Probing multiple electric-dipole-forbidden optical transitions in highly charged nickel ions

Highly charged ions (HCIs) are promising candidates for the next generation of atomic clocks, owing to their tightly bound electron cloud, which significantly suppresses the common environmental disturbances to the quantum oscillator. Here we propose and pursue an experimental strategy that, while focusing on various HCIs of a single atomic element, keeps the number of candidate clock transitions as large as possible. Following this strategy, we identify four adjacent charge states of nickel HCIs that offer as many as six optical transitions. Experimentally, we demonstrated the essential capability of producing these ions in the low-energy compact Shanghai-Wuhan Electron Beam Ion Trap. We measured the wavelengths of four magnetic-dipole ($M1$) and one electric-quadrupole ($E2$) clock transitions with an accuracy of several ppm with an innovative calibration method. Compared to earlier determinations, our measurements improved wavelength accuracy by an order of magnitude. Such measurements are crucial for constraining the range of laser wavelengths for finding the “needle in a haystack” narrow lines. In addition, we calculated frequencies and quality factors, and evaluated sensitivity of these six transitions to the hypothetical variation of the electromagnetic fine structure constant $\alpha$ needed for fundamental physics applications. We argue that all the six transitions in nickel HCIs offer intrinsic immunity to all common perturbations of quantum oscillators, and one of them has the projected fractional frequency uncertainty down to the remarkable level of ${10}^{-19}$.

Figure 1

Partial energy-level diagrams for highly charged nickel ions. Clock transitions are explicitly drawn. Magnetic-dipole ($M1$) transitions are shown in magenta and electric-quadrupole ($E2$) transitions in green. The labeling of transitions is the same as in Table 1.

Figure 2

Charge-state distribution of the Ni HCIs, obtained by averaging three measurements.

Figure 3

Scheme of observation and calibration of the measured lines. The Ni HCIs are trapped at the center of DT2 in SW-EBIT.

Figure 4

(a) A spectrum of line $a$ from ${\mathrm{Ni}}^{11+}$ and its calibration lines from Kr atom whose approximate wavelengths are labeled in the figure in nm. (b) Residuals of cubic polynomial fits of the calibration lines. The gray band is a 1-$\sigma$ confidence band. The uncertainties in the calibration lines are dominated by the line centroid uncertainties of the Gaussian fits. (c) Spectrum of line $a$ and its Gaussian fit.

Figure 5

The calibrated wavelengths of line $a$ in air derived from a series of 26 measurements. The wavelength uncertainty of each single spectrum was calculated as the quadrature of the line centroid uncertainty and the 1-$\sigma$ confidence interval of the fitted dispersion function. The weighted average wavelength is represented by the solid purple line and its uncertainty is represented by the lilac band.