Phase-Sensitive Cyclotron Frequency Measurements at Ultralow Energies

Abstract

A novel technique for a direct and coherent measurement of the modified cyclotron frequency of an ion in a Penning trap at energies close to the thermal cooling limit is presented. This allows a rapid and both precise and accurate determination of the free-space cyclotron frequency in real Penning traps despite the existence of electric and magnetic field imperfections and relativistic shifts. The demonstrated performance paves the way for considerably improved bound-state g-factor measurements on the 10 ppt level and mass measurements in the 1 ppt range and possibly below.

Electron g‐factor determinations in Penning traps

“…The series resonance shortcuts the thermal noise at the ion's oscillation frequency. Figure 4 shows a signal from a single trapped 28 Si 13+ ion in thermal equilibrium with the detection circuit at 4 K. In a similar way the perturbed cyclotron oscillation can be detected when the traps ring electrode is divided into two segments and the detection circuit attached between the segments. Provided that the effective voltage noise of the cryogenic amplifier is significantly lower than the thermal noise of the tank circuit, it is possible to cool the ion below the temperature of the environment.…”

“…Because of the high signal amplitude this method reduces the time needed for the cyclotron measurement by more than one order of magnitude, reducing the uncertainty from instabilities of trap parameters tremendously. It has been applied recently in an experiment on 28 Si 13+ [30]. The accuracy of the perturbed cyclotron frequency is of greatest importance for the precise determination of the free particle's cyclotron frequency as required for calibration of the magnetic field.…”

“…Figure 3 shows an example of cyclotron mode cooling of a single 28 Si 13+ ion. The presence of the trapped ion is then monitored by a minimum in the Fourier transform.…”

“…C 2013 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Figure 6 Fourier transform of the center part of the noise spectrum of a tuned circuit attached between two segments of a split ring electrode showing the increased noise amplitude at the perturbed cyclotron frequency of a single 28 Si…”

“…The phase of the cyclotron motion is read indirectly via the phase of the axial motion after the coupling pulse. using a novel method which allows to detect the phase of the cyclotron motion at energies below the detection threshold [28,29]. The cyclotron oscillation is excited by a pulse, followed by a free oscillation period during which the phase evolves freely.…”