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Atomic isotope shifts (ISs) are the isotope-dependent energy differences inthe atomic electron energy levels. These shifts serve an important role inatomic and nuclear physics, and particularly in the latter as signatures ofnuclear structure. Recently ISs have been suggested as unique probes of beyondStandard Model (SM) physics, under the condition that they be determinedsignificantly more precisely than current state of the art. In this work wepresent a simple and robust method for measuring ISs with ions in a Paul trap,by taking advantage of Hilbert subspaces that are insensitive to common-modenoise yet sensitive to the IS. Using this method we evaluate the IS of the$5S_{1/2}\leftrightarrow4D_{5/2}$ transition in $^{86}\text{Sr}^+$ and$^{88}\text{Sr}^+$ with a $1.6\times10^{-11}$ relative uncertainty to be570,264,063.435(9) Hz. Furthermore, we detect a relative difference of$3.46(23)\times10^{-8}$ between the orbital g-factors of the electrons in the$4D_{5/2}$ level of the two isotopes. Our method is relatively easy toimplement and is indifferent to element or isotope, paving the way for futuretabletop searches for new physics and posing interesting prospects for testingquantum many-body calculations and for the study of nuclear structure.

Precision measurement of atomic isotope shifts using a two-isotope entangled state