Laser cooling in the Penning trap: an analytical model for cooling rates in the presence of an axializing field

TL;DR

This paper develops an analytical model to determine laser cooling rates of ions in a Penning trap with an axializing field, showing improved cooling efficiency and frequency shifts consistent with experiments.

Contribution

An analytical model for laser cooling rates in Penning traps with axializing fields, predicting enhanced cooling and motional frequency shifts.

Findings

Axializing field averages cooling rates of radial motions.

Model predictions agree qualitatively with experimental frequency shifts.

Phase response analysis enables experimental determination of cooling rates.

Abstract

Ions stored in Penning traps may have useful applications in the field of quantum information processing. There are, however, difficulties associated with the laser cooling of one of the radial motions of ions in these traps, namely the magnetron motion. The application of a small radio-frequency quadrupolar electric potential resonant with the sum of the two radial motional frequencies has been shown to couple these motions and to lead to more efficient laser cooling. We present an analytical model that enables us to determine laser cooling rates in the presence of such an 'axializing' field. It is found that this field leads to an averaging of the laser cooling rates for the two motions and hence improves the overall laser cooling efficiency. The model also predicts shifts in the motional frequencies due to the axializing field that are in qualitative agreement with those measured in recent experiments. It is possible to determine laser cooling rates experimentally by studying the phase response of the cooled ions to a near resonant excitation field. Using the model developed in this paper, we study the expected phase response when an axializing field is present.