Application of the Continuous Stern-Gerlach Effect for Laser Spectroscopy of the ${}^{40}{\mathrm{Ar}}^{13+}$ Fine Structure in a Penning Trap

We report on the successful demonstration of a novel scheme for detecting optical transitions in highly charged ions. We applied it to determine the frequency of the dipole-forbidden $2p{{}^{2}P}_{1/2}-{{}^{2}P}_{3/2}$ transition in the fine structure of ${{}^{40}\mathrm{Ar}}^{13+}$ using a single ion stored in the harmonic potential of a Penning trap. Our measurement scheme does not require detection of fluorescence, instead it makes use of the continuous Stern-Gerlach effect. Our value of $679.216464(4{)}_{\mathrm{stat}}(5{)}_{\mathrm{syst}}\mathrm{THz}$ is in reasonable agreement with the current best literature values and improves its uncertainty by a factor of 24.

Figure 1

(Left) Level scheme for ${{}^{40}\mathrm{Ar}}^{13+}$ in which the strong magnetic field $B_0^{\mathrm{PT}}$ lifts the degeneracy of the Zeeman levels. The transition frequency ${\nu }_{1,2}$ between ${{}^{2}P}_{1/2}\text{and}{{}^{2}P}_{3/2}$ is about 679 THz, which corresponds to a wavelength of 441 nm. The two investigated transition cycles are shown in purple and blue; solid lines indicate the transitions driven by the laser and the dotted lines the possible channels for spontaneous decay. (right) Axial frequency difference $\mathrm{\Delta }{\nu }_z$ in ${\nu }_z^{\mathrm{AT}}$ for subsequent measurements after microwave irradiation. For 0 Hz no spin state transition happened, whereas a change of $\pm 0.3\mathrm{Hz}$ indicates a transition between the $|1/2,\pm 1/2⟩$ states, corresponding to the transitions indicated by the green and red arrows on the left-hand side.

Figure 2

Schematics (not to scale) of the combined microwave and laser in-coupling. The laser beam is depicted as a magenta line and the propagation path of the microwave in a waveguide structure is indicated by a purple arrow. The trap tower consist of the analysis trap (blue), the precision trap (green) and capture section (orange) for capturing and storing externally injected HCI. Compartments of the double-stage cryostat at different vacuum pressures and temperatures are separated by quartz glass windows and traversed by microwave horn antennas facing each other [21].

Figure 3

Typical resonances measured for different axial temperatures. The resonance in red is taken without any further cooling, whereas the green, respectively, cyan one were taken using adiabatic cooling only or, respectively, in addition to negative feedback cooling. The error bars are the maximum likelihood estimates for binomial attempts for obtaining a spin state transition at the respective frequency. The solid curve is a Gaussian line shape fitted with a maximum-likelihood fit routine. The shaded area shows the confidence band (68% level) of the fit. The datasets shown here correspond to measurement numbers 8, 9, and 12 in Fig. 4.

Figure 4

Centers of resonances taken with different sets of parameters with respect to laser power, laser irradiation time, with or without negative feedback applied or adiabatically cooled. Measurements 1–9 correspond to transition ${\nu }_1$ whereas measurements 10–13 are taken with transition ${\nu }_2$ (see Fig. 1). In both cases the center frequencies are corrected for the magnet field including the second-order Zeeman shift. The gray area represents the combined statistical and systematic error.