Measurement of differential polarizabilities at a mid-infrared wavelength in $^{171}\mathrm{Yb}^+$

An atom exposed to an electric field will experience Stark shifts of its internal energy levels, proportional to their polarizabilities. In optical frequency metrology, the Stark shift due to background black-body radiation (BBR) modifies the frequency of the optical clock transition, and often represents a large contribution to a clock's uncertainty budget. For clocks based on singly-ionized ytterbium, the ion's complex structure makes this shift difficult to calculate theoretically. We present a measurement of the differential polarizabilities of two ultra-narrow optical clock transitions present in $^{171}\mathrm{Yb}^+$, performed by exposing the ion to an oscillating electric field at a wavelength in the region of room temperature BBR spectra. By measuring the frequency shift to the transitions caused by a laser at $\lambda=7.17 \mu m$, we obtain values for scalar and tensor differential polarizabilities with uncertainties at the percent level for both the electric quadrupole and octupole transitions at 436nm and 467nm respectively. These values agree with previously reported experimental measurements and, in the case of the electric quadrupole transition, allow a 5-fold improvement in the determination of the room-temperature BBR shift. However, we note significant concerns over the validity of the uncertainty charactarization presented and draw the reader's attention to the Note on applicability section for a discussion.