Cyclotron-Frequency Stability via Single-Ion Fluorescence in a Penning Trap with a Cryogen-Free Superconducting Magnet

Abstract: In this work, we investigate the magnetic-field stability of a Penning trap operated with a cryogen-free superconducting magnet through cyclotron-frequency measurements of a single laser-cooled calcium ion using two complementary photon-based detection techniques: a pulsed optical method for determining the three ion eigenfrequencies and Fluorescence-Detected Fourier-Transform Ion-Cyclotron-Resonance (FD-FT-ICR). For the former technique, the data-analysis procedure was revisited, considering it as the dominant contribution to the measurement uncertainty and yielding a long-term magnetic-field drift $(1/B)(dB/dt) = -3.07(32)\times10<sup>{-9}$ $\mathrm{h}<sup>{-1}$. This value is comparable to those reported for high-precision Penning-trap experiments employing liquid-helium-based superconducting magnets. The short-term stability was investigated using the FD-FT-ICR technique, resulting in a minimum relative magnetic-field variation of $δB/B \simeq 5\times10<sup>{-8}$ for averaging times between 30 and 60 s. Furthermore, this technique enables direct cyclotron-frequency determinations on timescales as short as a few seconds, providing access to magnetic-field fluctuations that are generally not resolved in conventional Penning-trap experiments.