Rydberg matter (RM) is a novel metal-like material in the form of electronically excited clusters of atoms (e.g. K and H) or molecules (e.g. H
2). It is used as the inverted laser medium for IR in the RM laser. RM has recently been formed in its lowest state, which is proposed to be metallic hydrogen [Energy and Fuels 19 (2005) 2235]. An emitter material (K-doped iron oxide catalyst) that forms RM is studied by a specialized spectroscopic method, needed to detect the Rydberg states on the emitter surface. The spectroscopic method is phase-delay Rabi-flopping; it gives spectra from the time delay due to the periodic motion of the optical nutation vector. The formation of Rydberg species in the form of complexes K
*–M (M a general small molecule) and (K–M)
* is studied. So-called avoided transitions in K
+ ions are detected, of the same type as observed as transitions in the RM laser by stimulated emission. The formation and detection of Rydberg complexes containing H and H
2 is of great interest for metallic hydrogen production. Complexes with M = CH
2, H
2O (or OH), CHO, H
2 and M′H are observed. Avoided transitions in RM clusters
are also identified. The identification of H containing Rydberg complexes on the surface indicates that metallic hydrogen is formed by the same cluster desorption route as other RM clusters.