Francisco Javier Fernández

We use an electric-dipole laser-driven transition to precisely measure the cyclotron-frequency ratios of the pairs $^{42}$Ca$^+$-$^{40}$Ca$^+$, $^{44}$Ca$^+$-$^{40}$Ca$^+$ and $^{48}$Ca$^+$-$^{40}$Ca$^+$ in a 7-tesla Penning trap. A single laser-cooled ($T\approx 1$~mK) ion serves, together with photon-counting and/or photon-imaging units, as a radiofrequency detector covering a broad-band frequency spectrum, in the present case from kHz to a few MHz. Such detectors ($^{40,42,44,48}$Ca$^{\scriptsize{+}}$) allow measuring extremely small forces, with measured normalized sensitivities down to $7.4(3.5)$ yN$/\sqrt{\text{Hz}}$ and $24.9(9.9)$ yN$/\sqrt{\text{Hz}}$ in the MHz and kHz regime, respectively. The direct determination of the ions' amplitudes makes a cyclotron-frequency measurement process more robust against inhomogeneities of the magnetic field and/or deviations of the electric quadrupole field due to mechanical imperfections of the trap.

Two-ion crystals constitute a platform for investigations of quantum nature that can be extended to any ion species or charged particle provided one of the ions in the crystal can be directly laser-cooled and manipulated with laser radiation. This paper presents the formation of two-ion crystals for quantum metrology in a 7-tesla open-ring Penning trap. $^{40}$Ca$^+$ ions are produced either internally by photoionization or externally in a (Paul-trap) source, transported through the strong magnetic field gradient of the superconducting solenoid, and captured in-flight with a mean kinetic energy of a few electronvolts with respect to the minimum of the Penning-trap potential well. Laser cooling of the two-ion crystal in a strong magnetic field towards reaching the quantum regime is also presented with particular emphasis on the cooling of the radial modes.