser-microwave double-resonance spectroscopy of highly charged ions in a Penning trap. Such spectroscopy allows a highly precise measurement of the Zeeman splittings of fine- and hyperfine-structure levels due the magnetic field of the trap. We have performed detailed calculations of the Zeeman effect in the framework of quantum electrodynamics of bound states as present in such highly charged ions. We find that apart from the linear Zeeman effect, second- and third-order Zeeman effects also contribute to the splittings on a level of ${10}^{-4}$ and ${10}^{-8}$, respectively, and hence are accessible to a determination within the achievable spectroscopic resolution of the ARTEMIS experiment currently in preparation.

Figure 1

Level scheme of the $2{}^2{P}_J$ states of boronlike argon Ar${}^{13+}$ in an external magnetic field with higher-order contributions to the Zeeman effect (not true to scale).

Figure 2

Spectroscopy of the $2{}^2{P}_{1/2}$-$2{}^2{P}_{3/2}$ fine-structure transition, as in a boronlike argon ion Ar${}^{13+}$, with Zeeman effect. The level scheme (not true to scale) and all magnetic dipole transitions are shown. Solid arrows indicate excitation by laser photons, while dotted arrows are spontaneous decays. Gray double arrows represent microwave transitions.

Figure 3

Probe spectroscopy in the Zeeman-split fine-structure doublet. Solid arrows indicate the saturated probing and, optionally, pumping laser photons, while dotted arrows are spontaneous decays. Gray arrows represent microwave-stimulated transitions.

Figure 4

Pump spectroscopy in the Zeeman-split fine-structure doublet. Solid arrows indicate the saturated pumping laser photons, while dotted arrows are spontaneous decays. Projection-conserving decays of the states $|3/2,+1/2\rangle$ and $|3/2,-1/2\rangle$ are preferred. Gray arrows represent microwave-stimulated transitions.

Figure 5

Rabi spectroscopy in the Zeeman-split fine-structure doublet. The solid double arrow indicates coherent excitation or deexcitation by laser photons, while dotted arrows are spontaneous decays. Gray arrows represent microwave-stimulated transitions.

Figure 6

Schematic drawing of the setup. The superconducting magnet has been cut to allow a view of the trap and related components inside the room-temperature bore.

Figure 7

Schematic drawing of the trap. A cut has been applied for presentation of the trap interior.