  To operate an optical lattice clock at a fractional uncertainty below
$10^{-17}$, one must typically consider not only electric-dipole (E1)
interaction between an atom and the lattice light field when characterizing the
resulting lattice light shift of the clock transition but also higher-order
multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole
(M1) interactions. However, strongly incompatible values have been reported for
the E2-M1 polarizability difference of the clock states
$(5s5p)\,{}^{3}\mathrm{P}_{0}$ and $(5s^2)\,{}^{1}\mathrm{S}_{0}$ of strontium
[Ushijima et al., Phys. Rev. Lett. 121 263202 (2018); Porsev et al., Phys. Rev.
Lett. 120, 063204 (2018)]. This largely precludes operating strontium clocks
with uncertainties of few $10^{-18}$, as the resulting lattice light shift
corrections deviate by up to $1 \times 10^{-17}$ from each other at typical
trap depths. We have measured the E2-M1 polarizability difference using our
${}^{87}\mathrm{Sr}$ lattice clock and find a value of $\Delta
\alpha_{\mathrm{qm}} = -987^{+174}_{-223} \; \mathrm{\mu Hz}$. This result is
in very good agreement with the value reported by Ushijima et al.

Atomic Physics