Doppler sideband spectra for ions in a linear trap

The authors describe a spectroscopic measurement of the temperature and linear density of Hg⁺ ions held in a linear ion trap (LIT). The inferred temperature and number result from analysis of sidebands on the 40.5 GHz resonance line. The temperature of the ion cloud is determined by the Doppler-broadened line when microwave radiation is propagated along the axis of the LIT. When propagation is perpendicular to the trap axis, the microwave sidebands are displaced from the trap secular frequency by an amount dependent on the ion cloud size and temperature. A Monte Carlo simulation of the ion trajectories inside the cloud is used to model the position of these sidebands for a given cloud temperature, and a comparison with measured sideband position is used to determine ion number. In clock operation with 7 × 10^-14 τ^-1/2 stability, the method described here was used to measure a -8.8 × 10^-13 frequency offset due to second order Doppler shift at 650 K and a linear ion density of 2.5 × 10⁶/75 mm