  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.
