Hyperfine-induced quadrupole moments of alkali-metal atom ground states and their implications for atomic clocks

TL;DR

This paper calculates hyperfine-induced quadrupole moments in alkali-metal atoms and discusses their impact on atomic clock accuracy, revealing significant correlation effects especially in heavier atoms like Cs.

Contribution

It provides the first comprehensive evaluation of hyperfine-induced quadrupole moments across alkali metals using relativistic many-body theory, highlighting their implications for atomic clock precision.

Findings

Hyperfine-induced quadrupole moments are significantly enhanced in heavier alkali atoms.

Electric field gradients must be controlled below 30 V/cm² for Cs clocks to achieve 10⁻¹⁶ accuracy.

Correlation effects increase quadrupole moments by two orders of magnitude in heavy atoms.

Abstract

Spherically-symmetric ground states of alkali-metal atoms do not posses electric quadrupole moments. However, the hyperfine interaction between nuclear moments and atomic electrons distorts the spherical symmetry of electronic clouds and leads to non-vanishing atomic quadrupole moments. We evaluate these hyperfine-induced quadrupole moments using techniques of relativistic many-body theory and compile results for Li, Na, K, Rb, and Cs atoms. For heavy atoms we find that the hyperfine-induced quadrupole moments are strongly (two orders of magnitude) enhanced by correlation effects. We further apply the results of the calculation to microwave atomic clocks where the coupling of atomic quadrupole moments to gradients of electric fields leads to clock frequency uncertainties. We show that for $^{133}$Cs atomic clocks, the spatial gradients of electric fields must be smaller than $30 \, \mathrm{V}/\mathrm{cm}^2$ to guarantee fractional inaccuracies below $10^{-16}$.