  We propose a novel approach to probe new fundamental interactions using
isotope shift spectroscopy in atomic clock transitions. As concrete toy example
we focus on the Higgs boson couplings to the building blocks of matter: the
electron and the up and down quarks. We show that the attractive Higgs force
between nuclei and their bound electrons, that is poorly constrained, might
induce effects that are larger than the current experimental sensitivities.
More generically, we discuss how new interactions between the electron and the
neutrons, mediated via light new degrees of freedom, may lead to measurable
non-linearities in a King plot comparison between isotope shifts of two
different transitions. Given state-of-the-art accuracy in frequency comparison,
isotope shifts have the potential of being measured with sub-Hz accuracy, thus
potentially enabling the improvement of current limits on new fundamental
interactions. Candidate atomic system for this measurement require two
different clock transitions and four zero nuclear spin isotopes. We identify
several systems that satisfy this requirement and also briefly discuss existing
measurements. We consider the size of the effect related to the Higgs force and
the requirements for it to produce an observable signal.
