Markus Weber

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.

We discuss and measure the phase shift imposed onto a radially polarized light beam when focusing it onto an $^{174}\text{Yb}^{+}$ ion. In the derivation of the expected phase shifts we include the properties of the involved atomic levels. Furthermore, we emphasize the importance of the scattering cross section and its relation to the efficiency for coupling the focused light to an atom. The phase shifts found in the experiment are compatible with the expected ones when accounting for known deficiencies of the focusing optics and the motion of the trapped ion at the Doppler limit of laser cooling.