  Atomic isotope shifts (ISs) are the isotope-dependent energy differences in
the atomic electron energy levels. These shifts serve an important role in
atomic and nuclear physics, and particularly in the latter as signatures of
nuclear structure. Recently ISs have been suggested as unique probes of beyond
Standard Model (SM) physics, under the condition that they be determined
significantly more precisely than current state of the art. In this work we
present 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-mode
noise 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 be
570,264,063.435(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 to
implement and is indifferent to element or isotope, paving the way for future
tabletop searches for new physics and posing interesting prospects for testing
quantum many-body calculations and for the study of nuclear structure.
