  We investigate the potential to probe physics beyond the Standard Model with
isotope shift measurements of optical atomic clock transitions. We first derive
the reach for generic new physics above the GeV scale at the effective field
theory level, as well as estimate the limits on possible new spin-independent
forces mediated by sub-GeV states coupled to electrons and neutrons. We also
study the weak force and show that isotope shifts could provide strong
constraints on the $Z^0$ couplings to valence quarks, which complement
precision observables at LEP and atomic parity violation experiments. Finally,
motivated by recent experimental hints of a new 750 GeV resonance in diphotons,
we also consider the potential to probe its parity-preserving couplings to
electrons, quarks and gluons with this method. In particular, combining the
diphoton signal with indirect constraints from $g_e-2$ and isotope shifts in
Ytterbium allows to probe the resonance coupling to electrons with
unprecedented precision.
