Title: Hyperpolarizability and operational magic wavelength in an optical lattice clock,
Abstract: Optical clocks benefit from tight atomic confinement enabling extended
interrogation times as well as Doppler- and recoil-free operation. However,
these benefits come at the cost of frequency shifts that, if not properly
controlled, may degrade clock accuracy. Numerous theoretical studies have
predicted optical lattice clock frequency shifts that scale nonlinearly with
trap depth. To experimentally observe and constrain these shifts in an
$^{171}$Yb optical lattice clock, we construct a lattice enhancement cavity
that exaggerates the light shifts. We observe an atomic temperature that is
proportional to the optical trap depth, fundamentally altering the scaling of
trap-induced light shifts and simplifying their parametrization. We identify an
"operational" magic wavelength where frequency shifts are insensitive to
changes in trap depth. These measurements and scaling analysis constitute an
essential systematic characterization for clock operation at the $10^{-18}$
level and beyond.