Absolute single-ion thermometry

Abstract

We describe and experimentally implement a single-ion local thermometry technique with absolute sensitivity adaptable to all laser-cooled atomic ion species. The technique is based on the velocity-dependent spectral shape of a quasi-dark resonance tailored by two driving fields in a $J\ensuremath{\rightarrow}J$ transition such that the two fields can be derived from the same laser source, leading to a negligible relative phase shift. We validated the method and tested its performance in an experiment on a single $^{88}\mathrm{Sr}^{+}$ ion cooled in a surface radio-frequency trap. We first applied the technique to characterize the heating rate of the surface trap. We then measured the stationary temperature of the ion as a function of cooling laser detuning in the Doppler regime. The results agree with theoretical calculations, with an absolute error smaller than 100 $\ensuremath{\mu}\mathrm{K}$ at 500 $\ensuremath{\mu}\mathrm{K}$, in a temperature range between 0.5 and 3 mK and in the absence of adjustable parameters. This simple-to-implement and reliable method opens the way to fast absolute measurements of single-ion temperatures in future experiments dealing with heat transport in ion chains or thermodynamics at the single-ion level.