Experimental determination of the E2-M1 polarizability of the strontium clock transition

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.