  We discuss the possibility to measure particle couplings with stochastic
gravitational wave backgrounds (SGWBs). Under certain circumstances a sequence
of peaks of different amplitude and frequency -- a $stairway$ -- emerges in a
SGWB spectrum, with each peak probing a different coupling. The detection of
such signature opens the possibility to reconstruct couplings (spectroscopy) of
particle species involved in high energy phenomena generating SGWBs.
Stairway-like signatures may arise in causally produced backgrounds in the
early Universe, e.g. from preheating or first order phase transitions. As a
proof of principle we study a preheating scenario with an inflaton $\phi$
coupled to multiple $daughter$ fields $\lbrace \chi_j \rbrace$ with different
coupling strengths. As a clear stairway signature is imprinted in the SGWB
spectrum, we reconstruct the relevant couplings with various detectors.
