Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Hyperfine-mediated electric quadrupole shifts in Al+ and In+ ion clocks



Kyle P. Beloy, David R. Leibrandt, Wayne M. Itano


We evaluate the electric quadrupole moments of the 1S0 and 3P0 clock states of 27Al+ and 115In+. To capture all dominant contributions, our analysis extends through third order of perturbation theory and includes hyperfine coupling of the electrons to both the magnetic dipole and electric quadrupole moments of the nucleus. For 27Al+, a fortuitous cancellation leads to a suppressed frequency shift. This should allow for continued improvement of the clock without special techniques to control or cancel the shift, such as the averaging schemes that are critical to other optical ion clocks.
Physical Review A


aluminum, electric quadrupole moment, indium, ion clock, optical clock, optical frequency standard


Beloy, K. , Leibrandt, D. and Itano, W. (2017), Hyperfine-mediated electric quadrupole shifts in Al+ and In+ ion clocks, Physical Review A, [online], (Accessed June 13, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created April 6, 2017, Updated September 26, 2017