Hyperpolarizability and operational magic wavelength in an optical lattice clock

TL;DR

This paper experimentally investigates light-induced frequency shifts in an $^{171}$Yb optical lattice clock, revealing an operational magic wavelength that minimizes trap depth sensitivity, crucial for achieving ultra-high clock accuracy.

Contribution

The study experimentally demonstrates the nonlinear scaling of light shifts with trap depth and identifies an operational magic wavelength for improved clock stability.

Findings

Light shifts scale nonlinearly with trap depth.

An operational magic wavelength minimizes frequency shifts.

Temperature scales proportionally with trap depth.

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.