Penning-trap eigenfrequency measurements with optical radiofrequency detectors

TL;DR

This study employs optical radiofrequency detectors in a Penning trap to precisely measure cyclotron frequencies of calcium ions, demonstrating high sensitivity and robustness against magnetic and electric field inhomogeneities.

Contribution

It introduces a novel method using laser-cooled ions as broad-band RF detectors for high-precision frequency measurements in a Penning trap.

Findings

Achieved normalized sensitivities down to 7.4(3.5) yN/√Hz and 24.9(9.9) yN/√Hz.

Enabled robust cyclotron-frequency measurements against magnetic and electric field imperfections.

Demonstrated broad-band detection from kHz to MHz frequencies.

Abstract

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.