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

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 $10^{-16}$.

References in corpus (3)

• High-accuracy calculation of black-body radiation shift in ${}^{133}$Cs primary frequency standard
• Frequency shift of cesium clock transition due to blackbody radiation
• Hyperfine-mediated static polarizabilities of monovalent atoms and ions

Cited by in corpus (3)

• Hyperfine-mediated electric quadrupole shifts in Al${}^{+}$ and In${}^{+}$ ion clocks
• Role of hyperfine interaction in Landé $g$-factors of ${}^3{P}_0^o$ clock states
• Comprehensive Assessment of ${\mathrm{Th}}^{3+}$ Properties for Nuclear Clock and Fundamental Physics Applications