Sub-millikelvin spatial thermometry of a single Doppler-cooled ion in a Paul trap

We report on observations of the thermal motion of a single, Doppler-cooled ion along the axis of a linear radio-frequency quadrupole trap. We show that for a harmonic potential the thermal occupation of energy levels leads to a Gaussian distribution of the ion's axial position. The dependence of the spatial thermal spread on the trap potential is used for precise calibration of our imaging system's point spread function and sub-millikelvin thermometry. We employ this technique to investigate the laser detuning dependence of the Doppler temperature.