Shifting the phase of a coherent beam with a $^{174}$Yb$^+$ ion: influence of the scattering cross section

TL;DR

This paper measures and analyzes the phase shift of a focused radially polarized light beam caused by an $^{174}$Yb$^+$ ion, highlighting the role of atomic properties and scattering cross section in light-atom interactions.

Contribution

It provides experimental measurements of phase shifts in a focused ion-light system and incorporates atomic level properties and scattering cross section into the theoretical model.

Findings

Measured phase shifts align with theoretical predictions within experimental limitations.

Scattering cross section significantly influences the coupling efficiency between light and ion.

Experimental results are consistent with models considering optical and ion motion deficiencies.

Abstract

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.