# Measuring the temperature and heating rate of a single ion by imaging

## TL;DR

This paper introduces an imaging-based method to measure the temperature and heating rate of a single ion in a trap, allowing continuous monitoring without disrupting the cooling process.

## Contribution

The novel technique enables simultaneous measurement of ion temperature and heating rate while maintaining the ion in thermal equilibrium, unlike previous methods.

## Key findings

- Accurately determines ion temperature from spatial extent measurements.
- Measures anomalous heating rate without switching off cooling.
- Maintains the ion near the Doppler limit during measurements.

## Abstract

We present a technique based on high resolution imaging to measure the absolute temperature and the heating rate of a single ion trapped at the focus of a deep parabolic mirror. We collect the fluorescence light scattered by the ion during laser cooling and image it onto a camera. Accounting for the size of the point-spread function and the magnification of the imaging system, we determine the spatial extent of the ion, from which we infer the mean phonon occupation number in the trap. Repeating such measurements and varying the power or the detuning of the cooling laser, we determine the anomalous heating rate. In contrast to other established schemes for measuring the heating rate, one does not have to switch off the cooling but the ion is always maintained in a state of thermal equilibrium at temperatures close to the Doppler limit.